The frequency of the alternating current is 394/2π Hz. The resistance of the bulb's filament can be determined using Ohm's Law. The average power delivered to the light bulb can be calculated using the formula P = IV.
Explanation:(a) The frequency of the alternating current can be calculated using the angular frequency formula ω = 2πf. In this case, the angular frequency is 394 rad/s. So, we can rearrange the formula to find the frequency: f = ω/2π = 394/2π Hz.
(b) The resistance of the bulb's filament can be determined using Ohm's Law, which states that resistance (R) is equal to voltage (V) divided by current (I). In this case, the voltage is 120.0 V and the current is given by I = (0.644 A) sin [(394 rad/s)t].
(c) The average power delivered to the light bulb can be calculated using the formula P = IV, where I is the current and V is the voltage. In this case, the voltage is 120.0 V and the current is given by I = (0.644 A) sin [(394 rad/s)t].
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A train consists of a 4300-kg locomotive pulling two loaded boxcars. The first boxcar (just behind the locomotive) has a mass of 12,700 kg and the second (the car in the back) has a mass of 16,300 kg. Presume that the boxcar wheels roll without friction and ignore aerodynamics. The acceleration of the train is 0.569 m/s2. (a) With what force, in Newtons, do the boxcars pull on each other
To solve this problem we will apply the concepts related to Newton's second law, which defines force as the product between mass and acceleration. Mathematically this can be described as,
[tex]F = ma[/tex]
Here,
m = Mass
a = Acceleration
Taking as reference the mass of the second boxcar, the force applied would be
[tex]F = m_2 a[/tex]
[tex]F = (16300kg)(0.569m/s)[/tex]
[tex]F = 9274.7N[/tex]
Therefore the boxcars pull on each other with a force of 9274.7N
The boxcars pull on each other with equal and opposite forces, which can be calculated using the formula F = ma. The force that the boxcars pull on each other is 16521.1 N.
Explanation:When the locomotive pulls the first boxcar, it exerts a force on it. According to Newton's third law of motion, the first boxcar exerts an equal and opposite force on the locomotive. Similarly, when the first boxcar pulls the second boxcar, it exerts a force on the second boxcar, and the second boxcar exerts an equal and opposite force on the first boxcar. Therefore, the boxcars pull on each other with equal and opposite forces.
To calculate the magnitude of this force, we can use the formula F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the mass of the first and second boxcars together is 12,700 kg + 16,300 kg = 29,000 kg. Plugging in the values, we get F = (29,000 kg)(0.569 m/s²).
The force that the boxcars pull on each other is 16521.1 N (rounded to four significant figures).
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You are standing on a bathroom scale in an elevator in a tall building. Your mass is
64 kg. The elevator starts from rest and travels upward with a speed that varies with time according to v(t)=(3.0m/s2)t+(0.20m/s3)t2.
When
t=4.0s, what is the reading of the bathroom scale?
Using the concept of Newton's second law, as the elevator starts from rest and travels upward, the scale shows a value of 94.04 kg
Newton's Second Law of MotionAcceleration is the time derivative of velocity. Therefore acceleration can be given by;
[tex]a=a(t)=\frac{dv(t)}{dt} = \frac{d}{dt} (3t+0.2t^2) = 3+0.4t[/tex]
When t = 3s;
[tex]a= 3+(0.4\times 4)=4.6\,m/s^2[/tex]
As the elevator is moving upward the net force on the weighing scale is given using Newton's second law of motion;
[tex]F_{net}=m(a+g) =(64\,kg)\times (9.8\,m/s^2 +4.6\,m/s^2)=921.6\,N[/tex]
A weighing scale is usually caliberated to show the value in kilograms.
Therefore the weighing scale will show the reading;
[tex]m=\frac{F_{net}}{g} =\frac{921.6\,N}{9.8\,m/s^2}= 94.04\,kg[/tex]
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The apparent weight you would experience in the accelerating elevator is 925.12N. This higher reading is due to the addition of the upward acceleration of the elevator to the standard pull of gravity.
Explanation:To solve this question, we first need to find the elevator's acceleration. The acceleration is the derivative of the velocity: v(t)=(3.0m/s²)t+(0.20m/s³)t² with respect to time t. The derivative is a(t) = 3.0m/s² +2×(0.20m/s³)×t.
Substitute t=4.0s into a(t) to get a(4.0s) = 3.0m/s² + 2×0.2×4.0 = 4.6m/s². This is the acceleration at t=4.0s.
The apparent weight, or reading on the scale, is given by the equation: F=m(g+a), where m is the mass (64 kg), g is the acceleration due to gravity (9.8 m/s²), and a is the acceleration of the elevator. Thus the apparent weight is F=64(9.8+4.6)=925.12 N.
This is your weight when the elevator is accelerating upward; you would feel heavier due to the addition of the elevator's upward acceleration to the natural gravitational pull.
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You stand near the edge of a swimming pool and observe through the water an object lying on the bottom of the pool.
Which of the following statements correctly describes what you see?
a. The apparent depth of the object is less than the real depth.
b. The apparent depth of the object is greater than the real depth.
c. There is no difference between the apparent depth and the actual depth of the object.
Answer:
a. The apparent depth of the object is less than the real depth.
Explanation:
When we observe for any object lying at the bottom of the pool from the edge of the pool then we are actually viewing an object from an optically rarer medium into an optically denser medium.
The schematic shows the apparent view of the object due to the bending of the rays coming form the object to our eyes.
The rays when coming from a denser medium to a rarer medium they bend away from the normal of the interface.
The correct option is a. The apparent depth of the object is less than the real depth because of the refraction of light at the water-air interface.
Light bends away from the normal as it exits the water, making the object appear shallower than it actually is. When light travels from water to air, it bends away from the normal because water is denser than air.
This bending makes the object appear to be at a shallower depth than it actually is. The apparent depth of the object is therefore less than the real depth of the object.
To summarize, the correct statement is: The apparent depth of the object is less than the real depth. Option a is correct.
A charge Q is spread uniformly along the circumference of acircle of radius R. A point
particlewith charge q is placed at the center of this circle.The total force exerted on the
particle q can be calculated by Coulomb's law:
A) just use R for the distance D) result of the calculation iszero
B) just use 2R for the distance E) none of the above
C) just use 2πR for the distance
Answer:
D) result of the calculation is zero
Explanation:
Coulomb's Law is valid for only point-like particles. Since the ring is not a point-like, then we have to choose an infinitesimal portion (ds) of the ring, apply the Coulomb's Law to this portion and then integrate over the ring to find the total force.
The small portion (dq) will have the same charge density as the ring itself. Furthermore, the length of the infinitesimal portion is equal to the radius times the corresponding angle, dθ.
[tex]\lambda = \frac{Q}{2\pi R} = \frac{dq}{Rd\theta}\\dq = \frac{Qd\theta}{2\pi}[/tex]
Therefore, the force between the charge at the center and the small portion is
[tex]dF = \frac{1}{4\pi\epsilon_0}\frac{qdq}{R^2} = \frac{1}{4\pi\epsilon_0}\frac{qQd\theta}{2\pi R^2}[/tex]
Since force is a vector, we have separate its x- and y-components,
[tex]dF_x = \frac{1}{4\pi\epsilon_0}\frac{qQd\theta}{2\pi R^2}\cos(\theta)\\dF_y = \frac{1}{4\pi\epsilon_0}\frac{qQd\theta}{2\pi R^2}\sin(\theta)[/tex]
Now, we can integrate both of them over the ring.
[tex]F_x = \int\limits^{2\pi}_0 dF_x = \frac{1}{4\pi\epsilon_0}\frac{qQ}{2\pi R^2}\int\limits^{2\pi}_0\cos(\theta)d\theta = 0\\F_y = \int\limits^{2\pi}_0 dF_y = \frac{1}{4\pi\epsilon_0}\frac{qQ}{2\pi R^2}\int\limits^{2\pi}_0\sin(\theta)d\theta = 0[/tex]
Since the integration from 0 to 2π for sine and cosine functions results as zero.
Therefore, the force on the charge at the center of a uniformly distributed ring is equal to zero.
The total force exerted on a charge q placed at the center of a circle with a uniformly distributed charge Q along the circumference is zero due to the symmetry of the charge distribution.
Explanation:When a charge Q is spread uniformly along the circumference of a circle with radius R, and a point particle with charge q is placed at the center of this circle, we must apply Coulomb's law to calculate the force exerted on the charge q. Thanks to the symmetry of the charge distribution, the forces exerted by individual segments of the charged circumference on the central charge will cancel each other out in every direction. Hence, while the distance from the charge q to any point on the circle is R, the resulting total force on charge q will be zero due to symmetry.
It's important not to confuse the circumference with other distances, such as the diameter (2R) or the circumferential length (2πR), as these are not relevant for calculating the force on the central charge in this symmetric setup. Therefore, the correct answer is that the result of the calculation is zero (Option D), because the uniform distribution of charge Q around the circle results in an equilibrium of forces.
(a) If the electric field is zero in some region of space, the electric potential must also be zero in that region. a. true b. false (b) If the electric potential is uniformly zero in some region of space, the electric field must also be zero in that region. a. true b. false (c) If the electric potential is zero at a point, the electric field must also be zero at that point. a. true d. false (d) Electric field lines always point toward regions of lower potential. a. true b. false(e) The value of the electric potential can be chosen to be zero at any convenient point. a. true b. false (f) In electrostatics, the surface of a conductor is an equipotential surface. a. true b. false(g) Dielectric breakdown occurs in air when the potential is 3 times 106 V. a. true b. false
The correct options are a) a. false b) b. false c) a.True d) a.True e) a.True f) a.True g) b. false.
(a) The given statement is incorrect, An electric field is the gradient of the potential. when the Potential is constant The electric field is zero. The correct option is b. false
(b) If an electric field of space is zero, it does not imply that there is no charge . From Gauss law in its divergence form, It implies there are an equal number of opposite charges present. No statement can be said about the charges present in that region. The correct option is b. false.
(c) The statement is correct because the Intensity of an electric field is line integral of the electric potential. The correct otption is a. True
(d) Electric field lines always point from high potential to low potential. The correct option is a. True
(e) When the electric field strength is not zero, an electric potential is zero at all points on the equatorial line of the electric dipole. The correct option is a. True
(f) The statement is correct as conductors allow the free flow of charge within themselves. The correct statement is a. True
(g) It is incorrect as dielectric breakdown occurs when a charge buildup exceeds the electrical limit or dielectric strength of a material. The correct option is b. False
The options are a) false b) false c) True d) True e) True f) True g) false.
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Final answer:
The relationship between electric fields and electric potential is complex. Zero electric field does not guarantee zero electric potential, and equipotential surfaces arise when there is no change in potential, forming naturally around conductors in electrostatic conditions.
Explanation:
Addressing the statements related to electric fields and electric potential:
False: If the electric field is zero in some region of space, it does not imply that the electric potential is also zero; the potential could have a nonzero constant value.
True: If the electric potential is uniformly zero, the electric field must also be zero since a nonzero field would indicate a change in potential.
False: Zero electric potential at a point does not necessarily mean that the electric field is zero at that point.
True: Electric field lines always point from regions of higher to lower potential.
True: The value of the electric potential can be chosen to be zero at any convenient reference point.
True: In electrostatics, the surface of a conductor is an equipotential surface because the electric field within a conductor must be zero.
False: The breakdown voltage of air varies depending on conditions such as air density and humidity, and is generally accepted to be approximately 3×10⁶ V/m but the exact value can differ.
Suppose a negative point charge is placed at x = 0 and an electron is placed at some point P on the positive x-axis. What is the direction of the electric field at point P due to the point charge, and what is the direction of the force experienced by the electron due to that field?
O E along -X; F along –X
O E along +x; F along +x
O E along –x; F along +x
O E along +x; F along - x
Answer:
E along –x; F along +x
Explanation:
When a negative point charge is placed at x=0 and an electron is place at any point P on the positive x-axis the as we know that the like charges repel each other, but there will be no change in the natural tendency of the individual electric field lines. So the direction of the electric field lines at point P due to the point charge will be towards the negative x-axis.The direction of force on the electron due to the electric field of point charge at x=0 will be towards positive x-axis in accordance of the repulsion effect.The electric field at point P due to the negative point charge is directed along the -x axis, and the force experienced by the electron at point P due to this field is also along the -x axis.
Explanation:The electric field at point P due to the negative point charge at x = 0 is directed along the -x axis. This is because electric field lines always point away from positive charges and toward negative charges. Since the negative charge is located at x = 0, the electric field at point P, which is on the positive x-axis, points in the opposite direction, i.e., along the -x axis.
The force experienced by the electron at point P due to this electric field will be in the same direction as the electric field, i.e., along the -x axis. Like charges repel each other, so the negative point charge will exert a repulsive force on the electron.
gThe acceleration of gravity at the surface of Moon is 1.6 m/s2. A 5.0 kg stone thrown upward on Moon reaches a height of 20 m. (a) Find its initial velocity. (b) What is the time of flight to reach the max height
Answer:
(a) 8 m/s
(b) 5 s
Explanation:
(a)
Using newton's equation of motion,
v² = u²+2gs ..................... Equation 1
Where v = final velocity, u = initial velocity, g = acceleration due to gravity at the surface of moon, s = height reached.
make u the subject of the equation,
u² = v²-2gs
u = √(v²-2gs)................ Equation 2
Note: As the stone is thrown up, v = 0 m/s, g is negative
Given: v = 0 m/s, s = 20 m, g = -1.6 m/s²
Substitute into equation 2
u = √(0-2×20×[-1.6])
u = √64
u = 8 m/s.
(b)
Using,
v = u+ gt
Where t = time of flight to reach the maximum height.
Make t the subject of the equation,
t = (v-u)/g................................... Equation 3
Given: v = 0 m/s, u = 8 m/s, g = - 1.6 m/s²
Substitute into equation 3
t = (0-8)/-1.6
t = -8/-1.6
t = 5 seconds.
A partially divided tank contains two immiscible fluids oil (oil = 898 kg/m3 ) and water ( = 998 kg/m3 ). What is the height, h, of the oil column above the tank top? (8.0 cm)
Answer:
The height of the oil column above the tank top is 8 cm.
Explanation:
By applying Bernoulli's equation between point A and B as shown in the attached diagram
[tex]P_{atm}+\rho_{oil}g(h+0.12)=P_{atm}+\rho_{water}g(0.06+0.12)[/tex]
Here
P_atm is the atmospheric pressure.ρ_water=998 kg/m3ρ_oil=898 kg/m3g=9.8 m/s2[tex]P_{atm}+\rho_{oil}g(h+0.12)=P_{atm}+\rho_{water}g(0.06+0.12)\\898\times (h+0.12)=998 \times (0.06+0.12)\\(h+0.12)=\frac{998}{898} \times (0.18)\\h+0.12=0.20\\h=0.20-0.12\\h=0.08m \approx 8 cm[/tex]
So the height of the oil column above the tank top is 8 cm.
At a given location the airspeed is 20 m/s and the pressure gradient along the streamline is 100 N/m3. Estimate the airspeed at a point 0.5 m farther along the streamline.
Answer:
17.97m/s
Explanation:
Density of air (ρ)air=1.23 kg/m3, and
Air speed (V) =20 m/sec, pressure gradient along the streamline, ∂p/∂x = 100N/m^3.
The equation of motion along the stream line directions:
considering the momentum balance along the streamline.
γsinθ-∂p/∂x=ρV(∂V/∂x)
Neglecting the effect of gravity , then γ=ρg=0
So, ∂p/∂x= -ρV(∂V/∂x)
∂V/∂x= - 100/(20X1.23)= -4.0650407/S
Also δV/δx=∂V/∂x
∂V/∂x=-4.0650407/S and δx=0.5 m
δV = (-4.0650407/S) *(0.5m)
δV = -2.0325203 m/S
So net air speed will be V+δV= -2.0325203+20 ≅17.96748 m/s
Approximately, V+δV=17.97m/s.
Using Bernoulli's equation and the given pressure gradient, we can calculate the airspeed at a point 0.5 m further along the streamline to be approximately 45.83 m/s.
Explanation:To solve this problem, we can use Bernoulli's equation, which is a principle in fluid dynamics that states the total mechanical energy in a fluid system is constant if no energy is added or removed by work or heat transfer. It is formulated as p1 + 1/2 ρ v1² + ρgh1 = p2 + 1/2 ρ v2² + ρgh2.
In this case, we assume potential energy (ρgh) terms to be zero because there is no change in height, and the fluid (air) is incompressible. We are also given that the pressure gradient is 100 N/m³ which is effectively the change in pressure (Δp = p2 - p1), and the change in the distance along the streamline Δs = 0.5 m.
So we are left with: Δp + 1/2 ρ v1² = 1/2 ρ v2². Since ρ also cancels out, we are left with v2² = v1² + 2 Δp/ρ Δs. Plugging in given values we get v2 = √( 20² + 2*100*0.5) = √2100 = 45.83 m/s, assuming air density (ρ) is approximately 1.225 kg/m³ at sea level and at 15 °C.
Therefore, the airspeed at a point 0.5 m further along the streamline is approximately 45.83 m/s.
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A typical male sprinter can maintain his maximum acceleration for 2.0 s, and his maximum speed is 10 m/s. After he reaches this maximum speed, his acceleration becomes zero, and then he runs at constant speed. Assume that his acceleration is constant during the first 2.0 s of the race, that he starts from rest, and that he runs in a straight line. (a) How far has the sprinter run when he reaches his maximum speed? (b) What is the magnitude of his average velocity for a race of these lengths: (i) 50.0 m; (ii) 100.0 m; (iii) 200.0 m?
A perfectly spherical iron ball bearing weighs 21.91 grams. Derive the diameter of the ball bearing assuming an iron atom has an effective radius of 0.124nm and iron is BCC at room temperature. The answer should be in cm with 2 decimals of accuracy.
Final answer:
The diameter of the iron ball bearing, which weighs 21.91 grams and is composed of iron atoms organized in a BCC structure, is roughly 1.62 cm.
Explanation:
To derive the diameter of a spherical iron ball bearing weighing 21.91 grams, given that iron atoms have an effective radius of 0.124 nm and are arranged in a Body-Centered Cubic (BCC) structure at room temperature, we need to calculate the volume of the iron ball and then find the diameter using the volume of a sphere formula. First, we will use the density of iron (7.9 g/cm³) to find the volume of the ball bearing:
V = mass / density = 21.91 g / 7.9 g/cm³ = 2.77342 cm³
Next, we use the volume of a sphere formula V = (4/3)πr³, where V is the volume and r is the radius, to find the diameter (d = 2r):
r³ = V / ((4/3)π) = 2.77342 cm³ / ((4/3)π) ≈ 0.52733 cm³
r ≈ 0.8092 cm
d = 2 * r ≈ 2 * 0.8092 cm ≈ 1.6184 cm
Therefore, the estimated diameter of the iron ball bearing is approximately 1.62 cm.
A 1.00-kmkm length of power line carries a total charge of 230 mCmC distributed uniformly over its length. Find the magnitude of the electric field 65.1 cmcm from the axis of the power line, and not near either end (staying away from the ends means you can approximate the field as that of an infinitely long wire). Express your answer with the appropriate units.
Answer:
[tex]E = 6.38\times 10^6~N/C[/tex]
Explanation:
The question states that we can approximate the line as an infinite wire. In that case, the electric field can be found by Gauss' Law.
We should draw an imaginary cylindrical surface with an arbitrary height, h, around the wire. The radius of the cylinder should be equal to 65.1 cm.
Gauss' Law:
[tex]\int \vec{E}d\vec{a} = \frac{Q_{enc}}{\epsilon_0}[/tex]
The integral in the left-hand side is not to be taken, because we know the area of the cylinder. The enclosed charge in the right-hand side is equal to the charge of the portion of the wire inside the imaginary surface.
The charge density of the wire is
[tex]\lambda = \frac{Q}{L} = \frac{230 \times 10^{-3}}{1000} = 2.3 \times 10^{-4}[/tex]
The charge enclosed by the imaginary surface is
[tex]Q_{enc} = \lambda h = 2.3\times 10^{-4}h[/tex]
Finally, Gauss' Law yields
[tex]E2\pi rh = \frac{\lambda h}{\epsilon_0}\\E = \frac{\lambda}{2\pi \epsilon_0r} = \frac{2.3 \times 10^{-4}}{2\pi\epsilon_0(65.1\times 10^{-2})} = 6.38\times 10^6~N/C[/tex]
A three-point bend test is performed on a block of ZrO2 that is 8 in. long, 0.50 in. wide, and 0.25 in. thick and is resting on two supports 4 in. apart. When a force of 400 lb is applied, the specimen deflects 0.037 in. and breaks. Calculate (a) the flexural strength; and (b) the flexural modulus, assuming that no plastic deformation occurs.
The flexural strength of the ZrO2 block is 7680 lb/in^2. The flexural modulus of the ZrO2 block is 33546.74 lb/in^2.
Explanation:To calculate the flexural strength of the ZrO2 block, we need to use the formula:
Flexural strength = (3F * L) / (2 * b * h^2)
where F is the applied force, L is the distance between supports, b is the width of the block, and h is the thickness of the block. Substituting the given values, we have:
Flexural strength = (3 * 400 lb * 8 in.) / (2 * 0.50 in. * (0.25 in.)^2) = 7680 lb/in^2
To calculate the flexural modulus, we can use the formula:
Flexural modulus = (F * L^3) / (4 * b * h^3 * y)
where y is the deflection of the block. Substituting the given values, we have:
Flexural modulus = (400 lb * (4 in.)^3) / (4 * 0.50 in. * (0.25 in.)^3 * 0.037 in.) = 33546.74 lb/in^2
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A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 35 m/s2 for 35 s , then runs out of fuel. Ignore any air resistance effects. How long is the rocket in the air before hitting the ground?
Answer:
T = 295.57 s
Explanation:
given,
mass of the rocket = 200 Kg
mass of the fuel = 100 Kg
acceleration = 35 m/s²
time, t = 35 s
time taken by the rocket to hit the ground, = ?
Final speed of the rocket when fuel is empty
using equation of motion
v = u + a t
v = 0 + 35 x 35
v = 1225 m/s
height of the rocket where fuel is empty
v² = u² + 2 a s
1225² = 0 + 2 x 35 x h₁
h₁ = 21437.5 m
After 35 s the rocket will be moving upward till the final velocity becomes zero.
Now, using equation of motion to find the height after 35 s
v² = u² + 2 g h₂
0² = 1225² + 2 x (-9.8) h₂
h₂ = 76562.5 m
total height = h₁ + h₂
= 76562.5 m + 21437.5 m = 98000 m
now, time taken by before the rocket hit the ground
using equation of motion
[tex]s = u t +\dfrac{1}{2}at^2[/tex]
[tex]-13500 = 1225 t -\dfrac{1}{2}\times 9.8 \times t^2[/tex]
negative sign is used because the distance travel by the rocket is downward.
4.9 t² - 1225 t - 13500 = 0
[tex]t = \dfrac{-(-1225)\pm \sqrt{1225^2 - 4\times 4.9 \times (-13500)}}{2\times 4.9}[/tex]
t = 260.57 s
neglecting the negative sign
total time the rocket was in air
T = t₁ + t₂
T = 35 + 260.57
T = 295.57 s
Time for which rocket was in air is equal to 295.57 s.
A book slides off a horizontal tabletop. As it leaves the table’s edge, the book has a horizontal velocity of magnitude v0. The book strikes the floor in time t. If the initial velocity of the book is doubled to 2v0, what happens to (a) the time the book is in the air, (b) the horizontal distance the book travels while it is in the air, and (c) the speed of the book just before it reaches the floor? In particular, does each of these quantities stay the same, double, or change in another way? Explain.
Answer:
(a) The time the book is in the air stays the same.
(b) The horizontal distance the book travels doubles.
(c) The speed of the book just before it reaches the floor increases but not doubles.
Explanation:
The following kinematics equations will be used to solve this question:
[tex]v_y = v_{y_0} + a_yt\\y - y_0 = v_{y_0}t + \frac{1}{2}a_yt^2\\v_y^2 = v_{y_0}^2 + 2a_y(y - y_0)[/tex]
(a) Initially, the y-component of the velocity is zero. So, the x-component of the velocity is doubled.
We will use the second equation for both cases:
[tex]0 - y_0 = v_{y_0}t - \frac{1}{2}(g)t^2 = 0 - \frac{1}{2}gt^2\\0 - y_0 = v_{y_0}t_2 -\frac{1}{2}gt_2^2 = 0 - \frac{1}{2}gt_2^2\\t = t_2[/tex]
Since, the initial velocity in the y-direction is zero, and the height of the table is constant. The time it takes from the edge of the table to the floor is the same.
(b) For the horizontal distance the book travels, we should use the second equation again, and keep in mind that the acceleration in the x-direction is zero.
[tex]x - 0 = v_{x_0}t + \frac{1}{2}a_xt^2 = v_0t\\x_2 = 2v_0t_2 = 2v_0t[/tex]
Hence, the horizontal distance doubles.
(c) The vertical velocity does not change, since the initial velocity in the y-direction is zero. The horizontal velocity does not change along the motion, since the acceleration in the x-direction is zero. However, since the initial velocity in the x-direction doubles, the final velocity in the x-direction doubles as well.
[tex]v_x = v_{x_0} + a_xt = v_{x_0}[/tex]
However, this does not mean that final speed of the book will double. Because the speed of the object is calculated as follows:
[tex]v_{\rm final_1} = \sqrt{v_x^2 + v_y^2} = \sqrt{v_0^2 + v_y^2}\\v_{\rm final_2} = \sqrt{v_{x_2}^2 + v_y^2} = \sqrt{(2v_0)^2 + v_y^2}[/tex]
As can be seen from above, the final speed increases but not doubles.
Doubling the initial horizontal velocity of a book in projectile motion would result in the same time in the air, double the distance covered, and a higher (but not doubled) speed when it hits the floor.
Explanation:This question explores the concepts of projectile motion in physics. When we double the initial horizontal velocity of the book from v0 to 2v0, the following changes occur:
Time the book is in the air: This will stay the same. The time a projectile is in the air is determined by the vertical component of its motion alone. Thus, the horizontal velocity does not affect the time.Horizontal distance the book travels while it is in the air: This will double. The horizontal distance (d) a projectile travels is determined by the horizontal velocity (v) and the time it spends in the air (t). So, d=v*t. If we double the initial horizontal velocity, the distance will double as well.Speed of the book just before it reaches the floor: This will increase. The speed a projectile hits the floor with is determined by both its horizontal and vertical speeds. Doubling the initial horizontal velocity will result in a greater overall speed when it hits the floor, but not necessarily double the original speed.Learn more about Projectile Motion here:https://brainly.com/question/20627626
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How many times does a human heart beat during a person’s lifetime? How many gallons of blood does it pump? (Estimate that the heart pumps 50 cm3 of blood with each beat.)
Answer: The heart pumps 124.2 billion cm³ of blood in a lifetime
Explanation:
as an adult the pulse rate average must be around 72 beats per minute.
The heart beats about 103,680 times in a day.
There are 365 days in a year
number of heart beat in a year = 365 days x 103,680 = 37,843,200 beats in a year
For every the heart pumps 50cm³ of blood,
Hence,
Amount of blood pump in a year = 50 x 37,843,200 = 1,892,160,000cm³ of blood pumped in a year.
Using the estimated lifespan average an individual is 69 years
So in a life time,
The human heart pumps = 1,892,160,000 x 69 years = 124,200,000,000
If the heart pumps 50cm³ of blood per beat, the heart pumps a total of 130,559,040,000 cm³ (130.6 billion cm³) of blood in a LIFETIME.
The human heart beats approximately 108,000 times per day, amounting to nearly 3 billion beats in a 75-year lifespan and pumps about 2.6 million gallons of blood. To estimate the volume in cubic meters, we use the flow rate of 5 L/min over a 75-year period and convert liters to cubic meters.
Estimating Human Heart Beat and Blood Volume Pumped Over a Lifetime
The vital importance of the heart is evident in its tireless work throughout a person's life. Assuming an average heart rate of 75 beats per minute, we can estimate that a human heart beats about 108,000 times in one day, which amounts to more than 39 million times in one year, and nearly 3 billion times during a 75-year lifespan. When it comes to the volume of blood pumped, with each contraction pumping approximately 70 mL of blood, the heart pumps roughly 5.25 liters of blood per minute. This translates to about 14,000 liters per day, and over a year, the heart would pump approximately 10,000,000 liters, or roughly 2.6 million gallons of blood through an extensive network of vessels.
After fixing a flat tire on a bicycle you give the wheel a spin. If its initial angular speed was 6.36 rad/s and it rotated 14.7 revolutions before coming to rest, what was its average angular acceleration (assuming that the angular acceleration is constant)
To solve this problem we will apply the concepts related to the cinematic equations of angular motion. On these equations, angular acceleration is defined as the squared difference of angular velocity over twice the radial displacement. This is mathematically:
[tex]\alpha = \frac{\omega^2-\omega_0^2}{2\theta}[/tex]
Our values are,
[tex]\text{Initial angular velocity} = \omega_0 =6.36 rad/s[/tex]
[tex]\text{Final angular velocity} = \omega =0[/tex]
[tex]\text{Angular displacement} = \theta = 14.7rev = 29.4\pi rad[/tex]
Replacing,
[tex]\alpha = \frac{- 6.36^2}{29.4\pi}[/tex]
[tex]\alpha = -0.43rad/s^2[/tex]
Therefore the angular acceleration is [tex]-0.43rad/s^2[/tex]
A star (not Barnard's star) at a distance of 10 pc is observed to have a proper motion of 0.5 arcsec / year. What is its transverse speed in AU / year?
Answer:
The star will have a transverse speed of 315950.9 AU/year
Explanation:
d = 1/p
d = distance to star, measured in parsecs
p = parallax, measured in arcseconds = 0.5 arcsec/year
So, d = 1/0.5 = 2 parce
1 parsec = 3.26 light years
2 parce = 6.52 light years
⇒Transverse speed in AU / year = Distance/parallax
distance = 10pc = 2060000 AU
Transverse speed in AU / year = 2060000 Au/6.52 light years
Transverse speed = 315950.9 AU/year
Therefore, A star (not Barnard's star) at a distance of 10 pc observed to have a proper motion of 0.5 arcsec / year. Will have a transverse speed of 315950.9 AU/year
A 2.0m long pendulum is released from rest when the support string is at an angle of 25 degrees with the vertical. What is the speed of the bob at the bottom of the swing?
Answer:
[tex]v=1.92m/s[/tex]
Explanation:
Given data
Length h=2.0m
Angle α=25°
To find
Speed of bob
Solution
From conservation of energy we know that:
[tex]P.E=K.E\\mgh=(1/2)mv^{2}\\ gh=(1/2)v^{2}\\v^{2}=\frac{gh}{0.5}\\ v=\sqrt{\frac{gh}{0.5}}\\ v=\sqrt{\frac{(9.8m/s^{2} )(2.0-2.0Cos(25^{o} ))}{0.5}}\\v=1.92m/s[/tex]
Given values:
Length, h = 2.0 mAngle, α = 25°As we know,
The conservation of energy:
→ [tex]Potential \ energy = Kinetic \ energy[/tex]
or,
→ [tex]mgh = \frac{1}{2} mv^2[/tex]
or,
→ [tex]v^2 = \frac{gh}{0.5}[/tex]
[tex]= \sqrt{\frac{gh}{0.5} }[/tex]
By substituting the values, we get
[tex]= \sqrt{\frac{(9.8)(2.0-2.0 Cos (25^{\circ}))}{0.5} }[/tex]
[tex]= 1.92 \ m/s[/tex]
Thus the above answer is right.
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If the distance between the Earth and Moon were half what it is now, by what factor would the force of gravity between them be changed. That is, what is the ratio of the new force to the old force?
Answer:
4
Explanation:
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
[tex]m_1[/tex] = Mass of Earth
[tex]m_2[/tex] = Mass of Moon
r = Distance between Earth and Moon
Old gravitational force
[tex]F_o=\dfrac{Gm_1m_2}{r^2}[/tex]
New gravitational force
[tex]F_n=\dfrac{Gm_1m_2}{(\dfrac{1}{2}r)^2}[/tex]
Dividing the equations
[tex]\dfrac{F_n}{F_o}=\dfrac{\dfrac{Gm_1m_2}{(\dfrac{1}{2}r)^2}}{\dfrac{Gm_1m_2}{r^2}}\\\Rightarrow \dfrac{F_n}{F_o}=\dfrac{\dfrac{Gm_1m_2}{\dfrac{1}{4}r^2}}{\dfrac{Gm_1m_2}{r^2}}\\\Rightarrow \dfrac{F_n}{F_o}=4[/tex]
The ratio is [tex]\dfrac{F_n}{F_o}=4[/tex]
The new force would be 4 times the old force
If the distance between the Earth and Moon were halved, the force of gravity between them would be quadrupled.
Explanation:According to Newton's law of universal gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, this relationship is expressed as:
F= G*m*M/r^2
[tex]r^{2}[/tex]If the distance between the Earth and Moon were halved, the force of gravity between them would be quadrupled. This is because the force of gravity is inversely proportional to the square of the distance between two objects. So, if the distance is divided by 2, the new force would be multiplied by (2^2) = 4.
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If the focal length of a reflection telescope is 200 cm and the focal length of the eyepiece lens is 0.25 cm, what is the magnifying power of the telescope?
Answer:
800
Explanation:
Focal length of telescope, F = 200cm
Focal length of eyepiece, f = 0.25
The magnifying power of a telescope is given as the ratio of the focal length of the objective of the telescope to the focal length of the lens. Mathematically:
M = F/f
Therefore, when F = 200cm and f = 0.25cm:
M = 200/0.25
M = 800
Answer:
-48cm
Explanation:
the following data are given
focal length of telescope=200cm,
focal length of the eyepiece=0.25cm
From the genera formula used to find the magnifying power which is expressed as
[tex]M=-\frac{fx_{o}}{f_{e}}[1+\frac{f_{e}}{d}][/tex]
where
[tex]f_{e} = focal length of thr eye piece\\ f_{o} =focal length of the telescope\\[/tex]
and d=least distance of distinct vision=25cm
if we substitute values into the formula, we arrive at
[tex]M=-\frac{fx_{o}}{f_{e}}[1+\frac{f_{e}}{d}]\\M=-\frac{200cm}{0.25cm}[1+\frac{0.25cm}{25cm}]\\M=-800cm[1+0.01]\\M=-800cm(1.01)\\M=-808cm \\M=-808cm[/tex]
hence from the answer, we can conclude that the magnifying power of the telescope is -808cm
A baseball player friend of yours wants to determine his pitching speed. You have him stand on a ledge and throw the ball horizontally from an elevation 3.0m above the ground. The ball lands 30m away.
What is his pitching speed? Vox=38 m/s
Answer:
His pitching speed is 38 m/s.
Explanation:
Hi there!
Please see the attached figure for a better understanding of the problem.
The position of the ball at any time t is given by the following vector:
r = (x0 + v0 · t, y0 + 1/2 · g · t²)
Where:
r = position vector of the ball at time t.
x0 = initial horizontal position.
v0 = initial horizontal velocity.
t = time.
y0 = initial vertical position.
g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).
Let's place the origin of the frame of reference at the throwing point so that x0 and y0 = 0.
When the ball reaches the ground, its position vector will be r1 (see figure). Using the equation of the vertical component of the position vector, we can find the time at which the ball reaches the ground. At that time, the horizontal component of the position is 30 m and the vertical component is -3.0 m (see figure):
y = y0 + 1/2 · g · t² (y0 = 0)
y = 1/2 · g · t²
-3.0 m = 1/2 · (-9.8 m/s²) · t²
-3.0 m / -4.9 m/s² = t²
t = 0.78 s
Now, knowing that at this time x = 30 m, we can find v0:
x = x0 + v0 · t (x0 = 0)
x = v0 · t
30 m = v0 · 0.78 s
v0 = 30 m / 0.78 s
v0 = 38 m/s
His pitching speed is 38 m/s.
The pitching speed can be calculated using the horizontal distance and the height of the ledge. By considering the horizontal motion and the effects of gravity, the time taken can be determined. Substituting the given values into the appropriate equations, the pitching speed can be calculated as 38 m/s.
Explanation:The pitching speed can be calculated using the horizontal distance and the height of the ledge. To find the initial velocity, we can use the equation:
Vox = d / t
where Vox is the horizontal component of velocity, d is the horizontal distance, and t is the time taken. Since the ball is thrown horizontally, the vertical component of velocity is zero, and the only force acting on the ball is gravity in the downward direction. Therefore, we can use the equation:
[tex]h = 0.5 * g * t^2[/tex]
where h is the height of the ledge, g is the acceleration due to gravity, and t is the time taken. By rearranging the equation, we can find the time taken:
t = sqrt(2 * h / g)
Substituting the values given in the question, we can calculate the pitching speed:
Vox = d / t = d * sqrt(g / (2 * h))
Using the values d = 30m, h = 3.0m, and g = 9.8m/s^2, we can find the pitching speed:
Vox = 30m * [tex]sqrt(9.8m/s^2[/tex]) = 38 m/s
A person riding in a boat observes that the sunlight reflected by the water is polarized parallel to the surface of the water. The person is wearing polarized sunglasses with the polarization axis vertical.
If the wearer leans at an angle of 19.5 degrees to the vertical, what fraction of the reflected light intensity will pass through the sunglasses?
The angle of incidence, when there is perfect transmission is the polarization angle. The expression for the polarization is
[tex]\theta = 90-\phi[/tex]
Where
[tex]\theta[/tex] = Polarization angle
[tex]\phi[/tex] = Angle with the vertical axis
We have that the angle is
[tex]\theta = 90-19.5[/tex]
[tex]\theta = 70.5\°[/tex]
The ratio of the intensities depends on the cosine of the polarization angle. The polarization angle found from the wearer’s leaning angle can be used to find the fraction of the reflected ray intensity that will pass through the sunglasses.
Applying the Malus Law we have that
[tex]\frac{I}{I_0} = cos^2 \theta[/tex]
Here,
[tex]I[/tex] = Final intensity
[tex]I_0[/tex] = Initial intensity
Replacing we have,
[tex]\frac{I}{I_0} = cos^2 (70.5)[/tex]
[tex]\frac{I}{I_0} = 0.11[/tex]
Therefore the fraction of the reflected light intensity which passes through the sunglasses is 0.11
By applying Malus's Law, a person leaning at 19.5° while wearing polarized sunglasses with a vertical axis lets approximately 88.9% of the reflected, polarized light pass through.
A person riding in a boat observes that the sunlight reflected by the water is polarized parallel to the surface of the water. The person is wearing polarized sunglasses with the polarization axis vertical. If the wearer leans at an angle of 19.5 degrees to the vertical, we can determine the fraction of the reflected light intensity that will pass through the sunglasses using Malus's Law.Malus's Law states that the transmitted light intensity I through a polarizing filter is given by:I = Io cos²(θ)
where I is the transmitted intensity, Io is the initial light intensity, and θ is the angle between the light's polarization direction and the transmission axis of the filter.Since the observer leans at an angle of 19.5°, the angle between the polarized light and the vertical axis of the sunglasses is 19.5°. Applying Malus’s Law:I = Io cos²(19.5°)
First, compute cos(19.5°):cos(19.5°) ≈ 0.943
Then, square this value:(0.943)² ≈ 0.889
Therefore, the fraction of the reflected light intensity that will pass through the sunglasses is approximately 0.889 or 88.9%.
A compressed air tank contains 4.6 kg of air at a temperature of 77 °C. A gage on the tank reads 300 kPa. Determine the volume of the tank.
Answer : The volume of the tank is, 1.54 mL
Explanation :
To calculate the volume of gas we are using ideal gas equation:
[tex]PV=nRT\\\\PV=\frac{w}{M}RT[/tex]
where,
P = pressure of gas = 300 kPa = 2.96 atm
Conversion used : (1 atm = 101.325 kPa)
V = volume of gas = ?
T = temperature of gas = [tex]77^oC=273+77=350K[/tex]
R = gas constant = 0.0821 L.atm/mole.K
w = mass of gas = 4.6 kg = 4600 g
M = molar mass of air = 28.96 g/mole
Now put all the given values in the ideal gas equation, we get:
[tex](2.96atm)\times V=\frac{4600g}{28.96g/mole}\times (0.0821L.atm/mole.K)\times (350K)[/tex]
[tex]V=1541.98L=1.54mL[/tex] (1 L = 1000 mL)
Therefore, the volume of the tank is, 1.54 mL
Wile E. Coyote is once again pursuing the Roadrunner, chasing the bird in a rocket-powered car. Unsurprisingly, the Roadrunner outsmarts him, and he sails off a cliff in the desert. His velocity when he leaves the cliff is horizontal with a magnitude of 24m/s, but the rocket continues to provide a constant horizontal acceleration of 3m/s2 . The cliff is 29 meters tall. How far from the base of the cliff does the coyote crash into the ground? Assume the ground is flat.
Answer:
The coyote crashes 66 m from the base of the cliff.
Explanation:
Hi there!
The equation of the position vector of the Coyote is the following:
r = (x0 + v0 · t + 1/2 · a · t², y0 + 1/2 · g · t²)
Where:
r = postion vector of the Coyote at time t.
x0 = initial horizontal position.
v0 = initial horizontal velocity.
t = time.
a = horizontal acceleration.
y0 = initial vertical position.
g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).
Let's place the origin of the frame of reference at the edge of the cliff so that x0 and y0 = 0.
When the Coyote reaches the ground, the vertical component of its position vector (r1 in the figure) will be equal to -29 m. When the vertical component of the position vector is -29 m, the horizontal component will be equal to the horizontal distance traveled by the Coyote (r1x in the figure). So, let's find the time at which the y-component of the position vector is -29 m:
y = y0 + 1/2 · g · t² (y0 = 0)
-29 m = -1/2 · 9.8 m/s² · t²
t² = -29 m / -4.9 m/s²
t = 2.4 s
Now, let's find the x-component of the vector r1 in the figure:
x = x0 + v0 · t + 1/2 · a · t² (x0 = 0)
x = 24 m/s · 2.4 s + 1/2 · 3 m/s² · (2.4 s)²
x = 66 m
The coyote crashes 66 m from the base of the cliff.
The problem involves determining the distance Wile E. Coyote travels horizontally before he crashes into the ground. It involves the use of motion equations to first calculate the time it takes for the coyote to hit the ground and then the distance it travels horizontally. The calculated distance is roughly 65.4 meters.
Explanation:In this problem, we are asked to calculate the distance that Wile E. Coyote travels along the ground before he crashes.
To solve this, we need to use the laws of motion. First, since the coyote falls with a constant acceleration due to gravity, we can use the equation of motion to determine the time it takes for him to hit the ground:
29 = 0.5 * g * t2
By plugging in the acceleration due to gravity (g=9.8m/s2), we determine that t is approximately 2.44 seconds.
Next, we have to calculate how far the coyote travels horizontally. He starts with a velocity of 24m/s, but he also accelerates due to the rocket. So the distance he travels is given by:
x = v0t + 0.5*a*t2
Substituting the known values (v0 = 24m/s, a = 3m/s2, t = 2.44s), we find that the coyote travels roughly 65.4 meters along the ground before he crashes into it.
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Consider two concentric conducting spheres. The outer sphere is hollow and initially has a charge Q1 = -10Q deposited on it. The inner sphere is solid and has a charge Q 2 = +1Q on it. 1)How much charge is on the outer surface
Answer:
Q_out,shell = 9Q
Explanation:
Given:
- Q_in,shell = -10 Q
- Q_sphere = +1Q
Find:
How much charge is on the outer surface?
Solution:
The electric field in the material of both the sphere and shell must be zero. The only way for this to occur is if the charge inside the
inner surface of the shell is such that its charge plus the solid's charge is zero. The rest of the excess charge from the shell moves to the outside of the shell.
Hence,
Q_out,shell + Q_in,shell + Q_sphere = 0
Q_out,shell -10 Q + 1 Q = 0
Q_out,shell = 9Q
Final answer:
The charge on the outer surface of the hollow conducting sphere, which initially had a charge of -10Q and contains an inner sphere with a charge of +1Q, would be -9Q, as determined by Gauss' Law and the conservation of charge.
Explanation:
The student is asking about the charge distribution on concentric conducting spheres when one sphere is placed inside another and they each have different charges. According to Gauss' Law, when a charge is placed inside a conducting shell, it induces an equal and opposite charge on the inner surface of the shell to maintain an electric field of zero inside the material of the conductor. In the given scenario, the inner solid sphere has a charge of +1Q and the outer hollow sphere has a charge of -10Q.
By Gauss' Law, since the electric field inside a conductor must be zero, we know that the inner surface of the hollow outer sphere must have a charge of -1Q to cancel out the electric field from the +1Q charge of the inner solid sphere.
Considering charge conservation, if the outer sphere initially had a total charge of -10Q and now there is -1Q on the inner surface, the outer surface of the hollow sphere must have the remainder, which is -10Q + 1Q = -9Q. Therefore, the charge on the outer surface of the outer hollow sphere is -9Q.
A 1200-kg car initially at rest undergoes constant acceleration for 9.4 s, reaching a speed of 11 m/s. It then collides with a stationary car that has a perfectly elastic spring bumper. What is the final kinetic energy of the two car system?
To solve this problem we will apply the principle of conservation of energy and the definition of kinematic energy as half the product between mass and squared velocity. So,
[tex]KE_i = KE_f[/tex]
[tex]KE_f = \frac{1}{2} mv^2[/tex]
Here,
m = Mass
V = Velocity
Replacing,
[tex]KE_f = \frac{1}{2} (12000)(11)^2[/tex]
[tex]KE_f = 72600J[/tex]
Therefore the final kinetic energy of the two car system is 72.6kJ
The final kinetic energy of two car system is 72,600 Joules.
To understand more, check below explanation.
Energy conservation:The energy is neither be created nor be destroyed only transfer from one form to another form.
So that,
Initial kinetic energy = Final kinetic energy
It is given that, mass,m = 1200kg , speed, v = 11m/s.
As we know that,
Kinetic energy[tex]=\frac{1}{2}*m*v^{2}[/tex]
Substute above values in above formula.
[tex]K.E=\frac{1}{2}*1200*(11)^{2} \\\\K.E=600*121=72,600J[/tex]
Hence, the final kinetic energy of two car system is 72,600 Joules.
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A step-up transformer has 22 turns on the primary coil and 800 turns on the secondary coil. If this transformer is to produce an output of 5300 V with a 16- mA current, what input current and voltage are needed?
Final answer:
For a step-up transformer with 22 primary turns and 800 secondary turns, to produce an output of 5300 V at 16 mA, the required input voltage is 145.75 volts and the input current needed is 0.5818 amperes.
Explanation:
Calculating Input Current and Voltage for a Step-Up Transformer
The student's question involves a step-up transformer with a known number of turns in the primary and secondary coils, a given secondary voltage, and a secondary current. To find the required input current and voltage, we can use the transformer equations that relate the primary and secondary sides of the transformer:
Primary voltage (VP) / Secondary voltage (VS) = Number of turns in the primary coil (NP) / Number of turns in the secondary coil (NS)
Primary current (IP) * Number of turns in the primary coil (NP) = Secondary current (IS) * Number of turns in the secondary coil (NS)
We're given:
NP = 22 turns
NS = 800 turns
IS = 16 mA = 0.016 A
VS = 5300 V
To find the input voltage VP:
VP = (NP / NS) * VS = (22 / 800) * 5300 V = 145.75 V
To find the input current IP:
IP = (NS / NP) * IS = (800 / 22) * 0.016 A = 0.5818 A
Therefore, the required input voltage is 145.75 volts, and the required input current is 0.5818 amperes.
A proton is observed to have an instantaneous acceleration of 10 × 1011 m/s2. What is the magnitude of the electric field at the proton's location?
To solve this problem we will apply the concept of Newton's second law with which we will obtain the strength of the proton. We know the mass and the acceleration is given in the statement. Subsequently said Force by equilibrium can be matched the electrostatic force of Coulomb, defined as the product between the charge and the electric field. Our values are
[tex]m = 1.67*10^{-27}kg[/tex]
[tex]a = 10*10^{11} m/s^2[/tex]
Applying the Newton's second law,
[tex]F = ma[/tex]
[tex]F = (1.67*10^{-27}kg)( 10*10^{11} m/s^2)[/tex]
[tex]F = 1.67*10^{-15}N[/tex]
By the Coulomb's equation for electrostatic Force we have that
[tex]F = qE[/tex]
Remember that the charge of a proton is [tex]1.6*10^{-19}C[/tex]
Replacing we have,
[tex]1.67*10^{-15} = 1.6*10^{-19} E[/tex]
[tex]E = 10437.5 N/C[/tex]
Therefore the magnitude of the electric field at the proton's location is [tex]10437.5 N/C[/tex]
The magnitude of the electric field at the proton's location is 10,437.5 N/C.
The given parameters:
Acceleration of the proton, a = 10 x 10¹¹ m/s²Mass of proton, m = 1.67 x 10⁻²⁷ kgThe magnitude of the electric field at the proton's location is calculated as follows;
F = ma
F = qE
qE = ma
[tex]E = \frac{ma}{q} \\\\E = \frac{1.67 \times 10^{-27} \times 10\times 10^{11}}{1.6 \times 10^{-19}} \\\\E = 10,437.5 \ N/C[/tex]
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The storage coefficient of a confined aquifer is 6.8x10-4 determined by a pumping test. The thickness of the aquifer is 50 m and the porosity is 25%. Determine the fractions of the storage attributable to the expansibility of water and compressibility of the aquifer skeleton in terms of percentages of the storage coefficient of the aquifer.
Answer
given,
storage coefficient, S = 6.8 x 10⁻⁴
thickness of aquifer, t = 50 m
porosity of the aquifer, n = 25 % = 0.25
Density of the water, γ = 9810 N/m³
Compressibilty of water,β = 4.673 x 10⁻¹⁰ m²/N
We know,
S = γ t(nβ + α)
where, α is the compressibility of the aquifer
6.8 x 10⁻⁴ =9810 x 50 x (0.25 x 4.673 x 10⁻¹⁰+ α)
α = 1.269 x 10⁻⁹ m²/N
Expansability of water
= n t β γ
= 0.25 x 50 x 4.673 x 10⁻¹⁰ x 9810
= 5.73 x 10⁻⁵