In what regions of the electromagnetic spectrum is the atmosphere transparent enough to allow observations from the ground?

Answer:

Q'sphere=2.7*10^-9 C

Q'rod=-4.7*10^-9 C

Explanation:

given data:

charge on metallic sphere Qsphere=3.1*10^-9 C                ∴1n=10^-9

charge on rod Qrod =-4*10^-9 C  

no of electron n= 9.2×10^9 electrons

To find:

we are asked to find the charges Q'sphere on the sphere and Q'rod on the rod after the rod touches the sphere.

solution:

the total charge transferred when the rod touches the sphere equal to the no of electrons transferred multiplied by the charge of each electron:

Q(transferred)= nq_(e)

                       =(9.2×10^9)(1.6×10^-19)

                       =-1.312×10^-9 C

because electron are negative they move from the negatively charged rod to the positively charged rod so that new charged of the sphere is:

      Q'sphere =Qsphere+Q(transferred)

                       =(3.1*10^-9 )-(1.312×10^-9)

                       =2.7*10^-9 C

similarly the new charge of the rod is:

            Q'rod = Qrod-Q(transferred)

                      = (-6*10^-9 C)-(1.312*10^-9 C)

                      = -4.7*10^-9 C

∴note: there maybe error in calculation but the method is correct.

Final answer:

Upon contact, a metallic sphere and a negatively charged rod share their charges until equilibrium. The total charge of -0.9 nC is equalized, with 9.2×109 electrons changing the sphere's charge to +1.628 nC and the rod's charge to -2.528 nC.

Explanation:

When two charged objects come into contact, they share their charges until equilibrium is reached. This means each object will end up with the average charge. In the case of the metallic sphere with a charge of +3.1 nC and the negatively charged rod with a charge of -4.0 nC, the total charge before contact is (-4.0 nC) + (+3.1 nC) = -0.9 nC.

Since 9.2×109 electrons are transferred, we calculate the charge transferred using the charge of one electron, which is approximately -1.6×10-19 C. Multiplying the number of electrons by the charge of one electron gives us the total charge transferred: 9.2×109 × -1.6×10-19 C/electron ≈ -1.472 nC.

This charge is added to the metallic sphere and subtracted from the rod. So, the new charge on the sphere is +3.1 nC + (-1.472 nC) = +1.628 nC, and the charge on the rod is -4.0 nC - (-1.472 nC) = -2.528 nC. Both charges are now closer in magnitude, representing the sharing of charges due to contact.

Answer:

stone A is diamond.

Explanation:

given,

Volume of the two stone =  0.15 cm³

Mass of stone A = 0.52 g

Mass of stone B = 0.42 g

Density of the diamond =  3.5 g/cm³

So, to find which stone is gold we have to calculate the density of both the stone.

We know,

[tex]density[/tex][tex]\density = \dfrac{mass}{volume}[/tex]

density of stone A

[tex]\rho_A = \dfrac{0.52}{0.15}[/tex]

[tex]\rho_A = 3.467\ g/cm^3[/tex]

density of stone B.

[tex]\rho_B = \dfrac{0.42}{0.15}[/tex]

[tex]\rho_B = 2.8\ g/cm^3[/tex]

Hence, the density of the stone A is the equal to Diamond then stone A is diamond.

Neither of the stones is a real diamond because their densities, calculated using mass and volume, do not match the density of a real diamond.

The determination of whether a stone is a real diamond or a fake can be made by calculating the density of the stone. Density is calculated as the mass of an object divided by its volume. So, for stone A, the density is 0.52 g / 0.15 cm3 = 3.47 g/cm3, and for stone B, the density is 0.42 g / 0.15 cm3 = 2.8 g/cm3. The density of a real diamond is 3.5 g/cm3. Hence, neither stone A nor stone B is a real diamond as their densities are less than the density of a real diamond.

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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.

(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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Answer:

(a) Magnitude =3.18 km

(a) Angle =28.2°

Explanation:

(a) To find magnitude of this vector recognize

[tex]R_{x}=-2.8 km\\R_{y}=-1.5km[/tex]

Use Pythagorean theorem

[tex]R=\sqrt{(R_{x})^{2}+(R_{y})^{2} }\\ R=\sqrt{(-2.8)^{2}+(-1.5)^{2} }\\ R=3.18km[/tex]

(b)To find the angle use the trigonometric property

[tex]tan\alpha =\frac{opp}{adj}\\\ tan\alpha =\frac{R_{y} }{R_{x}}\\\alpha =tan^{-1}(\frac{(-1.5)}{(-2.8)})\\\alpha =28.2^{o}[/tex]

The answer details the vertical velocity needed and the horizontal distance required for a basketball player to complete a jump.

Vertical velocity: To rise 0.750 m above the floor, the athlete needs a vertical velocity of 5.43 m/s.

Horizontal distance: The athlete should start his jump 2.27 m away from the basket to reach his maximum height at the same time as he reaches the basket.

Answer:

[tex]v_0 = 16.82\ m/s[/tex]

Explanation:

given,

angle at which rock is thrown = 60°

rock lands at distance,d = 25 m

initial speed of rock, = ?

In horizontal direction

distance = speed x time

d = v₀ cos 60° t

25 = v₀ cos 60° t............(1)

now,

in vertical direction

displacement in vertical direction is zero

using equation of motion

[tex]s = ut +\dfrac{1}{2}gt^2[/tex]

[tex]0 =v_0 sin 60^0 t - 4.9 t^2[/tex]

[tex]v_o sin 60^0 = 4.9 t[/tex]

[tex]t = \dfrac{v_0 sin 60^0}{4.9}[/tex]

putting the value of t in equation (1)

[tex]25 = v_0 cos 60^0\times \dfrac{v_0 sin 60^0}{4.9}[/tex]

[tex]25 =\dfrac{v_0^2cos 60^0 sin 60^0}{4.9}[/tex]v

[tex]v_0^2 = 282.90[/tex]

[tex]v_0 = 16.82\ m/s[/tex]

Hence, the initial speed of the rock is equal to 16.82 m/s

Answer:

Cu = 1453.72J/Kg°C

The heat capacity of the liquid is 1453.72J/Kg°C

Explanation:

At equilibrium, assuming no heat loss to the surrounding we can say that;

Heat gained by ice + heat gained by cold water = heat loss by hot unknown liquid (24°C) + heat loss by aluminium calorimeter.

Given;

Mass of ice = mass of cold water = mc = 30g = 0.03kg

Mass of hot unknown liquid mh= 300g = 0.3kg

Mass of aluminium calorimeter ma= 100g = 0.1 kg

change in temperature cold ∆Tc = (4-0) = 4°C

Change in temperature hot ∆Th = 24-4 = 20°C

Specific heat capacity of water Cw= 4186J/Kg°C

Specific heat capacity of aluminium Ca = 900J/kg°C

Specific heat capacity of unknown liquid Cu =?

Heat of condensation of ice Li = 334000J/Kg

So, the statement above can be written as.

mcLi + mcCw∆Tc = maCa∆Th + mhCu∆Th

Making Cu the subject of formula, we have;

Cu = [mcLi + mcCw∆Tc - maCa∆Th]/mh∆Th

Substituting the values we have;

Cu = (0.03×334000 + 0.03×4186×4 - 0.1×900×20)/(0.3×20)

Cu = 1453.72J/Kg°C

the heat capacity of the liquid is 1453.72J/Kg°C

The torque required by the motor to spin a 220g, 23-cm-diameter plastic disk from 0 to 1800 rpm in 4.6 seconds, without considering the external forces, is 0.431 Nm.

In solving the question,

Torque

is our primary interest. We first need to convert rpm to rad/s since Torque calculations require SI units. The conversion can be done by the formula ω = 2π (frequency), and frequency is simply rpm/60. Hence, 1800 rpm is equivalent to 188.50 rad/s. Now, we use the Kinematics equation ω = ω

0

+ αt to calculate angular acceleration (α), where ω

0

is the initial angular velocity, and it is 0 rad/s in this case as the disk starts from rest, ω is the final angular velocity and is 188.50 rad/s, while t is the time of 4.6 seconds. Solving this gives us α=41 rad/s

2

. The Torque can now be calculated using τ=Iα where I (moment of inertia for a disk) = 0.5*m*r

2

. Substituting the values of m, r and α gives a Torque value of 0.431 Nm.

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Explanation:

Given that,

The dimensions of the largest building in the world is 632 m long, 710 yards wide, and 112 ft high. It basically forms a cuboid. The volume of a cuboidal shape is given by :

Since,

1 meter = 3.28084 feet

632 m = 2073.49 feet

1 yard= 3 feet

710 yards = 2130 feet

V = lbh

[tex]V=2073.49 \ ft\times 2130\ ft\times 112\ ft[/tex]

[tex]V=494651774.4\ ft^3[/tex]

[tex]V=4.94\times 10^8\ ft^3[/tex]

Also,

[tex]V=(4.94\times 10^8\ ft^3)(\dfrac{1\ m}{3.281})^3[/tex]

[tex]V=1.39\times 10^7\ m^3[/tex]

Hence, this is the required solution.

Answer:

27.1806500378 V

Explanation:

k = Coulomb constant = [tex]8.99\times 10^{9}\ Nm^2/C^2[/tex]

q = Charge = [tex]1.6\times 10^{-19}\ C[/tex]

r = Distance = [tex]5.292\times 10^{-11}\ m[/tex]

Voltage is given by

[tex]V=k\dfrac{q}{r}\\\Rightarrow V=8.99\times 10^9\dfrac{1.6\times 10^{-19}}{5.292\times 10^{-11}}\\\Rightarrow V=27.1806500378\ V[/tex]

The potential difference is 27.1806500378 V

Answer:

3.5 amperes

Explanation:

I = E/R

I = ?

E = 70volts

R = 20 Ohms

Therefore , I = 70/20

= 3.5 amperes

The angular displacement of the solid disk after 5 seconds is 0 rad.

To determine the angular displacement of the solid disk after 5 seconds, we can use the formula:

Δθ = ΔErot / (I * ω)

where Δθ is the angular displacement, ΔErot is the change in rotational kinetic energy, I is the moment of inertia of the disk, and ω is the angular velocity of the disk.

The moment of inertia of a solid disk rotating around an axis through its center perpendicular to its plane is given by:

I = (1/2) * m * r2

where m is the mass of the disk and r is the radius.

Given that ΔErot = 20 J/s, m = 4 kg, r = 2 m, and the disk starts from rest, we can calculate the angular displacement:

Δθ = ΔErot / (I * ω) = 20 / [(1/2) * 4 * 22 * ω]

Since the disk starts from rest, the initial angular velocity ω is 0. Therefore, the angular displacement after 5 seconds is:

Δθ = 20 / [(1/2) * 4 * 22 * 0] = 0 rad

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Answer:

0.0473m

Explanation:

345 ml = 0.000354 m3

6.5 cm = 0.065 m

20g = 0.02 kg

Since can is half filled with water, the water volume is 0.000354 / 2 = 0.000177 m cubed

Let water density be 1000kg/m3, the mass of this half-filled water is

1000*0.000177 = 0.177 kg

The total water-can system mass is 0.177 + 0.02 = 0.197 kg

For the system to stay balanced, this mass would be equal to the mass of the water displaced by the can submerged

The volume of water displaced, or submerged can is

0.197 / 1000 = 0.000197 m cubed

Then the volume of the can that is not submerged, aka above water level is

0.000354 - 0.000197 = 0.000157 m cubed

The base area of the can is

[tex]A = \pi r^2 = \pi (d/2)^2 = \pi (0.065)^2 = 0.003318 m squared[/tex]

The length of the can that is above water is

0.000157 / 0.003318 = 0.0473 m

The half-filled soda can displaces the equivalence of its own weight in water when placed in it. Half of the soda can's total volume will always be submerged since it is only half-filled i.e., half of the can's mass is displacing water.

The subject of this problem is the principles of buoyancy and volume. A half-filled soda can placed in water will displace its own weight of the water. The length of the can above the water level can be calculated using an understanding of volume and displacement.

First, calculate the volume of the can using the formula for the volume of a cylinder V = πr²h, where r is radius and h is height. Given the diameter of the can is 6.5 cm, the radius is 3.25 cm. The height can be calculated by rearranging the volume formula to find h. We know that the can's complete volume is 345 mL, so h (full can height) = V / (πr²).

From this, we can calculate the height of the can that is submerged in water. Since the can is half-filled, it displaces half its full weight in water. So half of the can's total volume will always be submerged. Therefore, the length of the can above the water will be half the total height of the can.

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Answer:

Acceleration, [tex]a=6.51\times 10^{10}\ m/s^2[/tex]                                                

Explanation:

Given that,

Electric field, E = 680 N/C

Speed of the proton, v = 1.3 Mm/s

We need to find the acceleration of the proton. We know that the force due to motion is balanced by the electric force as :

[tex]qE=ma[/tex]

a and m are the acceleration and mass of the proton.

[tex]a=\dfrac{qE}{m}[/tex]

[tex]a=\dfrac{1.6\times 10^{-19}\times 680}{1.67\times 10^{-27}}[/tex]

[tex]a=6.51\times 10^{10}\ m/s^2[/tex]

So, the acceleration of the proton is [tex]a=6.51\times 10^{10}\ m/s^2[/tex]. Hence, this is the required solution.

Answer:

The question is incomplete, below is the complete question,

"A water balloon is launched at a speed of (15.0+A) m/s and an angle of 36 degrees above the horizontal. The water balloon hits a tall building located (18.0+B) m from the launch pad. At what height above the ground level will the water balloon hit the building? Calculate the answer in meters (m) and rounded to three significant figures. A=12, B=2"

Answe:

12.1m

Explanation:

Below are the data given

Speed, V=(15+A) = 15+12=27m/s

Angle of projection, ∝=36 degree

Distance from building = 18+B=18+2=20m

Since the motion describe by the object is a projectile motion, and recall that  in projectile motion, motion along the horizontal path has zero acceleration and motion along the vertical path is under gravity,

the Velocity along the horizontal path is define as

[tex]V_{x}=Vcos\alpha \\V_{x}=27cos36\\V_{x}=21.8m/s[/tex]

the velocity along the Vertical path is

[tex]V_{y}=Vsin\alpha \\V_{y}=27sin36 \\V_{y}=15.87m/s[/tex]

Since the horizontal distance from the point of projection to the building is 20m, we determine the time it takes to cover this distance using the simple equation of motion

[tex]Velocity=\frac{distance }{time }\\ Time,t=27/21.8\\t=1.24secs[/tex]

The distance traveled along the vertical axis is given as

[tex]y=V_{y}t-\frac{1}{2}gt^{2}\\ t=1.24secs,\\V_{y}=15.87m/s\\g=9.81m/s[/tex]

if we substitute values, we arrive at

[tex]y=15.87*1.24-\frac{1}{2}9.81*1.24^{2}\\y=19.66-7.57\\y=12.118\\y=12.1m[/tex]

Hence the water balloon hit the building at an height of 12.1m

Answer:

22.8077659955 m deep

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

g = Acceleration due to gravity = 9.81 m/s² = a

[tex]v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 9.81\times 6.1+0^2}\\\Rightarrow v=10.9399268736\ m/s[/tex]

[tex]v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{10.9399268736-0}{9.81}\\\Rightarrow t=1.11518112881\ s[/tex]

Time taken to fall through the foam

[tex]3.2-1.11518112881=2.08481887119\ s[/tex]

Distance is given by

[tex]s=vt\\\Rightarrow s=10.9399268736\times 2.08481887119\\\Rightarrow s=22.8077659955\ m[/tex]

The vat is 22.8077659955 m deep

The depth of the vat obtained is 44.076 m

H = ½gt²

H = ½ × 9.8 × 3.2²

H = 4.9 × 10.24

H = 50.176 m

Depth of vat = H – h

Depth of vat = 50.176 – 6.10

Depth of vat = 44.076 m

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Answer:

Ventricular systole

Explanation:

This contraction causes an increase in pressure inside the ventricles, being the highest during the entire cardiac cycle. The ejection of blood contained in them takes place. Therefore, blood is prevented from returning to the atria by increasing pressure, which closes the bicuspid and tricuspid valves.

The highest pressure in the ventricles occurs during the ventricular systole phase of the cardiac cycle, when the ventricles are contracting to pump blood out to the body.

The pressure in the ventricles is highest during the ventricular systole phase of the cardiac cycle. At this point, the ventricles have filled up with blood and are contracting to pump this blood out into the body. This contraction greatly increases the pressure in the ventricles, leading to a peak pressure of around 120 mm Hg in the left ventricle, depending on the individual.

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The mathematical description that fits to find the circumference of a circle (Approximation we will make to the earth considering it Uniform) is,

[tex]\phi = 2\pi r[/tex]

Here,

r = Radius

The radius of the earth is 6378.01 km or 6378010m

Replacing we have that the circumference of the Earth is

[tex]\phi = 2\pi (6378010m)[/tex]

[tex]\phi = 40074000 m[/tex]

[tex]\phi = 40074*10^3 m[/tex]

Therefore the circumference of the Earth in m with 5 significant figures is [tex]40074*10^3 m[/tex] and using only trailing zeros the answer will be [tex]40074000m[/tex]

Answer:

It will go 96 times around the track.

Explanation:

Given that,

Distance covered by the race car, d = 765 km

Radius of the circular sprint track, r = 1.263 km

Let n times did it go around the track. It is given by :

[tex]n=\dfrac{d}{C}[/tex]

C is the circumference of the circular path, [tex]C=2\pi r[/tex]

[tex]n=\dfrac{d}{2\pi r}[/tex]

[tex]n=\dfrac{765}{2\pi \times 1.263}[/tex]

[tex]n=96.4[/tex]

Approximately, n = 96

So, it will go 96 times around the track. Hence, this is the required solution.

With a track radius of 1.263 km, the car completes approximately 96.50 laps.

The formula for the circumference (C) of a circle is: C = 2πr, where r is the radius of the circle, and π (pi) is approximately 3.14159. Using the given radius of 1.263 km, we can calculate the circumference of the track:

C = 2π(1.263 km) ≈ 2(3.14159)(1.263 km) ≈ 7.932 km (rounded to three decimal places).

Divide the total distance traveled by the circumference of the track:

Number of laps = Total distance traveled ÷ Circumference of the track
Number of laps = 765 km ÷ 7.932 km ≈ 96.50 laps.

Therefore, the race car would have completed approximately 96.50 laps around the track.

To solve this problem we will apply the concepts related to pressure, depending on the product between the density of the fluid, the gravity and the depth / height at which it is located.

For mercury, density, gravity and height are defined as

[tex]\rho_m = 846lb/ft^3[/tex]

[tex]g = 32.17405ft/s^2[/tex]

[tex]h_1 = 1in = \frac{1}{12} ft[/tex]

For the air the defined properties would be

[tex]\rho_a = 0.0075lb/ft^3[/tex]

[tex]g = 32.17405ft/s^2[/tex]

[tex]h_2 = ?[/tex]

We have for equilibrium that

[tex]\text{Pressure change in Air}=\text{Pressure change in Mercury}[/tex]

[tex]\rho_m g h_1 = \rho_a g h_2[/tex]

Replacing,

[tex](846)(32.17405)(\frac{1}{12}) = (0.0075)(32.17405)(h_2)[/tex]

Rearranging to find [tex]h_2[/tex]

[tex]h_2 = \frac{(846)(32.17405)(\frac{1}{12}) }{(0.0075)(32.17405)}[/tex]

[tex]h = 9400ft[/tex]

Therefore the elevation of the mountain top is 9400ft

The elevation of the mountain top is approximately 13,972 feet.

The difference in barometric pressure between the sea level and the top of the mountain represents the hydrostatic pressure exerted by the column of air. We can calculate the elevation of the mountain top by using the equation:

ΔP = ρgh

Where ΔP is the difference in pressure, ρ is the density of the air, g is the acceleration due to gravity, and h is the elevation. Rearranging the equation, we have:

h = ΔP / (ρg)

Substituting the given values, we have:

h = (30 - 29) in / (0.0075 lb/ft³ * 32.2 ft/sec²)

Simplifying the equation, we get:

h ≈ 13,972 ft

Therefore, the elevation of the mountain top is approximately 13,972 feet.

Answer:

(a) [tex]T_{1}=490N[/tex]

(b) [tex]T_{2}=240N[/tex]

Explanation:

For Part (a)

Given data

The box moves up at steady 5.0 m/s

The mas of box is 50 kg

As ∑Fy=T₁ - mg=0

[tex]T_{1}=mg\\T_{1}=(50kg)(9.8m/s^{2} ) \\T_{1}=490N[/tex]

For Part(b)

Given data

[tex]v_{iy}=5m/s\\ a_{y}=-5.0m/s^{2}[/tex]

As ∑Fy=T₂ - mg=ma

[tex]T_{2}=mg+ma_{y}\\T_{2}=m(g+ a_{y})\\T_{2}=50kg(9.8-5.0) \\T_{2}=240N[/tex]

The tension in the rope varies depending on whether the box is at rest, moving at a constant velocity, or accelerating. The tension equals the weight of the box when it's at rest or moving constantly, but it will be increased or decreased by the net force caused by acceleration when the box is speeding up or slowing down.

If the box is at rest, the tension in the rope is equal to the force of gravity. We can calculate this using the formula T = mg, where m is the mass of the box and g is the acceleration due to gravity. Therefore, T = (50 kg)(9.8 m/s²) = 490 N.

When the box moves upwards with a constant velocity, the tension in the rope also equals the weight of the box (T = mg), so the tension will stay the same at 490 N.

However, when the box is speeding up, the net force is the product of mass and acceleration. In this case, acceleration = 5.0 m/s². Using the equation Fnet = ma, we find that Fnet = (50 kg)(5 m/s²) = 250 N. The total tension now includes both the tension due to the box's weight and the additional force due to the acceleration. Therefore, T = T(g) + Fnet = 490 N + 250 N = 740 N.

Lastly, when the box is slowing down at 5.0 m/s², the net force acts in the opposite direction of the initial velocity. Using the same calculations, we find Fnet = 250 N. But this force now reduces the tension originally caused by the box's weight, so the total tension in the rope becomes T = T(g) - Fnet = 490 N - 250 N = 240 N.

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Answer:

[tex]1.15669\times 10^{-7}\ C[/tex]

Explanation:

[tex]\theta[/tex] = Angle with which the electric field is hung = 23°

m = Mass of ball = 5 g

E = Electric field = [tex]1.8\times 10^5\ N/C[/tex]

T = Tension

q = Charge

We have the equations

[tex]Tcos\theta=mg[/tex]

[tex]Tsin\theta=qE[/tex]

Dividing the equations

[tex]tan\theta=\dfrac{mg}{qE}\\\Rightarrow q=\dfrac{mgtan\theta}{E}\\\Rightarrow q=\dfrac{5\times 10^{-3}\times 9.81\times tan23}{1.8\times 10^5}\\\Rightarrow q=1.15669\times 10^{-7}\ C[/tex]

The magnitude of the charge is [tex]1.15669\times 10^{-7}\ C[/tex]

Answer:

At the origin (x' = 0 m)

Explanation:

Note: From the question, when the cart travels towards the origin, the magnitude of its exact position reduces with time.

The formula of speed is given as

S = d/t................. Equation 1

Where S = speed of the cart, d = distance covered by the cart over a certain time. t = time taken to cover the distance.

make d the subject of the equation,

d = St ................. Equation 2

Given: S = 2.0 m/s, t = 3.0 s

Substitute into equation 2

d = 2(3)

d = 6 m.

From the above, the cart covered a distance of 6 m in 3 s.

The exact position of the cart = Initial position-distance covered

x' = x-d............ Equation 3

Where x' = exact position of the cart 3 s later, x = initial position of the cart, d = distance covered by the cart in 3.0 s.

Given: x = +6.0 m, d = 6 m.

Substitute into equation 3

x' = +6-6

x' = 0 m.

Hence the cart will be at 0 m (origin) 3 s later

The cart will be at a position of 12.0 m after 3.0 seconds.

The cart is initially at a position of +6.0 m and is moving towards the origin with a constant speed of 2.0 m/s. We can use the formula for position to find its exact position after 3.0 seconds.

The formula for position is position = initial position + (velocity × time).

Plugging the values into the formula, we get:

position = 6.0 m + (2.0 m/s × 3.0 s) = 6.0 m + 6.0 m = 12.0 m.

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The sign of the point charge that produces a potential of -2.00 V at a distance of 1.00 mm is negative, and its magnitude is calculated to be approximately -2.22×10-13 C using Coulomb's law.

Explanation:

The question pertains to determining the sign and magnitude of a point charge based on the electric potential it produces at a specific distance. The electric potential (V) at a distance (r) from a point charge (q) is given by the equation V = k * q / r, where k is Coulomb's constant (k = 8.988×109 N·m2/C2). Since the potential is negative (-2.00 V), the point charge must have a negative sign. To find the magnitude, we rearrange the formula to solve for q: q = V * r / k.

Plugging in the values gives q = (-2.00 V * 1.00×10-3 m) / 8.988×109 N·m2/C2, which calculates to a charge magnitude of approximately -2.22×10-13 C.



The probable question is in the image attached.

Answer:

a) 2.67 m/s

b) 0.82 J

Explanation:

Amplitude A = 25 cm = 0.25 m

The period of the motion is the inverse of the frequency

[tex]T = \frac{1}{f} = \frac{1}{1.7} = 0.588 s[/tex]

So the angular frequency

[tex]\omega = \frac{2\pi}{T} = \frac{2\pi}{0.588} = 10.68 rad/s[/tex]

The speed at the equilibrium point is the maximum speed, at

[tex]v = \omega A = 10.68 * 0.25 = 2.67 m/s[/tex]

The spring constant can be calculated using the following

[tex]\omega^2 = \frac{k}{m} = \frac{k}{0.23}[/tex]

[tex]k = 0.23\omega^2 = 0.23*10.68^2 = 26.24 N/m[/tex]

The total energy of the oscillation is

[tex]E = kA^2 / 2 = 26.24*0.25^2 / 2 = 0.82 J[/tex]

Answer: 7.2V

Explanation:

Peak values or peak to peak voltage are calculated from RMS values, which implies VP = VRMS × √2, (assuming the source is a pure sine wave).

Since it's a sinusoidal voltage and measuring from an oscilloscope, the peak to peak voltage is gotten thus:

No of division X Volts/divisions

So, 3.6 x 2V = 7.2V

Final answer:

The peak-to-peak voltage of a sinusoidal signal covering 3.6 divisions on an oscilloscope set to 2 volts per division is 7.2 volts.

Explanation:

The question involves calculating the peak-to-peak voltage of a sinusoidal signal observed on an oscilloscope where the vertical scale is set to 2 volts per division. Given that the signal covers 3.6 divisions from positive to negative peak, we calculate the peak-to-peak voltage by multiplying the number of divisions the signal spans by the voltage per division.

To find the peak-to-peak voltage, we use the formula: Peak-to-Peak Voltage = Number of Divisions × Voltage per Division. Thus, the peak-to-peak voltage of the signal is 3.6 divisions × 2 volts/division = 7.2 volts.

The work done by the electric force on the moving point charge is approximately -5.09 × 10^-5 J.

Work done by the electric force is given by the equation W = q1 * q2 * (1/r1 - 1/r2), where q1 and q2 are the charges, r1 is the initial distance, and r2 is the final distance.

In this case, q1 = 2.30 μC, q2 = -5.00 μC, r1 = 0.170 m, and r2 = 0.250 m. Plugging these values into the equation and solving for W, we get:

W = (2.30 μC) * (-5.00 μC) * [1/√(0.170^2) - 1/√(0.250^2 + 0.250^2)]

After simplifying, the work done is approximately -5.09 × 10^-5 J.

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Answer:

Average acceleration = - 2 m/s^2

Explanation:

Given data:

Initial velocity = 11 m/s

Final velocity = 5.0 m/s

duration of change in velocity = 3 sec

Average acceleration [tex]= \frac{v - u}{\Delta t}[/tex]

Average acceleration [tex]= \frac{5 - 11}{3} = -2 m/s^2[/tex]

Average acceleration = - 2 m/s^2

here negative sign indicate that acceleration is proceed in downward direction.

Answer:

A) The expression of the electric field halfway between the plates, if the plates are in the plane Y-Z is:

[tex]\vec{E}=\displaystyle \frac{q}{LW\varepsilon_0}\vec{x}[/tex]

B) The expression for the magnitude of the electric field E₂ just in front of the plate two ends is:

[tex]|E_2|=\displaystyle \frac{q}{2LW\varepsilon_0}[/tex]

C) The charge density is:

[tex]\sigma_2=-4.2517\cdot10^{-3}C/m^2[/tex]

Completed question:

A capacitor is created by two metal plates. The two plates have the dimensions L = 0.49 m and W = 0.48 m. The two plates are separated by a distance, d = 0.1 m, and are parallel to each other.

A) The plates are connected to a battery and charged such that the first plate has a charge of q. Write an express of the electric field, E, halfway between the plates

B) Input an expression for the magnitude of the electric field, E₂. Just in front of plate two END

C) If plate two has a total charge of q =-1 mC, what is its charge density, σ in C/m2?

Explanation:

A) The expression of the field can be calculated as the sum of the field produced by each plate. Each plate can be modeled as 2 parallel infinite metallic planes. Because this is a capacitor connected by both ends to a battery, the external planes have null charge (the field outside the device has to be null by definition of capacitor). This means than the charge of each plate has to be distributed in the internal faces. Because this es a metallic surface and there is no external field, we can consider a uniform charge distribution (σ=cte). Therefore in this case for each plane:

[tex]\sigma_i=\displaystyle \frac{q_i}{LW}[/tex]

The field of an infinite uniform charged plane is:

[tex]\vec{E_i}=\displaystyle \frac{\sigma_i}{2\varepsilon_0}sgn(x-x_{0i})\vec{x} =\frac{q_i}{2LW\varepsilon_0}sgn(x-x_{0i})\vec{x}[/tex]

In this case, inside the capacitor, if the plate 1 is in the left and the plate 2 is in the right, the field for 0<x<d is:

[tex]\vec{E_1}\displaystyle=\frac{q}{2LW\varepsilon_0}sgn(x})\vec{x}=\frac{q}{2LW\varepsilon_0}\vec{x}[/tex]

[tex]\vec{E_2}\displaystyle=\frac{-q}{2LW\varepsilon_0}sgn(x-d})\vec{x}=\frac{q}{2LW\varepsilon_0}\vec{x}[/tex]

[tex]\vec{E}=\vec{E_1}+\vec{E_2}[/tex]

[tex]\vec{E}=\displaystyle \frac{q}{LW\varepsilon_0}\vec{x}[/tex]

B) we already obtain the expression of the field E₂ inside the space between the plates. Even if we are asked the expression just in front of the plate and not inside, the expression for |E₂| is still de same.

C) As seen above, we already obtain the charge density expression. Therefore we only have to replace the variables for the numerical values.

The electric field, E, halfway between the plates is (σ / ε₀). The electric field is written in terms of permittivity and surface charge density.

Given:
Length, L = 0.49 m

Width, W = 0.48 m

Distance, d = 0.1 m

Here:

E = electric field

σ = surface charge density

ε₀ = permittivity of free space

We must determine the surface charge density on each plate since the plates are wired to a battery and charged so that the first plate has a charge of q.

The area of the plate is:

Area of each plate (A) = L x W = 0.49 m x 0.48 m = 0.2352 m²

The surface charge density is given by:

σ = q / A

The electric field is computed as:

E = (σ / ε₀)

Hence, the electric field, E, halfway between the plates is (σ / ε₀). The electric field is written in terms of permittivity and surface charge density.

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#Complete question is:

A capacitor is created by two metal plates. The two plates have the dimensions L = 0.49 m and W = 0.48 m. The two plates are separated by a distance, d = 0.1 m, and are parallel to each other.

A) The plates are connected to a battery and charged such that the first plate has a charge of q. Write an express of the electric field, E, halfway between the plates

Answer:

D) The potential difference between the plates increases.

Explanation:

The capacitance of a parallel plate capacitor having plate area A and plate separation d is C=ϵ0A/d.  

Where ϵ0 is the permittivity of free space.  

A capacitor with increased distance, will have a new capacitance C1=ϵ0kA/d1

Where d1 = nd  

since d1 > d

therefore n >1

n is a factor derived as a result of the increased distance

Therefore the new capacitance becomes:

              C1=ϵ0A/d1

        C1= ϵ0A/nd

        C1= C/n  -------1

Where C1 is the capacitance with increased distance.

This implies that the charge storing capacity of the capacitor with increased plate separation decreases by a factor of (1/n) compared to  that of the capacitor with original distance.

Given points

The charge stored in the original capacitor Q=CV

The charge stored in the original capacitor after inserting dielectric  Q1=C1V1

The law of conservation of energy states that the energy stored is constant:

i.e Charge stored in the original capacitor is same as charge stored after the dielectric is inserted.

Charge before plate separation increase same as after plate separation increase

Q   = Q1

CV = C1V1

  CV = C1V1  -------2

We derived C1=C/n in equation 1. Inserting this into equation 2

   CV = (CV1)/n

   V1 = n(CV)/C

        = n V

Since n > 1 as a result of the derived new distance, the new voltage will increase