The question combines the principles of wave mechanics, specifically sinusoidal waves, to calculate the height of a resultant wave at a certain time and position. This is done by applying values to the formula y (x, t) = A sin (kx - wt +φ), where A, k, w and φ stand for amplitude, wave number, angular frequency and phase shift respectively. Applying the values of the moving sinusoidal waves, you can solve for the height of the resultant wave.
Explanation:A sinusoidal wave is represented by the equation y (x, t) = A sin (kx — wt + φ). Here A is the amplitude, k is wave number, w is the angular frequency and φ is the phase shift. Given two sinusoidal waves, moving through a medium, both having the equal amplitude (7.00 cm), wave number (k=3.00m−1) and angular frequency (ω=2.50s−1), but with one having a phase shift of π/12 radians, the resultant wave has an amplitude of AR = [2A cos(φ/2)] and a phase shift equal to half the original phase shift.
Applying these values to the equation y (x, t) = AR sin (kx - wt + φ/2), we have y = 2*7* cos(π/12/2) cm * sin(3.00m−1 *0.53m — 2.50s−1* 2.00s + π/12 /2), thus we can calculate the height of the resultant wave at a particular position and time.
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The height of the resultant wave at [tex]\( t = 2.00 \, \text{s} \) and \( x = 0.53 \, \text{m} \)[/tex] is:
[tex]\[ \boxed{-13.965 \, \text{cm}} \][/tex].
The height of the resultant wave at time [tex]\( t = 2.00 \, \text{s} \)[/tex] and position [tex]\( x = 0.53 \, \text{m} \)[/tex] is given by the sum of the two individual waves, taking into account their respective phase shifts.
The general equation for a sinusoidal wave moving in the positive x-direction is:
[tex]\[ y(x,t) = A \cos(kx - \omega t + \phi) \][/tex]
[tex]where \( A \) is the amplitude, \( k \) is the wave number, \( \omega \) is the angular frequency, \( \phi \) is the phase shift, \( x \) is the position, and \( t \) is the time.[/tex]
For the first wave with no phase shift, the equation is:
[tex]\[ y_1(x,t) = 7.00 \cos(3.00x - 2.50t) \][/tex]
For the second wave with a phase shift [tex]\( \phi = \frac{\pi}{12} \)[/tex], the equation is:
[tex]\[ y_2(x,t) = 7.00 \cos(3.00x - 2.50t + \frac{\pi}{12}) \]\\ At \( t = 2.00 \, \text{s} \) and \( x = 0.53 \, \text{m} \), we substitute these values into the equations for \( y_1 \) and \( y_2 \): \[ y_1(0.53,2.00) = 7.00 \cos(3.00 \cdot 0.53 - 2.50 \cdot 2.00) \] \[ y_1(0.53,2.00) = 7.00 \cos(1.59 - 5.00) \] \[ y_1(0.53,2.00) = 7.00 \cos(-3.41) \][/tex]
Since the cosine function is even, [tex]\( \cos(-3.41) = \cos(3.41) \)[/tex], we can write:
[tex]\[ y_1(0.53,2.00) = 7.00 \cos(3.41) \][/tex]
For the second wave:
[tex]\[ y_2(0.53,2.00) = 7.00 \cos(3.00 \cdot 0.53 - 2.50 \cdot 2.00 + \frac{\pi}{12}) \] \[ y_2(0.53,2.00) = 7.00 \cos(1.59 - 5.00 + \frac{\pi}{12}) \] \[ y_2(0.53,2.00) = 7.00 \cos(-3.41 + \frac{\pi}{12}) \] The resultant wave \( y \) is the sum of \( y_1 \) and \( y_2 \): \[ y(0.53,2.00) = y_1(0.53,2.00) + y_2(0.53,2.00) \] \[ y(0.53,2.00) = 7.00 \cos(3.41) + 7.00 \cos(-3.41 + \frac{\pi}{12}) \][/tex]
To find the numerical value, we calculate the cosines:
[tex]\[ y(0.53,2.00) = 7.00 \cos(3.41) + 7.00 \cos(-3.41 + \frac{\pi}{12}) \] \[ y(0.53,2.00) = 7.00 \cos(3.41) + 7.00 \cos(-3.41 + 0.2618) \] \[ y(0.53,2.00) = 7.00 \cos(3.41) + 7.00 \cos(-3.1482) \][/tex]
Using a calculator or trigonometric tables, we find:
[tex]\[ y(0.53,2.00) = 7.00 \cdot (-0.9956) + 7.00 \cdot (-0.9994) \] \[ y(0.53,2.00) = -6.9692 - 6.9958 \] \[ y(0.53,2.00) = -13.965 \][/tex]
Therefore, the height of the resultant wave at [tex]\( t = 2.00 \, \text{s} \) and \( x = 0.53 \, \text{m} \)[/tex] is:
[tex]\[ \boxed{-13.965 \, \text{cm}} \][/tex]
The negative sign indicates that the displacement is in the negative y-direction.
Four charges are the corners of a square with B and C on opposite corners. Charges A and D on the other two corners have equal charge while both B and C have a charge of +1.0 C. What is the charge on A so that the force B is zero?
Final answer:
The charge on A should be -2.0 C in order for the force on B to be zero.
Explanation:
In order for the force on charge B to be zero, the charge on A must be equal in magnitude but opposite in sign to the combined charge of charges C and D at the other corners of the square. Since both B and C have a charge of +1.0 C, A must have a charge of -2.0 C. This creates a symmetric distribution of charges, resulting in a net force of zero on charge B.
1000 kg of water initially at 6 m/s runs through a hydro-generator. If the water leaves the generator at velocity of 4 m/s, and the efficiency of the generator is 100%, how much electricity in kJ (2 significant figures) will we get?
Answer:
8.00 kJ
Explanation:
The first thing is to determine what quantities are there.
the mass of water = 1 000 kg
initial velocity, u = 6 m/s
final velocity, v = 4 m/s
the generator is operating at 100 % efficiency, so there is no energy loss.
The kinetic energy, Ek is converted to electrical energy, therefore Ek = electrical energy.
The kinetic energy is calculated as follows:
Ek = 1/2 mv²
= 1/2×(1 000)× (4)²
= 8 000 J/s
= 8.00 kJ Ans
If the horizontal circular path the riders follow has a 7.00 m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration whose magnitude is 2.25 times that due to gravity?
Explanation:
Radius , r = 7 m
Centripetal acceleration, a = 2.25 g = 22.07 m/s²
We have equation for centripetal acceleration
[tex]a=\frac{v^2}{r}[/tex]
Substituting
[tex]a=\frac{v^2}{r}\\\\22.07=\frac{v^2}{7}\\\\v=12.43m/s[/tex]
We have equation for frequency
[tex]f=\frac{2\pi }{\omega }\\\\f=\frac{2\pi r}{v}\\\\f=\frac{2\pi \times 7}{12.43}=3.54Hz[/tex]
Revolutions per minute = 3.54 x 60 = 212.4
Revolutions per minute of rider is 212.4
The secondary line-to-line voltage of a three-phase Y-Y-connected transformer bank is 115 VAC. What would be the secondary line to neutral voltage?
A. 199.2 V
B. 66.4 V
C. 84.2 V
D. 50 V
Answer:
B. 66.4 V
Explanation:
for a Y-Y connection (star connection), the relationship between the line voltages and the phase voltages is governed by the formula:
[tex]V_{L} = \sqrt{3} (V_{ph})[/tex]
Where [tex]V_{L}[/tex] = Line Voltage = 115 V (AC there just shows that the current is alternating current )
and [tex]V_{ph}[/tex] = Phase Voltage
⇒ [tex]V_{ph}[/tex] = [tex]V_{L}[/tex] / [tex]\sqrt{3}[/tex]
[tex]V_{ph}[/tex] = 115 / [tex]\sqrt{3}[/tex]
[tex]V_{ph}[/tex] = 66.4 V
Hence the secondary Line to neutral voltage is 66.4 Volts
The secondary line to neutral voltage is Option B 66.4 V.
Given that,
The secondary line-to-line voltage of a three-phase Y-Y-connected transformer bank is 115 VAC.Based on the above information, the calculation is as follows:
[tex]V_{ph} = V_L \div \sqrt{3}\\\\= 115 \div \sqrt{3}[/tex]
= 66.4 V
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The frequency output of a digital MAP sensor is reading 114 Hz. What is the approximate engine vacuum?
Answer:bob
Explanation:bc bob
Recoil is noticeable if we throw a heavy ball while standing on a skateboard. If instead we go through the throwing motion but hold onto the ball, without friction effects our net recoil will be
A) zero.
B) the same as before.
C) small, but noticeable.
Answer:
A) zero.
Explanation:
If we go through the throwing motion but still hold onto the ball, then there will be 2 events:
1. you undergo the throwing motion, giving the ball's acceleration
2. you decelerate the ball so you can still hold onto it
Event 1 and 2 roughly need the same energy, but with the opposite vector. The sum of energy used for both events should be zero so the net recoil will also be zero too.
Henrietta is going off to her physics class, jogging down the sidewalk at a speed of 3.95 m/s . Her husband Bruce suddenly realizes that she left in such a hurry that she forgot her lunch of bagels, so he runs to the window of their apartment, which is a height 39.9 m above the street level and directly above the sidewalk, to throw them to her. Bruce throws them horizontally at a time 6.50 s after Henrietta has passed below the window, and she catches them on the run. You can ignore air resistance.
Part A. With what initial speed must Bruce throw the bagels so Henrietta can catch them just before they hit the ground?
Express your answer using three significant figures.
Part B. Where is Henrietta when she catches the bagels?
Express your answer using three significant figures.
Answer:
Part A 12.9 m/s
Part B 36.9 m
Explanation:
Henrietta ran at 3.95 m/s. She was 6.5 seconds away from from the window when Bruce throws the bagel. This equates to a distance of d
[tex]d= 3.95\times6.5=25.675[/tex] (distance = speed x time)
If Bruce throws the bagel horizontally, the vertical component of the motion is purely under gravity with initial speed of 0 m/s. Using one of the equations of motion for the vertical motion,
[tex]h=ut+0.5at^2[/tex]
h = 39.9 m (height of the building)
a = 9.8 (acceleration of gravity)
[tex]t=\sqrt{\dfrac{2\times39.9}{9.8}}= 2.85[/tex]
During this time, Henrietta will have travelled another distance e
[tex]e =3.95\times2.85=11.2575[/tex]Therefore, Henrietta would have jogged a total distance of 25.675 + 11.2575 m = 36.9325 m.
The horizontal speed with which Bruce must throw the bagel is the total distance travelled by Henrietta divided by the time it takes to land vertically i.e.
[tex]v=\dfrac{36.9325}{2.85}=12.96[/tex]
Therefore, the speed of throw is 13.0 m/s.
Henrietta was 36.9 m from the window when she caught the bagel.
Part A. The speed at which the bagel was thrown horizontally is 12.9 m/s.
Part B. The total distance traveled by Henrietta when she caught the bagel from the window is 36.9325 m.
How do you calculate the speed of the bagel?Given that, the speed of Henrietta is 3.95 m/s. When Bruce throws the bagel, the time difference between both of them is 6.5 seconds. Hence the distance can be calculated as given below.
Distance D = Speed [tex]\times [/tex] Time
[tex]D = 3.95 \times 6.50[/tex]
[tex]D = 25.675 \;\rm m[/tex]
Part A
Given that Bruce throws the bagel horizontally, then during the motion, the initial speed will be zero and the vertical component will have gravitational acceleration. In this case, the time required in motion can be calculated by the equation given below.
[tex]s = ut + \dfrac {1}{2} at^2[/tex]
Where, s is the distance, a is the acceleration, t is time and u is the initial speed.
For the horizontal motion, s = 39.9 m, g = 9.8 m/s^2 and u = 0 m/s. The time will be,
[tex]39.9 = 0 + \dfrac {1}{2}\times 9.8\times t^2[/tex]
[tex]t = 2.85 \;\rm s[/tex]
The time required to reach the bagels is 2.85 seconds. But in this time, the distance traveled by Henrietta is given below.
[tex]D' = 2.85 \times 3.95[/tex]
[tex]D' = 11.2527 \;\rm m[/tex]
Hence the total distance traveled by Henrietta is given below.
Distance = 25.675 + 11.2527
Distance = 36.9325 m.
The speed of the bagel is calculated as given below.
Speed = Total Distance / Time
[tex]v = \dfrac {36.9325 }{2.85}[/tex]
[tex]v = 12.9 \;\rm m/s[/tex]
Hence we can conclude that the speed at which the bagel was thrown horizontally is 12.9 m/s.
Part B
The total distance traveled by Henrietta is 36.9325 m. At this distance, Henrietta catches the bagel from the window.
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An 8.6 m, 267 kg uniform ladder rests against a smooth wall. The coefficient of static friction between the ladder and the ground is 0.53 , and the ladder makes a 32.7 ◦ angle with the ground. How far up the ladder can a 1068 kg person climb before the ladder begins to slip? The acceleration of gravity is 9.8 m/s 2 . Answer in units of m.
Answer:
[tex]r_{P}=2.58 m[/tex]
Explanation:
If we want to find how far up the ladder can a person climb before the ladder begins to slip, the total force in the y-direction and the total torque must be zero, it is an equilibrium condition.
So, let's start whit y-direction forces.
[tex]\Sigma F_{y}=0[/tex]
[tex]N_{L}-W_{L}-W_{P}=0[/tex]
NL is the normal forceWL is the weight of the ladderWP is the weight of the personSo, we can find the normal force:
[tex]N_{L}=m_{L}g+m_{P}g=g(m_{L}+m_{P})=9.8(267+1068)=13083 N[/tex]
We know that the friction force is the product of the coefficient of static friction times the normal force. Let's find it.
[tex]F_{f}=\mu N_{L}=0.53*13083=6934 N[/tex]
Referent to the x-direction forces, we can say that the total sum must be equal to zero too.
[tex]\Sigma F_{x}=0[/tex]
[tex] -N_{wall}+F_{f}=0[/tex]
[tex] N_{wall}=F_{f}=6934 N[/tex]
Where N(wall) is the normal force due to the wall. (negative direction)Now, as we said before, the total torque must be zero, so we have:
[tex]\Sum \tau=\tau_{wall}+\tau_{L}+\tau_{P}=0[/tex] (1)
We will choose the pivot point at the bottom of the ladder, then we have:
Each force acting on the ladder must be perpendicular to the ladder, so we need to use the components.
[tex]\tau_{wall}=r_{wall}*N_{wall}sin(32.7)=8.6*6934*sin(32.7)=32215.8Nm[/tex] (positive due to the counterclockwise rotation)
[tex]\tau_{L}=r_{L}*W_{L}sin(57.3)=(8.6/2)*2616.6*sin(57.3)=-9468.2 Nm[/tex] (negative due to the clockwise rotation)
[tex]\tau_{P}=r_{P}*W_{P}sin(57.3)=r_{P}*10466.4*sin(57.3)=-r_{P}8807.6 Nm[/tex] (negative due to the clockwise rotation)
We use 57.3° because is the angle between the ladder weight vector and the ladder surface, we use the same angle to the person.
Now we can use (1) to find the distance
[tex]\Sum \tau=\tau_{wall}+\tau_{L}+\tau_{P}=32215.8-9468.2-r_{P}8807.6=0[/tex]
Therefore [tex]r_{P}=2.58 m[/tex]
I hope it helps you!
A statue is to be 'scaled down.' It will have its size changed without changing its shape. It starts with an initial volume of 3.25 m3 and ends up with a final volume of 1.00 m3 .
Answer:
The solution are in the explanation
Explanation:
Volume varies with the cube of the linear dimension
Ratio of volumes is 3:1, therefore the ratio of the linear dimensions is 3^(1/3):1 = 1.442:1
Smaller statue is 350/1.442 cm = 242.7 cm
C = pi*D, D is a linear dimension, so Ds = 50/1.442 = 34.67 cm
Area varies with the square of the linear dimension; so the ratio of the areas will be (1/3)^(2/3) = 0.48; the surface area of the smaller statue will be 0.48 that of the original
The mass of the model would vary directly with the volume, so the mass of the model will be 1/3 that of the original
If the masses of the models are the same, then the model must be made of a material 3x the density of that used for the original.
In mathematics, scaling down a shape involves reducing its size while keeping its shape unchanged. To scale down a statue, you need to determine the scale factor by dividing the final volume by the initial volume. Then, apply the scale factor to each dimension of the statue.
Explanation:In mathematics, scaling down a shape means reducing its size while keeping its shape unchanged. The process involves multiplying the dimensions of the shape by a scale factor less than 1.
In this case, the initial volume of the statue is 3.25 m3 and it needs to be scaled down to a final volume of 1.00 m3. To determine the scale factor, divide the final volume by the initial volume: 1.00/3.25 = 0.307.
Next, apply the scale factor to each dimension of the statue. If the dimensions of the statue were 2m x 2m x 2m, the scaled-down dimensions would be 2m x 2m x 2m x 0.307 = 0.614m x 0.614m x 0.614m.
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a 800 kg roller coaster cart is accelerated by a constant net force over a distance of 10 meters, as shown in the graph below: determine the speed of the cart after being accelerated for 10.0 meters.
Answer:
vf = 22.36[m/s]
Explanation:
First we must understand the data given in the problem:
m = mass = 800 [kg]
F = force = 20000[N]
dx = displacement = 10[m]
From newton's second we know that the sum of forces must be equal to the product of mass by acceleration.
[tex]F = m*a\\20000 = 800*a\\a = 20000/800\\a = 25 [m/s^2][/tex]
With the calculated acceleration, we can use the kinematics equations.
[tex]v_{f} ^{2} =v_{o} ^{2}+2*a*dx\\ v_{o} = initial velocity = 0\\a = acceleration = 25[m/s^2]\\dx= displacement = 10[m]\\[/tex]
The key to using this equation is to clarify that the initial velocity is zero since the body is at rest, otherwise the initial velocity would be an initial data.
[tex]v_{f} =\sqrt{2*25*10} \\v_{f} =22.36[m/s][/tex]
Another way of solving this problem is by means of the definition of work and kinetic energy, where work is defined as the product of the force by the distance.
W =F*d
W = 20000*10
W = 200000[J]
Kinetic energy is equal to work, therefore the value calculated above is equal to:
[tex]E_{k}=W =0.5*m*v_{f}^{2} \\200000=0.5*800*v_{f}^{2}\\v_{f}=\sqrt{\frac{200000}{0.5*800} } \\v_{f}=22.36[m/s][/tex]
Answer:
(A) 22.4 m/s
Explanation: hope this helps !
An airplane is flying at 95.0 m/s when the engine is turned off. As it glides, it experiences a force of drag so that is slows down at -0.700 m/s2. How far in meters will it travel in 1.00 minute ?
Explanation:
We have equation of motion s = ut + 0.5 at²
Initial velocity, u = 95 m/s
Acceleration, a = -0.700 m/s²
Time, t = 1 minute = 60 seconds
Substituting
s = ut + 0.5 at²
s = 95 x 60 + 0.5 x -0.700 x 60²
s = 4440 m
Distance traveled is 4440 m
The airplane travels 4440 m in 1 minute
To find the distance the airplane will travel in 1.00 minute, use the equation d = [tex]vi * t + (1/2) * a * t^2[/tex]e, vi is the initial velocity, t is the time, and a is the acceleration. Substitute the given values into the equation and solve to find the distance.
Explanation:To find the distance the airplane will travel in 1.00 minute, we need to use the equation:
d = vi * t +[tex](1/2) * a * t^2[/tex]
Where:
d = distance traveled
vi = initial velocity
t = time
a = acceleration
Using the given values:
vi = 95.0 m/s (initial velocity)
a = -[tex]0.700 m/s^2[/tex] (deceleration)
t = 1.00 minute = 60 seconds
Now we can substitute the values into the equation:
d = (95.0 * 60) + (1/2) * [tex](-0.700) * (60^2)[/tex]
Solving this equation will give us the distance traveled by the airplane in 1.00 minute.
According to ____, the ability to detect a stimulus depends not only on the intensity of the stimulus but also on other variables such as the level of noise in the system and your expectations.
Answer:
Signal detection theory
Explanation:
Signal detection theory states that stimulus ca be detected according to its intensity and a person's psychological and/or physical state. This means that we can notice things according to how strong they are but also, a person's characteristics like experience and physiological state like fatigue can affect the ability to detect them.
Because of this, the answer is that according to signal detection theory, the ability to detect a stimulus depends not only on the intensity of the stimulus but also on other variables such as the level of noise in the system and your expectations.
Final answer:
Signal detection theory explains how the ability to detect a stimulus is influenced by both the stimulus intensity and psychological factors such as motivation and expectations, with practical examples like air traffic control demonstrating its significance.
Explanation:
According to signal detection theory, the ability to detect a stimulus depends not only on the intensity of the stimulus but also on variables such as the level of noise in the system and your expectations. Factors such as motivation can shift our ability to discriminate between a true sensory stimulus and background noise. For example, expecting an important phone call may lead you to think you hear the phone ringing while taking a shower, even though it is not. Similarly, a mother might wake up to the quiet murmur of her baby amidst other sounds because she is motivated to detect that specific stimulus.
Signal detection theory is not only a concept of psychological interest but also has practical applications, such as improving the accuracy of air traffic controllers. They need to detect planes among many signals on the radar screen, demonstrating the relevance of this theory in safety-critical professions. Furthermore, the theory incorporates the notion of both absolute threshold and difference threshold (or just noticeable difference), emphasizing the role of sensory capabilities alongside psychological factors in perception.
At what angle with the ground should a projectile be thrown to reach the maximum distance? a.) 0° with the ground b.) 45° with the ground c.) 62° with the ground d.) 82° with the ground
Answer:
B
Explanation:
With projectiles, the maximum range is always achieved at a 45 degree launch angle.
Which of the following describes how net work is determined?
A. The difference in the initial and final forces applied
B. The net force on an object applied for a brief second
C. The initial force applied to an object over a distance
D. The net force on an object applied over a distance
Answer:
D. The net force on an object applied over a distance
Explanation:
Work can be defined as the product of force multiplied by a distance
Where
F = force [Newtons]
d = distance = [meters]
Therefore:
Work = F * d
Work in units of Joules [J]
How much kinetic energy is in a runner weighing 83 kg moving at a velocity of 16 m/s
Answer:
10,624J
Explanation:
KE = 1/2 m*v²
KE = 1/2 83*16²
KE = 41.5*256
KE = 10,624J
"Compared to infrared radiation, does ultraviolet radiation have longer or shorter wavelengths? Does ultraviolet radiation have higher or lower energy per photon?"
Answer:Ultraviolet radiation has shorter wavelengths and higher energy than infrared radiation.
Explanation: Electromagnetic radiation radiations which have both electrical and magnetic properties,they can be transmitted through space or through a medium.
It includes Gamma radiation, infra-red, visible light, Ultraviolet radiation etc they occur with different wavelength, the lower the wavelength the higher the Energy dissipated per photon. According to their order of decreasing wavelength and increased energy they are classified as follows.
RADIO WAVE, MICRO WAVE, INFRA-RED, VISIBLE LIGHT, ULTRAVIOLET RAY, X-RAY, GAMMA RAYS.
Ultraviolet radiation has shorter wavelengths and higher energy per photon compared to infrared radiation.
Explanation:Ultraviolet radiation has shorter wavelengths compared to infrared radiation. While infrared radiation has wavelengths between 700 nm and 1 mm, ultraviolet radiation has wavelengths between 100 nm and 400 nm.
Ultraviolet radiation also has higher energy per photon compared to infrared radiation. This is because energy is inversely proportional to wavelength, so shorter wavelengths have higher energy.
For example, ultraviolet radiation is responsible for causing sunburns and skin damage, which is evidence of its higher energy compared to infrared radiation.
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A motorist is driving at 20m/s when she sees that a traffic light 200m ahead has just turned red. She knows that this light stays red for 15s, and she wants to reach the light just as it turns green again. It takes her 1.0s to step on the brakes and begin slowing.
What is her speed as she reaches the light at the instant it turns green?
To stop just as the light turns green, the motorist needs to decelerate in a controlled manner. The effective time to cover the distance after seeing the red light is 14 seconds, disregarding the 1 second it takes to react and press the brakes. Therefore, as she reaches the traffic signal when it turns green, her speed is 0 m/s.
Explanation:This situation can be approached using the concept of kinematics in Physics. To solve it, we need to consider total time and total distance traveled. The motorist is driving towards the traffic light, which is 200m away, and the light stays green for 15 seconds. However, since it takes her 1 second to step on the brakes, effectively, she has 14 seconds to travel to the light.
Since she starts braking the car, she begins to decelerate. While decelerating, time is the only determinant of the distance covered, not the speed. As she reaches the light, the speed would be zero regardless of the initial speed or distance if the deceleration is constant. So, when the light turns green, her speed will be 0 m/s.
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In which mechanical test is a specimen deformed with a gradually increasing load that is applied uniaxially along the long axis of the specimen that contracts the specimen, i.e. the specimen is squeezed?
Answer:
Compression Test
Explanation:
The Specimen is undergoing a compression test. It is similar to tensile test with the difference that the force is compressive and applied along the direction of stress. Both Tensile and compression tests are performed on Universal Testing machine. Compression test is done to determine the product's reaction when it is compressed, squashed and crushed.
FM radio ________________. a. had a somewhat shorter range than AM radio, but better sound quality. b. was widely adopted in the 1950s, when radio started playing more music. c. had a scratchier sound that was okay for talk radio, but not for music. d. was able to carry signals farther than AM radio. e. was developed by Guglielmo Marconi.
Answer:
(A) FM Radio had a somewhat shorter ranger than AM radio, but better sound quality.
Explanation:
FM Radio was invented in 1933 by Edwin Armstrong who was an American engineer. FM stands for frequency modulation and AM stands for Amplitude Modulation.
FM is used for most broadcasts of music and FM radio stations use a very high-frequency range of radio frequencies.
In FM Radio, the sound is transmitted through changes in frequency. Both FM and AM radio signals experience frequent change in amplitude, they are far less noticeable on FM.
When switching between stations, FM antenna is alternating between different frequencies, and not amplitudes and this produces a much clearer sound and allows for smoother transitions with little to no audible static.
FM signals can be interfered by barriers and this could affect the signal strength. FM Radio signals are more clearer in a mountainous area that has no barrier.
AM radio was able to carry signals farther than AM radio.
A powerful motorcycle can accelerate from rest to 22.2 m/s (80 km/h) in only 3.42 s. What is its average acceleration?
Explanation:
We have equation of motion v = u + at
Initial velocity, u = 0 m/s
Final velocity, v = 22.2 m/s
Time, t = 3.42 s
Substituting
v = u + at
22.2 = 0 + a x 3.42
a = 6.49 m/s²
Acceleration is 6.49 m/s²
Average acceleration is 6.49 m/s²
The total number of stars in the observable universe is roughly equivalent to:
a. the number of grains of sand on all the beaches on Earth.
b. the number of grains of sand on Miami Beach.
c. infinity.
Answer:
The number of grains of sand on all the beaches on Earth
Explanation:
if we assume grain of sand has an average size , then the number of grains of sand on all the beaches on Earth is roughly [tex]7.5 \times 10^{18}[/tex]
The total number of stars in the observable universe is roughly equivalent to 1 billion trillion. which is roughly equal to the number of grains of sand on all the beaches on Earth.
If a positive test charge is placed in an electric field, what is the direction of the force on the test charge?
Explanation:
If a positive test charge is placed in an electric field, it will exert the force in the test charge in the direction of electric field vector. We know that the direction of electric field is given by electric field lines. The field lines for a positive charge is outwards. The electric force acting on the charge is given by :
F = q E
Hence, this is the required solution.
Final answer:
A positive test charge placed in an electric field will experience a force in the direction of the field lines, being repelled by positive charges and attracted to negative charges.
Explanation:
When a positive test charge is placed in an electric field, it experiences a force. This force is in the direction of the electric field lines. So, a positive test charge will be repelled by a positive charge and attracted to a negative charge, consistent with Coulomb's law, which states that like charges repel and unlike charges attract. Additionally, if a positive test charge is placed near two negative charges, it will be attracted towards both, as the electric field lines point towards negative charges.
The electric field vectors point in the direction that a positive test charge would move, which is away from positive charges and towards negative charges. By studying various positions of a test charge and the forces experienced, we can map out these vectors to visualize the electric field.
A student starts from the hostel and goes to his friend's house and then to his school. A is the displacement vector from the hostel to his friend's house. B is the displacement vector from his friend's house to school, and C is the direct path from the hostel to school. Which of the following vector operations is correct for the displacement from the hostel to his friend's house?
A) A - B.
B) A + B.
C) C - B.
D) C + B.
Answer:[tex]\vec{C}-\vec{B}[/tex]
Explanation:
Given
[tex]\vec{A}[/tex] is displacement of student from Hostel to house
[tex]\vec{B}[/tex] is displacement of student from house to school
And [tex]\vec{C}[/tex] is displacement of student from Hostel to school
According to the triangle law of vector addition
If two vectors are acting on a body simultaneously that are shown by magnitude and direction by two sides of a triangle taken in order then the third side is the resultant of two vectors that are taken in opposite direction.
[tex]\vec{A}+\vec{B}=\vec{C}[/tex]
[tex]\vec{A}=\vec{C}-\vec{B}[/tex]
so option c is correct
In Fig. 23-45, a small circular hole of radius R = 1.80 cm has been cut in the middle of an infinite, flat, nonconducting surface that has uniform charge density σ = 4.50 pC/m2 . A z axis, with its origin at the hole’s center, is perpendicular to the surface. In unitvector notation, what is the electric field at point P at z = 2.56 cm?
Answer:
The electric field at point a =( 0.232N/c)k
Explanation:
E = E1+E2=(6/2Eo)K+(-6/2Eo)[1-(2/(sqrtz^2+R^2)k
E= 6z/2Eo(sqrtz^2+R^2)k
E= (4.5×10^-12)×(2.56×10^-2) /2(8.85×10^-12)sqrt(2.56×10^-2)^2+(1.30×10^-2)^2k
E= 1.152×10^-13/(1.77×10^-11)×(2.8×10^-2)k
E= 1.152×10^-13/(4.956×10^-13)k
E=( 0.232N/c)K
Skid is floating in space 3 m from Mitch. Skid and his backpack have a combined mass 50 kg. Skid releases his 10 kg backpack, which reduces his mass. If the same gravitational force is to be maintained between them, what will be the new distance between Skid and Mitch.?
Answer:
Explanation:
attached below is the working to the question asked. I equated the two formulas because of the statement "If the same gravitational force is to be maintained between them" mentioned in the question. The new distance between them is 2.68m
0 mph and half the distance at 69.0 mph . On her return trip, she drives half the time at 31.0 mph and half the time at 69.0 mph .
Part AWhat is Julie's average speed on the way to Grandmother's house?
Express your answer with the appropriate units.
Part BWhat is her average speed on the return trip?
Express your answer with the appropriate units.
Answer:
a) v = 34.5 mph, b) v = 50 mph
Explanation:
The average speed is defined.
v = (x₂ -x₁) / (t₂ -t₁)
If the movement is with uniform speed we can also obtain the average speed, averaging the speeds with a time weight factor, if the time is equal for each speed
v = (v₁ + v₂) / 2
a) For the outward journey
v = (69.0 +0) / 2
v = 34.5 mph
b) For the return trip
v = (69.0 + 31.0) / 2
v = 50 mph
A tractor drives down highway 71 at a steady 12 km/hr. A Subaru WRX passes it at a steady 96 km/hr (possibly with a police car following it). Which vehicle has the smallest net force on it? (assume that the road at this point is both level and straight)
Answer:
neither one has a net force on it
Explanation:
Both vehicles are moving at steady velocity hence the acceleration zero.
since acceleration is zero , the net force on it is zero. therefore neither one has a net force on it
the measure of each exterior angle of a regular pentagon is ___ the measure of each exterior angle of a regular nonagon
Answer:
(a) 72°
(b) 40°
Explanation:
PENTAGON
First, we calculate the total angles in a Pentagon using:
180(n - 2)
Where n = number of sides of the polygon, in this case, 5.
Hence, the total angle in a polygon is
180(5 - 2) = 180 * 3 = 540°
Therefore, each angle will be:
540°/5 = 108°
Because the interior angle and exterior angle form a straight line (180°), the exterior angle of a regular pentagon will be:
180 - 108 = 72°
The exterior angle of a regular Pentagon is 72°
NONAGON
First, we calculate the total angles in a Nonagon using:
180(n - 2)
Where n = number of sides of the polygon, in this case, 9.
Hence, the total angle in a polygon is
180(9 - 2) = 180 * 7 = 1260°
Therefore, each angle will be:
1260°/9 = 140°
Because the interior angle and exterior angle form a straight line (180°), the exterior angle of a regular nonagon will be:
180 - 140 = 40°
The exterior angle of a regular Nonagon is 40°
Final answer:
Each exterior angle of a regular pentagon, which measures 72 degrees, is greater than each exterior angle of a regular nonagon, which measures 40 degrees, because the sum of the exterior angles of any polygon is always 360 degrees.
Explanation:
The question asks how the measure of each exterior angle of a regular pentagon compares to the measure of each exterior angle of a regular nonagon. To answer this, first, we need to understand that the sum of the exterior angles of any polygon is always 360 degrees, no matter the number of sides. Therefore, to find the measure of each exterior angle of a polygon, we simply divide 360 degrees by the number of sides.
For a pentagon, which has five sides, each exterior angle has a measure of 360 ÷ 5 = 72 degrees. For a nonagon, which has nine sides, each exterior angle has a measure of 360 ÷ 9 = 40 degrees. Therefore, the measure of each exterior angle of a regular pentagon is greater than the measure of each exterior angle of a regular nonagon.
A 150 g baseball pitched at a speed of 45 m/s is hit straight back to the pitcher at a speed of 60 m/s. What is the magnitude of the average force on the ball from the bat if the bat is in contact with the ball for 9.5 ms?
Answer:
The average force is 1578.94 N.
Explanation:
Given that,
Mass of baseball = 150 g
Speed = 45 m/s
Speed of pitcher = 60 m/s
Time = 9.5 ms
We need to calculate the average force
Using formula of impulse
[tex]J=\Delta p[/tex]
[tex]J=m\Delta v[/tex]...(I)
[tex]J=F\Delta t[/tex]....(II)
From equation (I) and (II)
[tex]F=\dfrac{m(v_{f}-v_{i})}{\Delta t}[/tex]
Where, m = mass of baseball
[tex]v_{f}[/tex] = final velocity
[tex]v_{i}[/tex] = Initial velocity
[tex]\Delta t[/tex] = time
Put the value into the formula
[tex]F=\dfrac{150\times10^{-3}\times(60-(-40))}{9.5\times10^{-3}}[/tex]
[tex]F=1578.94\ N[/tex]
Hence, The average force is 1578.94 N.
Answer:
F = 1657.89 N
Explanation:
given,
mass of the baseball, m = 150 g
initial speed, u = 45 m/s
final speed, v = 60 m/s
time of contact,t = 9.5 ms
we know,
impulse is equal to change in momentum
J = m (v - u)
J = 0.15 x (60-(-45))
J = 0.15 x 105
J = 15.75 Kg.m/s
We also know that impulse
J = F x Δ t
F x 9.5 x 10⁻³ = 15.75
F = 1657.89 N
The magnitude of the average force is equal to F = 1657.89 N
A racquetball strikes a wall with a speed of 30 m/s and rebounds with a speed of 26 m/s. The collision takes 20 ms. What is the average acceleration of the ball during collision?
a. zero
b. 1500 m/s2
c. 1300 m/s2
d. 200 m/s2
e. 2800 m/s2
Answer:
e. 2800 m/s²
Explanation:
Acceleration: This is the rate of change of velocity. The S.I unit of acceleration is m/s²
Applying Newton's equation of motion,
a = (v-u)/t ................................... Equation 1
Where a = acceleration, v = Final velocity, u = Initial velocity, t = time.
Note: Let the direction of the initial velocity be negative, and the direction of the final velocity be positive
Given: v = 26 m/s, u = -30 m/s, t = 20 ms = 0.02 s
Substitute into equation 1
a = [26-(-30)]/0.02
a = (26+30)/0.02
a = 56/0.02
a = 2800 m/s².
Hence the right option is e. 2800 m/s²