Momentum, Impulse, and KE Question?

In summary, two fan carts labeled A and B are placed on opposite sides of a table with their fans pointed in the same direction as shown in the figure below. Cart A is weighted with iron bars so it is twice as heavy as cart B. When the fans are turned on, they cause the air to exert a constant force on the cart independent of its mass. Assume that friction is small enough to be neglected. The fans are set with a timer so that after they are switched on, they stay on for a fixed length of time, Δt, and then are turned off. cart A starts off with more momentum because it has more mass. However, after the fans are turned off, the two objects have the
  • #1
FlatEarth
6
0
I was doing a physics problem on my homework and was not sure which of the three questions below i got wrong as I got a 2/3. I believe the second one might be wrong, but I'm not to sure.
Two fan carts labeled A and B are placed on opposite sides of a table with their fans pointed in the same direction as shown in the figure below. Cart A is weighted with iron bars so it is twice as heavy as cart B. When the fans are turned on, they cause the air to exert a constant force on the cart independent of its mass. Assume that friction is small enough to be neglected. The fans are set with a timer so that after they are switched on, they stay on for a fixed length of time, Δt, and then are turned off.

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A. Just after the fans are turned off, which of the following statements are true about the momenta of the two carts? pA = pB
B. Just after the fans are turned off, which of the following statements are true about the kinetic energies of the two carts? KEA
C. Which of the following statements are true? The momentum of each cart is conserved.
Answer 1:

pA = pB


Answer 2:KEA < KEB

Answer 3:The momentum of each cart is conserved.
 
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  • #2
Please give your reasoning for each of your answers. (Yes, one of your answers is clearly wrong.)
 
  • #3
Doc Al said:
Please give your reasoning for each of your answers. (Yes, one of your answers is clearly wrong.)
1. I assumed that constant force and fix time would cause both objects to have equal impulses. With impulse (F*delta T) being equal to momentum, I assumed the two objects would be equal.

2. I did some plug an chug of made up numbers and found that if the mass was twice as large and both objects need to equal the same impulse, then the speed/velocity would be larger for the smaller object.

3. Because of my answer to one I felt that this response is necessary for 1 to be right.
 
  • #4
Doc Al said:
Please give your reasoning for each of your answers. (Yes, one of your answers is clearly wrong.)
these are the questions and choices
(a) Just after the fans go off, which of the following statements are true about the momenta of the two carts?


  • (i) pA > pB
    (ii) pA = pB
    (iii) pA < pB
(b) Just after the fans go off, which of the following statements are true about the kinetic energies of the two carts?


  • (i) KA > KB
    (ii) KA = KB
    (iii) KA < KB
(c) Which of the following statements are true? You may choose as many as you like, or none. If you choose none, write N.


  • (i) After the fan is turned on, each cart moves at a constant velocity,
    but the two velocities are different from each other.
    (ii) The kinetic energy of each cart is conserved.
    (iii) The momentum of each cart is conserved.
 
  • #5
FlatEarth said:
1. I assumed that constant force and fix time would cause both objects to have equal impulses. With impulse (F*delta T) being equal to momentum, I assumed the two objects would be equal.
Good.

FlatEarth said:
2. I did some plug an chug of made up numbers and found that if the mass was twice as large and both objects need to equal the same impulse, then the speed/velocity would be larger for the smaller object.
Good.

FlatEarth said:
3. Because of my answer to one I felt that this response is necessary for 1 to be right.
Are the initial and final momentums equal?
 
  • #6
Doc Al said:
Good.Good.Are the initial and final momentums equal?
I don't think they would be
 
  • #7
FlatEarth said:
I don't think they would be
Of course not. They start at rest and end up moving with some velocity. So what does that tell you about what is or isn't conserved?
 
  • #8
Doc Al said:
Good.Good.

just found out there is a forth otpi
Doc Al said:
Of course not. They start at rest and end up moving with some velocity. So what does that tell you about what is or isn't conserved?
I got it there is a fourth selection, which is that none of them are true.
 
  • #9
FlatEarth said:
I got it there is a fourth selection, which is that none of them are true.
There you go. Good!
 
  • #10
Doc Al said:
There you go. Good!
Thanks
 

1. What is momentum?

Momentum is a measure of an object's motion, determined by its mass and velocity. It is a vector quantity, meaning it has both magnitude and direction.

2. How is momentum calculated?

Momentum is calculated by multiplying an object's mass by its velocity. The formula is p = mv, where p represents momentum, m represents mass, and v represents velocity.

3. What is impulse?

Impulse is the change in an object's momentum over a period of time. It is equal to the force applied to the object multiplied by the time interval during which the force is applied. The formula for impulse is J = FΔt, where J represents impulse, F represents force, and Δt represents the change in time.

4. How is impulse related to momentum?

Impulse and momentum are directly related. The impulse on an object is equal to the change in its momentum. This means that if the impulse on an object is increased, its change in momentum will also increase.

5. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is determined by an object's mass and velocity, and is calculated using the formula KE = 1/2 mv^2, where KE represents kinetic energy, m represents mass, and v represents velocity.

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