Impulse-Momentum Question Help?

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In summary, the lighter cart moved to the left at 0.5m/s after the collision. The change in momentum delivered to the large cart was 4sqr(3) kg m/s to the right.
  • #1
dylanhouse
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A 1.0 kg cart traveling at 1.0m/s right hits a 4.0kg cart at rest. After the collision, the lighter cart is observed to move to the left at 0.5m/s. What impulse did the interaction deliver to the massive cart (magnitude and direction)? What is the carts velocity after the collision?

I calculated an impulse of 1.5 kg m/s right, though I'm not sure if this is correct. I'm not sure of the procedure for this question.
 
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  • #2
Kinetic energy is conserved in perfectly elastic collisions.

Initial KE of 1kg cart = 0.5 x 1 x 1^2
= 0.5 joules

Final KE of 1kg cart = 0.5 x 1 x 0.5^2
= 0.125 joules

As kinetic energy is conserved, KE of the 4kg cart is equal to 0.5-0.125
= 0.375 joules

0.375 = 0.5 x 4 x v^2
v^2 = 3
v = sqr(3) m/s

Impulse = change in momentum

Initial momentum = 0 as the cart is at rest.

Final momentum = mv
= 4sqr(3) kg m/s

The impulse exerted on the large cart = 4sqr(3) Ns to the right and produced a velocity of sqr(3) m/s also to the right.
 
  • #3
dylanhouse said:
A 1.0 kg cart traveling at 1.0m/s right hits a 4.0kg cart at rest. After the collision, the lighter cart is observed to move to the left at 0.5m/s. What impulse did the interaction deliver to the massive cart (magnitude and direction)? What is the carts velocity after the collision?

I calculated an impulse of 1.5 kg m/s right, though I'm not sure if this is correct. I'm not sure of the procedure for this question.

The change of momentum of a body is equal to the impulse it gained in the interaction. The change is momentum of the light cart is m(v2-v1), (negative) and it delivers impulse of the same magnitude, but positive for the more massive cart. (Newton's Third Law) The total momentum is conserved when there is no external force!

You got the correct magnitude of the impulse. It is equal to the change of momentum of the heavier cart. You can determine the change of velocity from that.


ehild
 
  • #4
TysonM8 said:
Kinetic energy is conserved in perfectly elastic collisions.

According to the given data, it is not a perfectly elastic collision. You can not use conservation of energy. But conservation of momentum holds for every collision.


ehild
 
  • #5


Hello, thank you for reaching out for assistance with this impulse-momentum question. Your calculated impulse of 1.5 kg m/s right is correct, as impulse is equal to the change in momentum, which can be calculated using the equation I = mΔv. In this case, the change in momentum for the massive cart is equal to (4.0 kg)(0.5 m/s) = 2.0 kg m/s to the left. Therefore, the impulse delivered to the massive cart is equal to the negative of this value, or 2.0 kg m/s to the right.

To determine the final velocity of the carts after the collision, we can use the principle of conservation of momentum, which states that the total momentum of a system remains constant in the absence of external forces. This means that the initial momentum of the system (1.0 kg * 1.0 m/s + 4.0 kg * 0 m/s = 1.0 kg m/s to the right) is equal to the final momentum of the system (1.0 kg * -0.5 m/s + 4.0 kg * v2 = 1.0 kg m/s to the right).

Solving for v2, we get v2 = 0.25 m/s to the right. Therefore, after the collision, the massive cart will be moving to the right at a velocity of 0.25 m/s.

I hope this explanation helps you understand the procedure for solving this type of question. Let me know if you have any further questions. Keep up the good work!
 

What is impulse-momentum?

Impulse-momentum is a physical concept that describes the relationship between the force applied to an object and its resulting change in momentum. It is a fundamental principle in classical mechanics and is often used to analyze collisions and other dynamic systems.

How is impulse-momentum related to Newton's laws of motion?

Impulse-momentum is closely related to Newton's laws of motion, specifically the second law which states that the net force applied to an object is equal to the rate of change of its momentum. This means that the impulse applied to an object will result in a change in its momentum, in accordance with the second law.

What is the difference between impulse and momentum?

Impulse and momentum are related but distinct physical quantities. Impulse is the force applied to an object over a period of time, while momentum is the product of an object's mass and velocity. In other words, impulse is a change in momentum.

How is impulse-momentum used to analyze collisions?

Impulse-momentum is commonly used to analyze collisions between objects. By applying the principle of conservation of momentum, we can determine the momentum of each object before and after the collision, and use the impulse-momentum relationship to calculate the forces involved in the collision.

Can impulse-momentum be applied to non-linear systems?

Impulse-momentum can be applied to both linear and non-linear systems, as long as the principles of conservation of momentum and the impulse-momentum relationship are followed. However, the calculations may become more complex in non-linear systems due to the changing forces and velocities involved.

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