Momentum, collision of two cars problem

In summary, two carts with masses of 3.0 kg and 5.0 kg, initially moving in opposite directions with speeds of 1.0 m/s and 2.0 m/s respectively, collide head-on. After the collision, the 3.0 kg cart is moving in the opposite direction with a speed of 1.0 m/s. Using the conservation of momentum, the final velocity of the 5.0 kg cart can be calculated to be 0.8 m/s in the opposite direction. The direction of positive and negative velocities can be chosen as desired, as long as it is consistent.
  • #1
Erenjaeger
141
6

Homework Statement


A 3.0 kg cart moving to the right with a speed of 1.0 m/s has a head-on collision with a 5.0 kg cart that is initially moving to the left with a speed of 2.0 m/s. After the collision, the 3.0 kg cart is moving to the left with a speed of 1.0 m/s. What is the final velocity of the 5.0 kg cart?

Homework Equations


P=mv

The Attempt at a Solution


I took the initial momentum of both cars and added them for the total initial momentum which was 3⋅1+5⋅2 = 13 kg m/s
so because of the conservation of momentum Pf=Po so the final total momentum will have to be 13 kg m/s also.
so Pftotal = Pcar 1 + Pcar 2
car 1 is now moving to the left with a velocity of 1m/s so its momentum is still 3 kg m/s
so 13=3+Pcar 2
and we know the mass of car 2 is 5kg so 13=3+2⋅V and we see the momentum of car 2 would have to be 10 kg m/s to result in a final total momentum of 13kg m/s so wouldn't the velocity have to be 2m/s ?? but on the answer sheet it says the final velocity is 0.8m/s to the left.
 
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  • #2
Erenjaeger said:
I took the initial momentum of both cars and added them for the total initial momentum which was 3⋅1+5⋅2 = 13 kg m/s
Are both cars moving in the same direction? Remember that momentum is a vector: it has both magnitude and direction.
 
  • #3
gneill said:
Are both cars moving in the same direction? Remember that momentum is a vector: it has both magnitude and direction.
Oh true, right so using the same method but assuming movement to the right is in the positive direction and movement to the left is in the negative direction, I should arrive at the correct answer ?
 
  • #4
Erenjaeger said:
Oh true, right so using the same method but assuming movement to the right is in the positive direction and movement to the left is in the negative direction, I should arrive at the correct answer ?
How you assign positive and negative for each velocity is up to you. You should get the right answer as long as you are consistent. It usually helps to achieve consistency if you pick one positive direction for all velocities on a given axis.
 
  • #5
Erenjaeger said:
Oh true, right so using the same method but assuming movement to the right is in the positive direction and movement to the left is in the negative direction, I should arrive at the correct answer ?
Sure, that would work. It's usually best to decide on your coordinate system before you start doing calculations.
 
  • #6
No offense. But you haven't really tried to address the problem at play here in an optimal manner! What is the formula you initially tried to use in order to solve the problem aside from P=mv?
 

1. What is momentum?

Momentum is a property of a moving object that describes its quantity of motion. It is calculated by multiplying the object's mass by its velocity.

2. How is momentum conserved in a collision of two cars?

In a collision between two cars, the total momentum remains constant. This means that the sum of the momentums of the two cars before the collision is equal to the sum of the momentums after the collision.

3. What factors affect the momentum of a car?

The momentum of a car is affected by its mass and velocity. A car with a greater mass or higher velocity will have a greater momentum compared to a car with a lower mass or velocity.

4. How is the collision between two cars analyzed?

The collision between two cars can be analyzed using the laws of conservation of momentum and energy. The initial and final momentums of the two cars can be calculated to determine the change in momentum and the extent of the collision.

5. Can the momentum of a car be changed during a collision?

Yes, the momentum of a car can change during a collision. This change in momentum is caused by the forces acting on the car during the collision. The direction and magnitude of these forces determine the change in momentum.

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