Momentum before and after the collision and relative velocities.

In summary: Thank you for your input! In summary, the ball moves with a velocity of 20 ms-1 relative to the ground after the collision.
  • #1
Jfex
2
0

Homework Statement


If the truck was not stationary but was moving horizontally towards the ball at 25 ms-1, what would be the speed of the ball, relative to the ground, after the collision (in ms-1)?
Mass of ball = 0.2 kg
Mass of truck = 20 tonnes
Initial velocity of ball = 20 ms-1 (to the right)
Initial velocity of the truck = 25 ms-1 (to the left)
This is also a perfectly elastic collision

Homework Equations


P = mv


The Attempt at a Solution


So what I did first was equated the sum of the initial momentum's to the sum of the final momentum's to try and figure out what the final velocity of the ball was however it just gave me 20 which is incorrect.

so...

m1v1initial + m2v2initial = m1v1final + m2v2final

I found that because we can cancel the final and initial momentum's of the truck due to its change of velocity being negligible I can equate the initial and final momentum's of the ball. However when I do this it gives me a velocity of 20 which is still incorrect.

Thank you in advance.
 
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  • #2
Jfex said:

The Attempt at a Solution


So what I did first was equated the sum of the initial momentum's to the sum of the final momentum's to try and figure out what the final velocity of the ball was however it just gave me 20 which is incorrect.

so...

m1v1initial + m2v2initial = m1v1final + m2v2final

I found that because we can cancel the final and initial momentum's of the truck due to its change of velocity being negligible I can equate the initial and final momentum's of the ball. However when I do this it gives me a velocity of 20 which is still incorrect.

Thank you in advance.


You can not ignore the change of momentum of the truck. The change of the velocity is small, but multiplied by the big mass, the magnitude is exactly the same as that of the change of momentum of the ball. Write up conservation of energy and use both equations to solve for the velocity of the ball.


ehild
 
  • #3
Sorry I'm not to sure how that will help because now I'm left with two variables; the final velocity of the final velocity of the ball?

0.2*20 + 20000*25 = 0.2*vfinal + 20000*vfinal

I'm not sure what you mean?
 
  • #4
The collision is elastic. Use also the equation for conservation of energy.
Also, check the signs of the initial velocities. The ball and car move in opposite directions.

ehild
 
Last edited:
  • #5


I would first like to clarify the units used in this problem. The mass of the truck is given in tonnes, but the mass of the ball is given in kilograms. For consistency and easier calculations, it would be best to convert the mass of the truck to kilograms (1 tonne = 1000 kg).

Now, let's consider the momentum before and after the collision. The initial momentum of the ball is 0.2 kg x 20 ms^-1 = 4 kgms^-1. The initial momentum of the truck is 20,000 kg x 25 ms^-1 = 500,000 kgms^-1.

During the collision, the ball and truck will exert equal but opposite forces on each other, resulting in a change in their velocities. Since this is a perfectly elastic collision, the total momentum of the system (ball + truck) will remain constant.

After the collision, the final momentum of the ball and truck will be equal to the initial momentum (4 kgms^-1 and 500,000 kgms^-1 respectively). Therefore, the final velocity of the ball can be calculated as 4 kgms^-1 / 0.2 kg = 20 ms^-1.

However, this is the velocity of the ball relative to the truck. To find the velocity of the ball relative to the ground, we need to take into account the initial velocity of the truck (25 ms^-1 to the left). This means that the final velocity of the ball relative to the ground will be 20 ms^-1 to the right, since the truck's initial velocity will be cancelled out by the ball's final velocity.

In conclusion, the speed of the ball, relative to the ground, after the collision will be 20 ms^-1. It is important to note that this assumes perfect conditions and does not take into account any external factors such as air resistance.
 

1. What is momentum?

Momentum is a physical quantity that represents the motion of an object. It is calculated by multiplying an object's mass by its velocity.

2. What is the law of conservation of momentum?

The law of conservation of momentum states that the total momentum of a closed system before and after a collision remains constant, as long as there are no external forces acting on the system.

3. How does momentum change before and after a collision?

In an isolated system, the total momentum before a collision is equal to the total momentum after the collision. However, the individual momenta of the objects involved in the collision may change due to the transfer of momentum between them.

4. What is the difference between elastic and inelastic collisions?

In an elastic collision, both the total momentum and the total kinetic energy of the system are conserved. In an inelastic collision, only the total momentum is conserved, and some kinetic energy is lost in the form of heat, sound, or deformation.

5. How do relative velocities affect the outcome of a collision?

The relative velocities of the objects involved in a collision affect the transfer of momentum between them. Objects with higher relative velocities will experience a greater change in momentum during a collision.

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