TBR physics collisions help

[iololiol]

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Example 4.4a
A 0.5-kg ball traveling at 10 m/s collides with a stationary 2.0-kg ball and rebounds in the opposite direction at 6 m/s. What is true of the speed of the 2.0- kg ball after collision?
A. The2.0-kgballmovesat10m/s.
B. The2.0-kgballmovesat6m/s.
C. The2.0-kgballmovesat4m/s.
D. The2.0-kgballmovesat2.5m/s.


Solution
This is a collision like the one seen in Case 5, where the impact ball rebounds off of an initially stationary ball. Intuitively we know that the 2.0-kg ball will be moving faster than 2.5 m/s, the speed it would have attained had the impact ball come to rest. Because the impact ball rebounds, the 2.0-kg ball gets all of the transferred momentum plus some recoil momentum. The recoil momentum is small, its exit speed should be just a little greater than 2.5 m/s, making choice C the most probable answer. To solve precisely, we can apply the following math:

I do not get this intuitively why it is C and how momentum is transferred?

 

[N1st]

Example 4.4a
A 0.5-kg ball traveling at 10 m/s collides with a stationary 2.0-kg ball and rebounds in the opposite direction at 6 m/s. What is true of the speed of the 2.0- kg ball after collision?
A. The2.0-kgballmovesat10m/s.
B. The2.0-kgballmovesat6m/s.
C. The2.0-kgballmovesat4m/s.
D. The2.0-kgballmovesat2.5m/s.


Solution
This is a collision like the one seen in Case 5, where the impact ball rebounds off of an initially stationary ball. Intuitively we know that the 2.0-kg ball will be moving faster than 2.5 m/s, the speed it would have attained had the impact ball come to rest. Because the impact ball rebounds, the 2.0-kg ball gets all of the transferred momentum plus some recoil momentum. The recoil momentum is small, its exit speed should be just a little greater than 2.5 m/s, making choice C the most probable answer. To solve precisely, we can apply the following math:

I do not get this intuitively why it is C and how momentum is transferred?

In collisions, momentum is always conserved. If you have two objects with masses m1 and m2, and the first is moving at velocity v, and the second is initially stationary, the total momentum of the system is m1v + m2*0 = m1v.

In this case, the initial momentum is 0.5 kg * 10 m/s = 5 kg m/s, so that must be the final momentum as well.

The first object with m1 is moving in the opposite direction after the collision at a velocity of - 6 m/s, so its momentum is -3 kg m/s. The total still needs to add up to 5, so the other object must have a mometum of 8 kg m/s. Since its mass is 2 kg, 8 kg m/s / 2 kg = 4 m/s. Notice it is positive, so it is moving in the direction the m1 was originally moving.

By the way, collisions can either be completely inelastic, completely elastic, or partly inelastic. The only time kinetic energy is conserved is in completely elastic collisions (where the objects bounce off each other). In a completely inelastic collision, both masses move at the same speed after the collision because they have stuck together. Kinetic energy isn't conserved because some energy is lost to heat.