Question
hange the mass of the red ball to match that of the green ball.
a. Which ball has greater momentum now?
b. How has the total momentum changed?
c. Predict what will happen to the motion of the balls after they collide.
a. Which ball has greater momentum now?
b. How has the total momentum changed?
c. Predict what will happen to the motion of the balls after they collide.
Ask by Kelly Schwartz. in the United States
Mar 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
a. The ball with the higher speed has greater momentum.
b. The total momentum has decreased because the red ball now has less momentum than before.
c. After colliding, the green ball will slow down, and the red ball will speed up, exchanging their momenta.
Solution
Momentum is given by
If we now set the mass of the red ball equal to the mass of the green ball (let’s call this common mass
Thus, with equal masses the magnitude of momentum depends solely on the speed. If, for example, the green ball is moving faster (i.e.
So the ball with the higher speed has the greater momentum.
Assume that before this change the red ball had a different mass, say
while the green ball had momentum
After changing the red ball’s mass to
If the original mass
and therefore the total momentum of the system,
will have decreased by the reduction in the red ball’s momentum. (If no external forces act and the speeds were maintained during the change, then the decrease in mass directly decreases momentum.)
In collisions, momentum is conserved (if no external forces act). With both balls having the same mass, the outcome of the collision will depend largely on the type of collision (elastic or inelastic) and their initial speeds. In many cases (for example, in an elastic collision with one ball moving faster than the other):
- The faster (green) ball will transfer some of its momentum to the slower (red) ball.
- If the collision is head‐on and elastic, the moving ball may slow down considerably or even come nearly to rest, while the red ball gains speed.
- The precise outcome will obey conservation of both momentum and energy (in an elastic collision) and might resemble collisions of billiard balls where equal-mass objects exchange speeds.
Thus, after the collision you can expect an exchange of speeds and momentum between the balls, leading to a change in their motions consistent with the principles of momentum conservation.
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Simplify this solution The Deep Dive
If you change the mass of the red ball to match that of the green ball, they will have the same momentum if they are moving at the same velocity. However, if one ball is moving faster than the other, the ball with the greater velocity will have greater momentum.
The total momentum before the collision will remain the same, as momentum is conserved in a closed system. Therefore, the sum of the momenta of the two balls will equal the total momentum after the collision unless an external force acts on the system.
After they collide, several scenarios could play out depending on whether the collision is elastic or inelastic. In an elastic collision, both kinetic energy and momentum are conserved, which could lead to either ball bouncing off in a different direction or one ball transferring some of its momentum to the other. In an inelastic collision, one or both balls may stick together, moving as one mass after the collision, resulting in a change in their velocities.
