Question
b. What about the green ball?
c. What about the total momentum of both the red and green ball?
6. Now change the elasticity to
c. What about the total momentum of both the red and green ball?
6. Now change the elasticity to
Ask by Hampton Cross. in the United States
Mar 26,2025
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Answer
b. The Green Ball
After the collision, the green ball gains momentum and starts moving. Its final momentum is determined by the collision’s details, such as mass and speed.
c. Total Momentum of Both Balls
The total momentum before and after the collision remains the same. Initially, the red ball has momentum
6. Collision with
In a perfectly elastic collision, both momentum and kinetic energy are conserved. The red ball slows down, and the green ball speeds up, with the exact speeds determined by their masses. If the balls have equal mass, the red ball stops, and the green ball moves at the red ball’s initial speed.
Solution
b. The Green Ball
Assume that before the collision the red ball is moving and the green ball is at rest. During the collision the red ball exerts a force on the green ball; by Newton’s third law, the green ball experiences an impulse and gains momentum. In other words, even though the green ball had no momentum initially, after the collision its momentum is nonzero—it increases from zero to a value determined by the details of the collision (mass, speed, etc.).
Mathematically, if the green ball has mass
c. Total Momentum of Both Balls
The law of conservation of momentum tells us that the total momentum of an isolated system remains constant during a collision. If the red ball has mass
After the collision the red ball (now with speed
Thus, conservation of momentum requires
This equation expresses that the total momentum of both balls remains
6. Collision with
An elasticity of
where we assume the green ball is initially at rest. These formulas show that:
- The red ball’s speed changes to
, which depends on the difference . - The green ball, initially stationary, moves with speed
after the collision—acquiring momentum from the red ball.
In the special case where
-
The red ball comes to rest, since
-
The green ball takes on the red ball’s initial speed, because
Thus under
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Simplify this solution Beyond the Answer
When you see a green ball in a physics scenario, it’s not just a prop! Imagine it bouncing around with its red counterpart: they both possess mass and velocity, meaning they have momentum. The green ball’s behavior during a collision can teach us about energy transfer in elastic collisions, where this little guy springs back to life after each impact, maybe even showing off some fancy moves!
When we consider the total momentum of both the red and green balls, we’re diving into the physics pool of conservation laws. Optimistically, if no external forces are acting on them, their combined momentum before and after the collision remains constant. So, whether they clump together or bounce off each other like best friends, the total momentum does not change, which is like a secret rule in the world of physics: keep the balance!
