Answer :
Due to the fact that force equals the time rate of change of momentum (F = d p/dt), both balls take the same amount of time to come to rest. If we apply the same force and both balls start off with the same momentum, stopping them will take the same amount of time.
What is momentum ?
momentum is the result of a particle's mass and velocity. Being a vector quantity, momentum possesses both magnitude and direction. According to Isaac Newton's second equation of motion, the force applied on a particle is equal to the time rate of change of momentum. Check out Newton's laws of motion.
According to Newton's second law, if a particle is subjected to a constant force for a specific amount of time, the result of the force and time (referred to as the impulse) is equal to the change in momentum. On the other hand, a particle's momentum represents the length of time needed for a consistent force to bring it to rest.
Due to the fact that force equals the time rate of change of momentum (F = d p/dt), both balls take the same amount of time to come to rest. If we apply the same force and both balls start off with the same momentum, stopping them will take the same amount of time.
Because the ping-pong balls' momenta (p = m .v) are equivalent, the ball with the greater velocity has the greater kinetic energy, hence stopping it requires a greater distance. The ping-pong ball must have more kinetic energy because it travels faster than the bowling ball despite having a smaller inertial mass. This implies that the ping-pong ball requires more work than the bowling ball. Because work is the product of force and displacement (W = F.D, where force for both balls is assumed to be equal), or because work is directly proportional to displacement, the distance needed to stop a ping-pong ball is higher than one for a bowling ball.
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