Final answer:
The change in momentum of a bouncing steel ball can be determined by using free-fall kinematics to calculate the ball's velocity before and after it rebounds off a hard floor. The change in momentum is found by taking the difference in momentum values before and after the collision.
Step-by-step explanation:
Calculating the Change in Momentum During a Bounce
The question involves a steel ball bouncing off a hard floor and requires the use of free-fall kinematics to calculate the change in momentum. The process can be broken down into several parts:
Calculate the velocity of the ball just before it strikes the floor.
Calculate the velocity of the ball just after it rebounds.
Use the calculated velocities to determine the change in momentum.
To calculate the velocity before impact, we use the formula v = √(2gh), where g is the acceleration due to gravity (9.81 m/s2) and h is the height (1.50 m). This gives us the initial velocity upon impact. Similarly, to calculate the velocity after bouncing to a height of 1.45 m, we use the same formula with h as 1.45 m. The change in momentum is the difference in momentum before and after the collision, considering the mass of the ball remains constant.
To calculate the acceleration during the contact with the floor and the compression of the ball, we apply Newton's second law and kinematics equations, respectively.
Momentum is conserved during the collision, so the ball's momentum after the bounce must be equal and opposite to its momentum before the bounce. If any kinetic energy is lost, it could be due to non-conservative forces like friction, sound, or deformation of the ball or floor.