Question

As shown in the figure (Figure 1) , a superball with mass m equal to 50 grams is dropped from a height of hi=1.5m . It collides with a table, then bounces up to a height of  hf=1.0m . The duration of the collision (the time during which the superball is in contact with the table) is tc=15ms . In this problem, take the positive y direction to be upward, and use g=9.8m/s2 for the magnitude of the acceleration due to gravity. Neglect air resistance.

Find the y component of the momentum, pbefore,y, of the ball immediately before the collision.

Find the y component of the momentum of the ball immediately after the collision, that is, just as it is leaving the table.

Find Jy, the y component of the impulse imparted to the ball during the collision.

Find the y component of the time-averaged force Favg,y, in newtons, that the table exerts on the ball.

Find Kafter?Kbefore, the change in the kinetic energy of the ball during the collision, in joules.

Answer 1

A ball of mass m = 50 g = 0.05 kg is dropped from height .

The final height of the ball is .

The y component of the momentum, pbefore,y, of the ball immediately before the collision can be determined as follows:

According to law of conservation of energy initial potential energy is equal to final kinetic energy.

        

           

Therefore, the momentum of the ball is

The velocity is in downward direction, thus, the momentum is

(2) The y component of the momentum of the ball immediately after the collision, that is, just as it is leaving the table can be determined as follows:

The final height of the ball is .

According to law of conservation of energy initial potential energy is equal to final kinetic energy.

Therefore, the momentum of the ball is

(3) Jy, the y component of the impulse imparted to the ball during the collision can be determined as follows:

The impulse is defined as change in momentum.

      

(4) The y component of the time-averaged force Favg,y, in newtons, that the table exerts on the ball can be determined as follows:

The impulse of the ball can also be defined as: product of average force and time.

        

Therefore, the average force is,

     

(5) The change in the kinetic energy of the ball during the collision is,

          

          

Therefore, the change in kinetic energy is,