Ball A leaves the edge of a level table with speed upsilon_Ai and falls 10 the f

Question

Ball A leaves the edge of a level table with speed upsilon_Ai and falls 10 the floor. At the instant hall A leaves the table edge another identical ball. B, is leased from rest at the height of the table top and also fails to the floor. It is observed that the balls reach the floor at the same time. a. In each question below, consider the interval that begins when the balls begin falling and ends just before they reach the floor. i. Is the magnitude of the impulse imparted to ball B greater than. less than, or equal to the magnitude of the impulse imparted to ball A? Explain your reasoning. ii. In the spaces provided at right, draw an arrow to indicate the direction of the impulse imparted to each ball. Explain your reasoning. iii. Is the work done on ball B greater than, less than, or equal to the work done on ball A? Explain your reasoning. In each question below, consider the balls just before they reach the floor. i. Is the magnitude of the momentum of ball B greater than, less than, or equal to the magnitude of the momentum of ball A? Explain your reasoning. ii. Is the kinetic energy of ball B greater than, less than, or equal to the kinetic energy of ball A? Explain your reasoning.

Explanation / Answer

a )

H = uy t + 1/2 g t2

= 0 + 1/2 g t2

t = ( 2 H / g )1/2

the equation

Vy2 - uy2 = 2 g h

Vy = ( 2 g h )1/2

resultant velocity of A is VA = ( u2 + 2 g h )1/2  

the initial velocity is zero

mA = mB  

the direction of impulse of both A and B are in downside.

the work done by the gravitational force

WA = WB = m g h

b )

the impulse is dPA = m ( u2 + 2 g h )1/2  

dPA = m ( 2 g h )1/2  

ball A is more than ball B

KEA = 1/2 m V2

= 1/2 m ( v + 2 g h )1/2  

and

KEB = 1/2 m ( 2 g h )1/2  

ball A is more than ball B

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