Question

Part 1

While leaning out a window that is 6.5 m above the ground, you drop a 0.60 kg basketball to a friend at ground level. Your friend catches the ball at a height of 1.2 m above the ground. Determine the following.

(a)

the amount of work done (in J) by the force of gravity on the ball

___________ J

(b)

the gravitational potential energy (in J) of the ball-earth system, relative to the ground when it is released

______ J

(c)

the gravitational potential energy (in J) of the ball-earth system, relative to the ground when it is caught

_______J

(d)

the ratio of the change (PE_f − PE₀) in the gravitational potential energy of the ball-earth system to the work done on the ball by the force of gravity

change in PE/W=_________

Part 2

A child with a weight of 110 N swings on a playground swing attached to 2.10 m long chains. What is the gravitational potential energy (in J) of the child-earth system relative to the child's lowest position at the following times?

(a)

when the chains are horizontal

______ J

(b)

when the chains make an angle of 30.0° with respect to the vertical

______ J

(c)

when the child is at his lowest position

________ J

Answer 1

(a)

the amount of work done (in J) by the force of gravity on the ball

W = m*g*(h1-h2) = 0.6*9.81*(6.5-1.2) = 31.1958 J

(b)

the gravitational potential energy (in J) of the ball-earth system, relative to the ground when it is released

Ui = m*g*h1 = 0.6*9.81*6.5 = 38.259 J

(C)

the gravitational potential energy (in J) of the ball-earth system, relative to the ground when it is caught

Uf = m*g*h2 = 0.6*9.81*1.2 = 7.0632 J

(c)

change in PE/W = (7.056 - 38.259)/31.1958 = -1

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part(2)

(a)

gravitational potential energy (in J) of the child-earth system

height h = L

U1 = m*g*h

U1 = m*g*L = 110*2.1 = 231 J

(b)

gravitational potential energy (in J) of the child-earth system

height h = L*(1-costheta)

U2 = m*g*h

U2 = m*g*L*(1-costheta)

U2 = 110*2.1*(1-cos30) = 30.95 J

(C)

height h = 0

U3 = 0