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} −
*PE*_{0}) 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**

**====================================**

**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**

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