Use the worked example above to help you solve this problem. A 53.0 kg skier is

Question

Use the worked example above to help you solve this problem. A 53.0 kg skier is at the top of a slope, as shown in the figure. At the initial point , she is 9.0 m vertically above point .
(a) Setting the zero level for gravitational potential energy at , find the gravitational potential energy of this system when the skier is at and then at . Finally, find the change in potential energy of the skier-Earth system as the skier goes from point to point .

(b) Repeat this problem with the zero-level at point
PEi =
PEf =
?PE =

(c) Repeat again, with the zero level 2.00 m higher than point .
PEi =
PEf =
?PE =

EXERCISE!
Use the values from PRACTICE IT to help you work this exercise. If the zero level for the gravitational potential energy is selected to be midway down the slope, 4.50 m above point , find the initial potential energy, the final potential energy, and the change in potential energy as the skier goes from point to in the figure.

initial =
final =
change =

Explanation / Answer

mass of the skier m = 53 kg vertical height h = 9 m a) initial potential energy of the skier is            (P.E)i = mgh                       = (53 kg)(9.8 m/s2)(9 m)                       = 4674.6 J                       = 4.67*103 J at bottom (height h = 0 m) , final potential energy is          (P.E)f = mgh                     = mg(0)                     = 0 J difference between in potential energy between A and B is      (P.E)f - (P.E)i = 0 J - 4.674*103 J                             = - 4.67*103 J .............................................................. b) potential energy of the skier is            (P.E)i = mgh                       = 0 J potential energy   (P.E)f = mgh                                         = (53 kg)(9.8 m/s2)(-9 m)                                         = - 4.67*103 J difference between in potential energy is difference between in potential energy is                  (P.E)f - (P.E)i = - 4.67*103 J - 0 J                                          = - 4.67*103 J              ............................................................................. c) potential at point A :         (P.E)i = mgh                   = (53 kg)(9.8 m/s2)(9 m - 2 m)                   = 3635.8 J                   = 3.63*103 J potential at point B :         (P.E)f= mgh                   = (53 kg)(9.8 m/s2)(- 2 m)                   = -1038.8 J                   = -1.04*103 J change in potential energy is   (P.E)f - (P.E)i = - 1.04*103 J - 3.63*103 J                              = - 4.67*103 J     ......................................................................................... ......................................................................................... initial potential energy is                  (P.E)i = mgh                             = (53 kg)(9.8 m/s2)(4.5 m)                             = 2337.3 J                             = 2.337*103 J                              = 2.337 kJ final potential energy is                  (P.E)f = mgh                             = (53 kg)(9.8 m/s2)(-4.5 m)                             = -2337.3 J                             = -2.337*103 J                             = -2.337 kJ change in potential energy is (P.E)f - (P.E)i = - 2.337*103 J - 2.337*103 J                            = - 4.67*103 J                              = - 4.67 kJ       potential at point B :         (P.E)f= mgh                   = (53 kg)(9.8 m/s2)(- 2 m)                   = -1038.8 J                   = -1.04*103 J change in potential energy is   (P.E)f - (P.E)i = - 1.04*103 J - 3.63*103 J                              = - 4.67*103 J     ......................................................................................... ......................................................................................... initial potential energy is                  (P.E)i = mgh                             = (53 kg)(9.8 m/s2)(4.5 m)                             = 2337.3 J                             = 2.337*103 J                              = 2.337 kJ                              = 2.337 kJ final potential energy is                  (P.E)f = mgh                             = (53 kg)(9.8 m/s2)(-4.5 m)                             = -2337.3 J                             = -2.337*103 J                             = -2.337 kJ                             = -2.337 kJ change in potential energy is (P.E)f - (P.E)i = - 2.337*103 J - 2.337*103 J                            = - 4.67*103 J                              = - 4.67 kJ                          = - 4.67*103 J                              = - 4.67 kJ      

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