PRACTICE IT Use the worked example above to help you solve this problem. A 66.0 kg skier is at the top of a slope, as shown in the figure. At the initial point O, she is 9.0 m vertically above point (a) Setting the zero level for gravitational potential energy at energy of this system when the skier is at O and then at energy of the skier-Earth system as the skier goes from point O to point O. ,find the gravitational potential Finally, find the change in potential PE, - PE, = APE (b) Repeat this problem with the zero-level at point PE,- PE, APE= (c) Repeat again, with the zero level 2.00 m higher than point PE, = PE, - APE

Principles of Physics: A Calculus-Based Text
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Chapter6: Energy Of A System
Section6.6: Potential Energy Of A System
Problem 6.7QQ: A ball is connected to a light spring suspended vertically as shown in Figure 6.17. When pulled...
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GOAL Calculate the change in gravitational potential
energy for different choices of reference level.
PROBLEM A 60.0 kg skier is at the top of a slope, as
shown in the figure. At the initial point O, she is 10.0 m
vertically above point ®. (a) Setting the zero level for
gravitational potential energy at O, find the gravitational
potential energy of this system when the skier at O and
then at O. Finally, find the change in potential energy of the
skier-Earth system as the skier goes from point to point
O. (b) Repeat this problem with the zero level at point
O. Repeat again, with the zero level 2.00 m higher than
is
10.0 m
point O
STRATEGY Follow the definition and be careful with signs.
O is the initial point, with gravitational potential energy PE,.
and O is the final point, with gravitational potential energy PEr. The location chosen for y -O is also the
zero point for the potential energy, because PE - mgy
SOLUTION
(A) Let y - 0 at O. Calculate the potential energy at O and at ®, and calculate the change in potential
energy.
Find PE, the potential energy at O
PE, - gy, - (60.0 kg)(9.80 m/s)(10.0 m)-
5.88 x 10'
PE, - 0 at O by choice. Find the
PE, - PE, -0 - 5.88 x 10' )- -5.88 x 103
difference in potential energy between
O and D.
(B) Repeat the problem if y = 0 at O, the new reference point, so that PE = 0 at O
Find PE, noting that point O is now at
PE, =mgy, = (60.0 kg)(9.80 m/s)(-10.0 m) =
y= -10.0 m.
-5.88 x 10' )
PE, - PE, = -5.88 x 10 ) - 0 = -5.88 x 10')
(C) Repeat the problem, if y -0 two meters above O.
Find PE, the potential energy at O
PE, = y, = (60.0 kg)(9.80 m/s)(8.00 m) =
4.70 x 10'J
Find PE, the potential energy at 0.
PE, - mgyy- (60.0 kg)(9.80 m/s?)(-2.00 m)-
-1.18 x 10')
Compute the change in potential
PE, - PE, = -1.18 x 10 1 - 4.70 x 10' =
energy.
-5.88 x 10)
LEARN MORE
REMARKS These calculations show that the change in the gravitational potential energy when the skier
goes from the top of the slope to the bottom is -5.88 x 10 ), regandies of the zero level selected.
QUESTION If the angle of the slope is increased, the change of gravitational potential energy between
the two heights: (Select all that apply.)
V remains the same.
O depends only on the difference between the two heights.
O sometimes decreases and sometimes increases.
O
depends on the path followed.
increases.
O decreases.
PRACTICE IT
Use the worked example above to help you solve this problem. A 66.0 kg skier is at the top of a slope, as
shown in the figure. At the initial point O, she is 9.0 m vertically above point O.
(a) Setting the zero level for gravitational potential energy at O, find the gravitational potential
energy of this system when the skier is at O and then at 0. Finally, find the change in potential
energy of the skier-Earth system as the skier goes from point Oto point
PE, -
PE, =
APE -
(b) Repeat this problem with the zero-level at point O
PE, -
PE, =
APE =
(c) Repeat again, with the zero level 2.00 m higher than point O
PE, =
PE,-
APE =
Transcribed Image Text:GOAL Calculate the change in gravitational potential energy for different choices of reference level. PROBLEM A 60.0 kg skier is at the top of a slope, as shown in the figure. At the initial point O, she is 10.0 m vertically above point ®. (a) Setting the zero level for gravitational potential energy at O, find the gravitational potential energy of this system when the skier at O and then at O. Finally, find the change in potential energy of the skier-Earth system as the skier goes from point to point O. (b) Repeat this problem with the zero level at point O. Repeat again, with the zero level 2.00 m higher than is 10.0 m point O STRATEGY Follow the definition and be careful with signs. O is the initial point, with gravitational potential energy PE,. and O is the final point, with gravitational potential energy PEr. The location chosen for y -O is also the zero point for the potential energy, because PE - mgy SOLUTION (A) Let y - 0 at O. Calculate the potential energy at O and at ®, and calculate the change in potential energy. Find PE, the potential energy at O PE, - gy, - (60.0 kg)(9.80 m/s)(10.0 m)- 5.88 x 10' PE, - 0 at O by choice. Find the PE, - PE, -0 - 5.88 x 10' )- -5.88 x 103 difference in potential energy between O and D. (B) Repeat the problem if y = 0 at O, the new reference point, so that PE = 0 at O Find PE, noting that point O is now at PE, =mgy, = (60.0 kg)(9.80 m/s)(-10.0 m) = y= -10.0 m. -5.88 x 10' ) PE, - PE, = -5.88 x 10 ) - 0 = -5.88 x 10') (C) Repeat the problem, if y -0 two meters above O. Find PE, the potential energy at O PE, = y, = (60.0 kg)(9.80 m/s)(8.00 m) = 4.70 x 10'J Find PE, the potential energy at 0. PE, - mgyy- (60.0 kg)(9.80 m/s?)(-2.00 m)- -1.18 x 10') Compute the change in potential PE, - PE, = -1.18 x 10 1 - 4.70 x 10' = energy. -5.88 x 10) LEARN MORE REMARKS These calculations show that the change in the gravitational potential energy when the skier goes from the top of the slope to the bottom is -5.88 x 10 ), regandies of the zero level selected. QUESTION If the angle of the slope is increased, the change of gravitational potential energy between the two heights: (Select all that apply.) V remains the same. O depends only on the difference between the two heights. O sometimes decreases and sometimes increases. O depends on the path followed. increases. O decreases. PRACTICE IT Use the worked example above to help you solve this problem. A 66.0 kg skier is at the top of a slope, as shown in the figure. At the initial point O, she is 9.0 m vertically above point O. (a) Setting the zero level for gravitational potential energy at O, find the gravitational potential energy of this system when the skier is at O and then at 0. Finally, find the change in potential energy of the skier-Earth system as the skier goes from point Oto point PE, - PE, = APE - (b) Repeat this problem with the zero-level at point O PE, - PE, = APE = (c) Repeat again, with the zero level 2.00 m higher than point O PE, = PE,- APE =
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