5 CONSERVATION OF ENERGY 5.8 Power
AThe work WJ done by the external force in extending the spring from 0 to x is
Hence,
WJ =x
fJ dx = k
0x
x dx =
01
k x^2.
2WJ = 0.5 × 807.7 × 0.13^2 = 6.83 J.Worked example 5.4: Roller coaster ride
Question: A roller coaster cart of mass m = 300 kg starts at rest at point A, whose
height off the ground is h 1 = 25 m, and a little while later reaches point B, whose
height off the ground is h 2 = 7 m. What is the potential energy of the cart relative
to the ground at point A? What is the speed of the cart at point B, neglecting the
effect of friction?
Answer: The gravitational potential energy of the cart with respect to the ground
at point A is
UA = m g h 1 = 300 × 9.81 × 25 = 7.36 × 104 J.
Likewise, the potential energy of the cart at point B is
UB = m g h 2 = 300 × 9.81 × 7 = 2.06 × 104 J.Hence, the change in the cart’s potential energy in moving from point A to point
B is
∆U = UB − UA = 2.06 × 104 − 7.36 × 104 = −5.30 × 104 J.B
h 1
h 2∫ ∫