The car in the loop-the-loop shown weighs 400 lb with its passengers. It starts

Question

The car in the loop-the-loop shown weighs 400 lb with its passengers. It starts at a height h from the ground at rest. if it has speed 45 ft/s at the end of the ride, and R = 12 ft, find:

a) the kinetic energy, potential energy, and total energy at points a and b.

b) the value of h.

The car in the loop-the-loop shown weighs 400 lb with its passengers. It starts at a height h from the ground at rest. if it has speed 45 ft/s at the end of the ride, and R = 12 ft, find: a) the kinetic energy, potential energy, and total energy at points a and b. b) the value of h.

Explanation / Answer

a)

1 ft = 0.3048 meters

1 lb = 4.4482 N

point (a):

total energy = E_total = 0.5 m v^2

E_total = 0.5*(400*4.4482/9.8)*45*0.3048*45*0.3048 = 17078 J

E_potential = m g R = (400*4.4482)*12*0.3048 = 6507.9 J

E_kinetic = 17078 - 6507.9 = 10570 J

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point (b):

total energy = E_total = 0.5 m v^2

E_total = 0.5*(400*4.4482/9.8)*45*0.3048*45*0.3048 = 17078 J

E_potential = m g R = (400*4.4482)*2*12*0.3048 = 13016 J

E_kinetic = 17078 - 13016 = 4062 J

b)

m g h = 0.5 m v^2

h = 0.5/g v^2

h = 0.5/9.8 * (45*0.3048*45*0.3048)

h = 9.60 m

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