Question

A 9.0 kg sphere of copper is sitting at the top of a 22 ft flagpole. a. How much potential energy does the sphere have on top of the flagpole? b. Suppose the sphere was placed on the top of the pole by a remote control toy helicopter. How much work did helicopter do to place the sphere on top of the pole? c. Suppose a gust of wind blows the sphere off the pole, how much kinetic energy would the sphere have right when it impacts the ground? d. How much potential and kinetic energy would the sphere have after it fell 11 ft? Try to answer this question without formulas.

Answer 1

a)
Potential energy, PE = m * g * H
Where m is the mass of the sphere and H is the height of the flagpole.

H = 22 ft = 6.7056 m
Substituting values,
PE = 9 * 9.8 * 6.7056
= 591.4 J

b)
Work done, W = Potential energy of the ball
W = 591.4 J

c)
Potential energy at the top is converted into kinetic energy at the bottom
KE = 1/2 * m * v² = PE
Where v is the velocity at the bottom
v² = (2 * PE) / m
= (2 * 591.4) / 9
= 131.4
v = SQRT[131.4]
= 11.46 m/s

d)
At the halfway, potential energy and kinetic energy are the same.
Using the conservation of energy, total energy at the top = total energy at the halfway.
591.4 = PE_halfway + KE_halfway
= 2 * PE_halfway
PE_halfway = 591.4/2 = 295.7 J

Kinetic energy at the halfway = Potential energy at the halfway = 295.7 J