Question

1. You throw a ball from the top of a 50 m high building at 12 m/s straight upward. The ball misses the building on the way down. The mass of the ball is 2 kg.

a. Using energy considerations, how high does the ball go?

b. Using energy considerations, what is the magnitude of the velocity just as it strikes the ground?

c. What is the work done by the force of gravity on the ball while the ball is travelling upward?

d. What is the total work done by the force of gravity on the ball?

Answer 1

here,

height , h0 = 50 m

initial speed , u = - 12 m/s

mass of ball , m = 2 kg

a)

the maximum height , hmax = h + u^2/2g

using conservation of energy

0.5 *m * u^2 + m * g * h = m * g * hmax

0.5 * 12^2 + 9.81 * 50 = 9.81 * hmax

hmax = 57.3 m

b)

let the magnitude of velcoity when it hits the grounf be v

using conservation of energy

0.5 *m * v^2 = 0.5 * m * u^2 + m * g * h0

0.5 * v^2 = 0.5 * 12^2 + 9.81 * 50

solving for v

v = 33.5 m/s

c)

the work done by the force of gravity on the ball while the ball is travelling upward , W = - m * g * ( hmax - h)

W = - 2 * 9.81 * ( 57.3 - 50) J

W = - 144 J

d)

the total work done by the force of gravity on the ball , W2 = m * g * h0

W2 = 2 * 9.81 * 50 J

W2 = 981 J