A ball weighing 4.0 kg at a height of 3.0 m has a total mechanical energy of 150 J.

A ball weighing 4.0 kg at a height of 3.0 m has a total mechanical energy of 150 J. What is the kinetic energy of the body at this height? How fast is the body moving?

m = 4 kg.

g = 9.8 m / s2.

h = 3 m.

W = 150 J.

Wк -?

V -?

The total mechanical energy W of a body is the sum of kinetic Wc and potential energy Wp: W = Wc + Wp.

The kinetic energy of the translational motion of the body is determined by the formula: Wк = m * V2 / 2.

The potential energy of a body Wp of mass m, raised to a height h above the earth’s surface, is determined by the formula: Wp = m * g * h, where g is the acceleration of gravity.

W = Wк + m * g * h.

Wк = W – m * g * h.

Wk = 150 J – 4 kg * 9.8 m / s2 * 3 m = 32.4 J.

V = √ (2 * Wк / m).

V = √ (2 * 32.4 J / 4 kg) = 4 m / s.

Answer: the body has kinetic energy Wк = 32.4 J and has a speed V = 4 m / s.