A ball with a mass of 100 g rolls along a horizontal plane at a speed of 50 cm / s.

A ball with a mass of 100 g rolls along a horizontal plane at a speed of 50 cm / s. Can he climb up the slope to a height of 2.5 cm? Do not take friction into account.

m = 100 g = 0.1 kg.

g = 9.8 m / s2.

V = 50 cm / s = 0.5 m / s.

h = 2.5 cm = 0.025 m.

hmax -?

If friction is neglected during the motion of the ball, then the law of conservation of total mechanical energy is valid for its motion. The total mechanical energy of the ball E remains constant.

The total mechanical energy E consists of kinetic Ek = m * V2 / 2 and potential En = m * g * h: E = Ek + En.

When the ball rolls on a horizontal surface, the total mechanical energy consists only of kinetic energy: E = Ek.

E = m * V ^ 2/2.

E = 0.1 kg * (0.5 m / s) ^ 2/2 = 0.0125 J.

When raised to the maximum height, the ball will have only potential energy: E = En.

E = m * g * hmax.

h = E / m * g.

hmax = 0.0125 J / 0.1 kg * 9.8 m / s = 0.0127 m.

The ball can rise to a height of hmax = 0.0127 m = 1.27 cm.

Answer: the ball cannot rise to a height of h = 2.5 cm.