The mathematical pendulum, deviating from the equilibrium position, rises to a height of 10 cm.

The mathematical pendulum, deviating from the equilibrium position, rises to a height of 10 cm. At what speed does the ball of the pendulum pass through the equilibrium position?

h = 10 cm = 0.1 m.

g = 10 m / s2.

V -?

To solve this problem, we will use the law of conservation of total mechanical energy.

At the initial moment of time, the mathematical pendulum has only potential energy En, the value of which is determined by the formula: En = m * g * h.

At the beginning of movement, potential energy begins to transform into kinetic energy, at the moment of passing the equilibrium position, the body has only kinetic energy Ek.

Ek = m * V ^ 2/2.

En = Ek.

m * g * h = m * V ^ 2/2.

g * h = V ^ 2/2.

V = √ (2 * g * h).

V = √ (2 * 10 m / s2 * 0.1 m) = 1.4 m / s.

Answer: when passing the equilibrium position, the ball will have a speed of V = 1.4 m / s.