The swing passes the balance position at a speed of 6 km / h. A boy weighing 50 kg acts on the swing

The swing passes the balance position at a speed of 6 km / h. A boy weighing 50 kg acts on the swing seat with a force of 0.54 kN. determine the length of the ropes

V = 6 km / h = 1.6 m / s.

m = 50 kg.

g = 9.8 m / s ^ 2.

F = 0.54 kN = 540 N.

L -?

Two forces act on the boy at the moment of passing the equilibrium position: the gravity force m * g directed vertically downward, the seat reaction force N directed vertically upward.

Let’s write 2 Newton’s law: m * a = N – m * g.

According to Newton’s 3 Laws, the force with which the boy presses on the seat F, with the same force the seat presses on the boy N: F = N.

m * a = F – m * g.

We express the centripetal acceleration by the formula: a = V ^ 2 / L.

m * V ^ 2 / L = F – m * g.

L = m * V ^ 2 / (F – m * g).

L = 50 kg * (1.6 m / s) ^ 2 / (540 N – 50 kg * 9.8 m / s ^ 2) = 2.56 m.

Answer: the length of the swing ropes is L = 2.56 m.