A lamp weighing 1.7 kg is suspended from the middle of a weightless cable 20 m long, as a result of which

A lamp weighing 1.7 kg is suspended from the middle of a weightless cable 20 m long, as a result of which the cable sags by 10 cm. The points at which the cable is fixed are at the same height. Determine the cable tension.

L = 20 meters – the length of the weightless cable;

h = 10 centimeters = 0.1 meters – the distance over which the cable sags;

m = 1.7 kilograms is the mass of the lamp suspended from the middle of the cable;

g = 10 m / s ^ 2 – acceleration of gravity.

It is required to determine the thread tension T (Newton).

Since the lamp is suspended strictly to the middle of the cable, 2 equal forces T will act on the lamp from the cable side, the projection of which on the Y axis will be T * cos (a), where a is the angle between the direction of the force T and the vertical. Then, according to Newton’s second law:

m * g = 2 * T * cos (a)

m * g = 2 * T * h / (L / 2)

m * g = 4 * T * h / L

T = L * m * g / (4 * h) = 20 * 1.7 * 10 / (4 * 0.1) = 340 / 0.4 = 850 Newtons.

Answer: the pulling force of the cable is 850 Newton.