Question

You pull downward with a force of 26.9 N on a rope that passes over a disk-shaped pulley of mass 1.44 kg and radius 0.0765 m. The other end of the rope is attached to a 0.630-kg mass. Calculate the tension in the rope on both sides of the pulley. Enter tension for the part of the rope that you are pulling on first. Then enter the tension for the part of the rope with the mass.

Answer 1

Given is : -

Force F = 26.9 N

Mass of the pulley M = 1.44 kg

Radius R = 0.0765 m

Mass attached at the other side is m = 0.630 kg

Now,

Let the acceleration of mass m be a, then using Newton's second law we get

or

eq-1

and if T₂ is the tension on the other side then

eq-2

Since the mass is moving upwards therefore T₂ must be greater than T₁

so

or

by plugging the value from eq-1 we get

or

by plugging all the values we get

which gives us

by plugging this value in eq-1 we get

or

which gives us

Hence,

The tension of the part of the rope that you are pulling on first is T₂ = 26.9 N

The tension for the part of the rope with mass is T₁ = 15.8461 N