A block of mass M=2 kg is swung on a rope in a veritcal circle(the direction of motion is vertical to the ground) of radius r. When the block is at the top of the circle, the tension in the rope is measured to be 10N. What is the tension in the rope when the block is at the bottom of the circle?

Answer 1

If the speed at the top is v1, then the tension there is:

T1 = m [v1^2/r - g]

It is given that T1 = 10 N

At the bottom the tension will be:

T2 = m [v2^2/r + g]

where v2 is the speed at the bottom.

Using conservation of energy, you find:

1/2 v2^2 - 1/2 v1^2 = 2 r g ---->

v2^2/r - v1^2/r = 4 g

If you subtract the equation for T2 and T1 and insert the above relation between v2 and v1, you get:

T2 - T1 = 6 m g

Answer 2

127.6