Uniform Circular Motion

Question

How would I determine the tension in a cord attached to a ball (mass 0.20kg) swinging around at a speed of 3.7 m/s?

Answer 1

Good Morning,

If the ball is to the right of the circular path.

Draw Free body diagram

Tension points to the left

Force of weight points down

Sum forces towards the centripetal direction (Center of rotation)

T = m * a_c = m * V^2/r

T = 0.2 * (3.7^2/r)

If the ball is at the bottom of the circular path.

Draw Free body diagram

Sum forces towards the centripetal direction (Center of rotation)

T - mg = a_c = m * V^2/r

T = m * V^2/r + mg

Please note based on the expressions generated, you can see how the tension of the cord changes depending on the position of the ball.

Aside from this you can use the principle of conservation of energy to find the tension of the cord.

Please let me know if you have further questions