Question

True or False?
A small sphere of mass 1 kg is attached to the end of a cord of length 1 m and rotated in a vertical circle about a fixed point O. If the speed at the uppermost point of the trajectory is 1 m/s, the sphere will have a circular trajectory (will move in a circle).
Use g = 9.8 m/s².

Answer 1

Answer:

False.  the system does not complete the circle movement

Explanation:

For this exercise, we must find the rope tension at the highest point of the path,

          -T - W = m a

The acceleration is centripetal

           a = v² / R

           T = ma - mg

           T = m (v² / R - g)

The minimum tension that the rope can have is zero (T = 0)

          v² / R - g = 0

          v = √ g R

Let's find out what this minimum speed is

          v = √ 9.8 1

          v = 3.13 m / s

We see that the speed of the body is less than this, so the system does not complete the movement.