Question

A ball with a mass of 0.500 kg connected to a string spins in a circle with a speed of 5.90m/s. If thestring exerts a force of 9.50 N, on the ball as it spins along the circular path. What is the radius of thecircular path of the ball in meters?

Answer 1

Given information:

Mass of ball = 0.500 kg

Speed of ball = 5.90 m/s

Force = 9.50 N

Radius of the circular path = ?

Solution:

The force acting on the ball is given by

$F=ma$

Where m is the mass and a is the circular acceleration of the ball.

The circular acceleration of the ball is given by

$a=\frac{v^2}{r}$

Substituting (a) into the above equation, we get

$F=\frac{mv^2}{r}$

Re-writing the equation for radius (r), we get

$r=\frac{mv^2}{F}$

Finally, substitute the given values and solve for radius (r)

$r=\frac{mv^2}{F}=r=\frac{0.500\cdot(5.90)^2}{9.50}=1.83\: m$

Therefore, the radius of the circular path of the ball is 1.83 meters.