Chapter 6.2, Problem 24SSC

To determine

The force that must be exerted on a ball to move it in a circle.

Answer to Problem 24SSC

  $60.83\text{N}$

Explanation of Solution

Given:

The 7.3kg ball is to be moved in a circle of radius 0.75m with a speed 2.5m/s.

Formula used:

The centripetal force acting on an object is

  $F=m{a}_c$

Where, $a_c=\frac{v^2}{r}$ is the centripetal acceleration, $v$ is the velocity of the object and r is the radius.

Calculation:

The force required to be exerted on the ball to move it in a given circle should be equal to the centripetal force on the ball.

  $F=F_c=m{a}_c=\frac{m{v}^2}{r}$

Using given values in above equation,

  $\begin{array}{c}T=\frac{7.3{\left(2.5\right)}^2}{0.75}\\ =60.83\text{N}\end{array}$

Conclusion:

Thus, the required force on the ball is $60.83\text{N}$ .