Question

A child rides on a playground merry-go-round, from the center. The merry-go-round makes one complete revolution every 5 s. How large is the net force on the child? In what direction does the net force act?

Short answer

The net force is 66.3Nand its direction is radial.

Step-by-step solution

Identification of given data

Mass m=30kg

Radius r=1.4kg

Time T=5s

Definition of force.

A force is a push or pull on an object caused by the interaction of the thing with another object. Every time two things interact, a force is exerted on each of them. The two items no longer feel the force after the interaction ends. The net force is calculated by finding the vector sum of all the forces acting on the object. The direction of the net force is given by the direction of acceleration vector of the object

Finding the net force and the direction of the net force.

The relation between tangential speed and angular frequency is$v=\omega r$

From Newton's second law and knowing that the radial acceleration in uniform circular motion is given by$\frac{v^2}{r}$.

_{$$\begin{gathered} F=ma \\ =m\frac{v^2}{r} \\ =m{\omega }^{2}r \end{gathered}$$...........(i)}

The relation between angular frequency and period

$\left(\omega =\frac{2\mathrm{\pi }}{T}\right)$

Put this value in equation (i)

$$\begin{gathered} F=m{\omega }^{2}r \\ =m\frac{4{\mathrm{\pi }}^2\mathrm{r}}{T^2} \\ =30\times \frac{4{\mathrm{\pi }}^2\times 1.4}{5^2} \\ =66.3N \end{gathered}$$

Thus, the net force is 66.3N and it acts radially