Question

1. A child sitting 1.2 m from the center of a merry-go-round moves with a speed of 1.1 m/s.
Calculate A) the centripetal acceleration of the child and B) the net horizontal force exerted on the
child (mass = 22.5 Kg)

Answer 1

Answers:

A) $1m/s^{2}$

B) 22. 5 N

Explanation:

A) Since this situation is related to uniform circular motion, the centripetal acceleration $a_{C}$ of the child is calculated by:

$a_{C}=\frac{V^{2}}{r}$

Where:

$V=1.1 m/s$ is the speed

$r=1.2 m$ is the child's distane to the center (the radius)

Hence:

$a_{C}=\frac{(1.1 m/s)^{2}}{1.2 m}$

$a_{C}=1.008 m/s^{2} \approx 1 m/s^{2}$

B) Knowing th centripetal acceleration and the mass $m=22. 5 kg$ of the child, we can calculate the net horizontal force $F$ by:

$F=m a_{C}$

$F=(22. 5 kg)(1 m/s^{2})$

$F=22. 5 N$