Question

a child on a spinning playground ride is 0.36 m from the center of the ride. the centripetal force on the child is 10 n. what is the mass of the child if the child has a tangential speed of 0.54 m/s? 3.7 kg 13 kg 23 kg 79 kg

Explanation:

Step1: Recall centripetal force formula

The centripetal force formula is \(F = m\frac{v^{2}}{r}\), where \(F\) is centripetal force, \(m\) is mass, \(v\) is tangential speed, and \(r\) is the radius.

Step2: Rearrange formula to solve for mass

Rearrange \(F = m\frac{v^{2}}{r}\) to \(m=\frac{F\times r}{v^{2}}\).

Step3: Substitute values

Given \(F = 10\space N\), \(r=0.36\space m\), \(v = 0.54\space m/s\). Substitute into \(m=\frac{F\times r}{v^{2}}\):

$$ m=\frac{10\times0.36}{0.54^{2}}=\frac{3.6}{0.2916}\approx 12.35\approx13\space kg $$

Answer:

13 kg