Solution Found!
Solved: A child places a picnic basket on the outer rim of
Chapter 6, Problem 96(choose chapter or problem)
A child places a picnic basket on the outer rim of a merry-goround that has a radius of 4.6 m and revolves once every 30 s.
(a) What is the speed of a point on that rim?
(b) What is the lowest value of the coefficient of static friction between basket and merrygo-round that allows the basket to stay on the ride?
Questions & Answers
QUESTION:
A child places a picnic basket on the outer rim of a merry-goround that has a radius of 4.6 m and revolves once every 30 s.
(a) What is the speed of a point on that rim?
(b) What is the lowest value of the coefficient of static friction between basket and merrygo-round that allows the basket to stay on the ride?
ANSWER:Step 1 of 3
You need two concepts to solve this problem.
One is that of circular motion and another of static friction.
Circular motion:
The speed of the object at any point in circular motion is given by:
\(v=\frac{\text { circumference }}{\text { period of revolution }}\)
\(\text { Circumference }=2 \pi R\)
\(\text { period of revolution }=t\)
\(v=\frac{2 \pi R}{t} \ldots \ldots \ldots \ldots \ldots \ldots(1)\)
Static Friction:
For the basket not to slip, the minimum static frictional force should be equal to the centripetal force acting of the basket.
\(\begin{array}{l}
f_{\text {smin }}=F_{\text {centripetal }} \\
f_{\text {smin }}=\frac{m v^{2}}{R}
\end{array}\)
We know that frictional force is given by,
\(f_{\text {smin }}=\mu_{s} m g\)
Therefore:
\(\begin{array}{l}
f_{\text {smin }}=\mu_{s} m g=\frac{m v^{2}}{R} \\
\mu_{s} m g=\frac{m v^{2}}{R} \dots \dots (2)
\end{array}\)