Question

You are at a playground with a see-saw and a large merry-go-round. You put your phone on the see-saw and find it slides when it is tilted at an angle of 38 degrees. How far can you put your phone from the center of the merry-go-round (in m) when it makes one rotation every 3 s

Answer 1

Answer: r_max = 1.75m

Explanation:

Below is a rather brief analysis to solving this problem.

The phone starts sliding when along incline,

when F_net = m g sin(theta) - fs_max = 0

and fs_max = us N = us m g cos(theta)

m g sin(theta) - us m g cos(theta) =

us = tan(theta) = tan38 = 0.781

On merry - go - round,

fs_max = us N = us m g

Using F = m a

fs_max = m w^2 r_max and w = 2pi / T

us m g = m (2 pi / T)^2 (r_max)

0.781 x 9.81 = (2 pi / 3)^2 (r_max)

r_max = 1.75 m

cheers i hope this helped !!