Question

A child with a mass of 40 kg sits on the edge of a merry-go-round at a distance of 3.0 m from its axis of rotation. The merry-go-round accelerates from rest up to 0.4 rev/s in 10 s. If the coefficient of static friction between the child and the surface of the merry-go-round is 0.6, does the child fall off before 5 s?

a) Yes, the child falls off before 5 s.
b) No, the child remains on the merry-go-round after 5 s.
c) Insufficient information to determine.
d) The acceleration of the merry-go-round is irrelevant to the child's stability.

Answer 1

To determine if the child falls off before 5 seconds, we need to calculate the angular acceleration and compare it to the critical value of static friction.

Step-by-step explanation:

To determine if the child falls off before 5 seconds, we need to calculate the angular acceleration and compare it to the critical value of static friction. This can be done by using the equation:

f = μN

Where f is the frictional force, μ is the coefficient of static friction, and N is the normal force. In this case, the normal force is equivalent to the weight of the child, which is mg. Since the merry-go-round starts from rest, the angular acceleration can be calculated using the equation:

α = Δω/Δt

where Δω is the change in angular velocity and Δt is the time interval.

Finally, we can determine if the child falls off before 5 seconds by comparing the calculated angular acceleration to the critical value of static friction. If the angular acceleration is greater, the child will fall off before 5 seconds. If the angular acceleration is equal or less, the child will remain on the merry-go-round after 5 seconds.