Static friction between two objects.

[Matt_h]

a child (m=30kg) sits 5m from the axis of rotation on a flat turn table which makes a full rotation every 8 seconds.

A. find the childs period (t) and frequency (f)
Full rotation every 8 seconds, T=8
Frequency = inverse of period = 1/8

B. What is the tangential velocity of the child?
Vtan=ωR
w=D(θ)/dt
(2pi/8)*5= 3.926

C. What is the centripetal acceleration of the child? what must the centripetal force acting on the child be?
Acentripetd=v^2/R
3.926^2/5=3.082
F=ma
30*3.082=92.48

D. If this is the fastest the child can go without slipping off the turntable, determine the coefficient of friction between the child and the table surface.

I can't figure out what equation to use.
the only equations i have written down from class are
F_s-max=μ_s*F_N
F_k=μ_k*F_N

Any help would be great

 

[ehild]

a child (m=30kg) sits 5m from the axis of rotation on a flat turn table which makes a full rotation every 8 seconds.

A. find the childs period (t) and frequency (f)
Full rotation every 8 seconds, T=8
Frequency = inverse of period = 1/8

Correct.

B. What is the tangential velocity of the child?
Vtan=ωR
w=D(θ)/dt
(2pi/8)*5= 3.926

If you want to keep 4 significant digits, round off properly.

C. What is the centripetal acceleration of the child? what must the centripetal force acting on the child be?
Acentripetd=v^2/R
3.926^2/5=3.082
F=ma
30*3.082=92.48

D. If this is the fastest the child can go without slipping off the turntable, determine the coefficient of friction between the child and the table surface.

I can't figure out what equation to use.
the only equations i have written down from class are
F_s-max=μ_s*F_N
F_k=μ_k*F_N

Any help would be great

The force of static friction provides the centripetal force for motion along the circle. You are right, the maximum static friction is μ_sF_N.

What is N?

ehild