Can you please help me with my physics?

Question

1. A coin is placed 12.5 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached, at which point the coin slides off. What is the coefficient of static friction between the coin and the turntable?

2. A 1100 kg car rounds a curve of radius 70 m banked at an angle of 12°. If the car is traveling at 90 km/h, will a friction force be required?
If so, how much force? (Enter zero if there is no friction force.)

Estimate the force a person must exert on a string attached to a 0.110 kg ball to make the ball revolve in a horizontal circle of radious 0.600 m. The ball makes 1.80 revolutions per second. Do not ignore the weight of the ball. In particular, find the magnitude of FT, and the angle it makes with the horizontal. [Hint: Set the horizontal component of FT equal to maR; also, since there is no vertical motion, what can you say about the vertical component of FT?]
FT = N
= °

Answer 1

1)
the force on the coin is
m*ω^2*r
which is balanced by friction
m*g*µs
until it slides.
If 36 rpm is when it slides that's
36*2*3.14/60 rad/sec
or 3.77 rad/s

µs=3.77^2*0.125/9.81
µs=0.1811

2.)
Consider the forces parallel to the road surface
Centripetal
cos(12)m*v^2/r
cos(12)*m*(90/3.6)^2/70
m*8.73

Gravity
m*9.81*sin(12)
m*2.04

Yes, friction is required to keep the car from sliding upward on the road surface

the force is
1100*(8.73-2.04)
7360 N

3.)
There are three forces on the ball:
centripetal
m*ω^2*R
where ω=1.8*2*3.14 rad/s

Gravity
m*g

and the tension in the string, T

Relating by summing forces in the horizontal and vertical:
T*cos(θ)=m*ω^2*R
T*sin(θ)=m*g

divide
tan(θ)=g/(ω^2*R)

θ=7.29 degrees

T=8.50 N

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