A cat dozes on a stationary merry-go-round, at a radius of 6.9 m from the center of the ride. The operator turns on the ride and brings it up to its proper turning rate of one complete rotation every 7.3 s. What is the least coefficient of static friction between the cat and the merry-go-round that will allow the cat to stay in place?
centripetal force= friction force
m*w^2 r= mu*mg
w=2PI/period= 2PI/7.3 rad/sec
solve for mu.
what is your "m" in your equations stand for?
i really wanna know that why is centripetal force equal to frictional force???
n a request...
free body diagram please!!
please...
To determine the least coefficient of static friction between the cat and the merry-go-round that will allow the cat to stay in place, we can analyze the forces acting on the cat.
1. Centripetal Force: The cat requires a centripetal force to keep it moving in a circular path. This force is provided by the static friction between the cat and the merry-go-round.
2. Centrifugal Force: There is also a centrifugal force acting on the cat, which tries to push the cat away from the center of the merry-go-round.
At the point where the cat is about to slip, the static friction force will be at its maximum value. This maximum friction force is equal to the product of the coefficient of static friction (μs) and the normal force (Fn) acting on the cat.
To find the normal force, we can consider the gravitational force acting on the cat. Since the cat is on a horizontal surface, the normal force will be equal in magnitude and opposite in direction to the gravitational force.
The formula for the centripetal force is:
Fc = (m * v^2) / r
where
- Fc is the centripetal force,
- m is the mass of the cat,
- v is the linear velocity of the cat, and
- r is the radius of the merry-go-round.
From the given information, we know the radius (r = 6.9 m) and the time taken to complete one rotation (T = 7.3 s). We can calculate the linear velocity (v) using the formula:
v = (2π * r) / T
Once we have the linear velocity, we can find the centripetal force (Fc).
Next, we equate the maximum static friction force (μs * Fn) to the centripetal force (Fc) and solve for the coefficient of static friction (μs).
Let's plug in the values and calculate step by step to find the answer.