(b)A coin is placed 20 cm from the axis of a rotating turntable of variable speed. This speed is gradually increased and the coin remains fixed on the turntable until a rate of 36 rpm is reached. At this point, the coin slides off. What is the coefficient of static friction between the coin and the turntable?
im completely comfused by this one
do i need to use angular speed somehow?
set centripetal force to equal friction force.
Yes, angular speed is going to be used.
Yes, you are correct. To solve this problem, you need to use the concept of angular speed and the coefficient of static friction.
Let's break down the problem step by step:
Step 1: Understand the given information.
- A coin is placed 20 cm away from the axis of a rotating turntable.
- The turntable's speed is gradually increased until it reaches 36 rpm.
- At this point, the coin slides off.
Step 2: Convert the given information.
- Convert the 36 rpm to radians per second. Recall that 1 revolution = 2π radians.
- 36 rpm * (2π radians/1 revolution) = 72π radians/second.
Step 3: Identify the forces acting on the coin.
- There are two forces at play here: the centripetal force and the force of static friction.
- The centripetal force keeps the coin moving in a circular path, while the static friction opposes the tendency of the coin to slide off the turntable.
Step 4: Derive the equation.
- The centripetal force is provided by the frictional force between the coin and the turntable.
- The maximum frictional force before the coin slides off is given by:
- Ffriction = μs * N
- Where μs represents the coefficient of static friction and N represents the normal force.
Step 5: Calculate the normal force.
- The normal force is the force exerted by the turntable on the coin perpendicular to the turntable's surface. Since the coin is stationary and not moving upwards or downwards, the normal force is equal to the weight of the coin.
- The weight of the coin is given by:
- Weight = m * g
- Where m represents the mass of the coin and g represents the acceleration due to gravity.
Step 6: Calculate the coefficient of static friction.
- Equate the maximum frictional force (Ffriction) to the centripetal force:
- Ffriction = μs * N
- mv^2/r = μs * mg (v is the tangential velocity, r is the radius)
- v^2/r = μs * g
- (72π)^2 / 0.20 = μs * 9.8
Step 7: Solve for the coefficient of static friction (μs).
- Plug in the known values and solve for μs.
- μs = ((72π)^2) / (0.20 * 9.8)
- μs ≈ 14.56
Therefore, the coefficient of static friction between the coin and the turntable is approximately 14.56.