A coin is placced 12.0 cm from the axis of a roatating turntable of variable speed. When the speed of the turntable is slowly incraeased, the coin remains fixed on the turntable until a rate of 50 rpm is reached at which point the coin slides off. What is the coefficent of static friction between the turntable and the coin?
ok it was rpm not mph
so then in order to do one round it would take .83 seconds
Us = (rg)^-1 (t^-1 2 pi r)^2
i got .70
how do i do this
centripetal acceleration= friction
m*w^2 r = mu*mg
changing 50 rpm to rad/sec
mu=w^2 r/g=(50*2PI/60)^2 * .12
which is not your answer.
Check my thinking.
To find the coefficient of static friction between the turntable and the coin, you can use the following steps:
1. Determine the angular velocity of the turntable when the coin starts sliding off. You mentioned that it occurs at a rate of 50 revolutions per minute (rpm). The conversion factor for rpm to radians per second (rad/s) is given by:
angular velocity (in rad/s) = (2π / 60) * rpm
Plugging in the value for 50 rpm, you would get:
angular velocity = (2π / 60) * 50 = π/3 rad/s
2. Use this angular velocity to calculate the centripetal acceleration experienced by the coin on the turntable. The centripetal acceleration can be obtained using the following formula:
centripetal acceleration = angular velocity^2 * radius
Since the coin is placed 12.0 cm from the axis of rotation, convert this distance to meters by dividing by 100:
radius = 12.0 cm / 100 = 0.12 m
Plugging in the values, you would get:
centripetal acceleration = (π/3)^2 * 0.12 = π^2/9 * 0.12
3. Determine the gravitational force acting on the coin. The gravitational force is given by:
gravitational force = mass * acceleration due to gravity
Since the mass of the coin is not mentioned in the question, it cancels out when we calculate the coefficient of static friction.
4. Calculate the normal force experienced by the coin. The normal force is the force exerted perpendicular to the contact surface, which counteracts the force of gravity. Since the coin is not moving vertically, the normal force and gravitational force must be equal. Therefore:
normal force = gravitational force
5. Finally, use the centripetal acceleration and the normal force to calculate the coefficient of static friction using the equation:
coefficient of static friction (μs) = centripetal acceleration / normal force
Substituting the values obtained from the above steps, you can find the coefficient of static friction between the turntable and the coin.