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 mph is reached at which point the coin slides off. What is the coefficent of static friction between the turntable and the coin?
I got this for my equation but it game the wrong answer
Mu s = (rg)^-1 v^2
could you please tell me how to do this problem
centrifugal force, Fc
= mrω², or
= mv²/r
where
m=mass, kg
ω = rotational velocity in radians/s.
v=tangential speed m/s
normal force, Fn
=mg
Coefficient of friction, μ
=Fc/Fn
Note: I have a doubt about the value 50 mph for the tangential velocity. It is not a normal unit for a turntable. Please check.
Net Force Radial = m a radial = F radial = Ffr
ma radial = Us Fn
ma radial = Us m g
cancel out mass
a radial = Us g
a radial = r^-1 v^2
r^-1 v^2 = Us g
Us = (rg)^-1 V^2
don\'t see what I did wrong
50 mph is in the question in the book
Us = (rg)^-1 V^2
Us = (.12 m (9.80 kg^-1 N))^-1 (22.35 s^-1 m)^2
Us = 420
back of book says .34
If you work back from μ=0.34, r=0.12 and g=9.8, you will get v=0.632 m/s, or when divided by r, ω=5.27 radians/s, or 1.42 mph for v.
I believe there is something wrong with the question.
To solve this problem, let's first break it down into steps:
Step 1: Convert the speed of the turntable from mph to m/s.
- Since all the other units in the equation are in the metric system, it's best to convert the speed to meters per second. We'll use the conversion factor: 1 mile = 1609.34 meters, and 1 hour = 3600 seconds.
speed_mph = 50 mph
speed_mps = speed_mph * (1609.34 m/1 mile) * (1 hour/3600 seconds)
Step 2: Calculate the angular velocity of the turntable.
- The angular velocity, ω, measures how fast an object rotates. It is related to the linear speed, v, and the radius, r, through the equation: v = rω. We need to find ω.
radius = 12.0 cm = 0.12 m
angular_velocity = speed_mps / radius
Step 3: Calculate the acceleration due to rotation.
- The acceleration due to rotation, a, is given by: a = rω^2.
acceleration = radius * (angular_velocity)^2
Step 4: Calculate the coefficient of static friction.
- The coefficient of static friction, μs, can be determined using the equation: μs = a / g, where g is the acceleration due to gravity (approximately 9.8 m/s²).
coefficient_of_friction = acceleration / 9.8
Now, you can insert the values you've obtained into the equation to calculate the coefficient of static friction.