A penny is placed on a rotating turntable.?

Question

A penny is placed on a rotating turntable. Where on the platter does the penny require the largest frictional force to remain in place?
a) equal force is required on all places on the platter
b) the center of the turntable
c) halfway between the center and the edge of the turntable
d) the edge of the turntable

Answer 1

The frictional force = u_k * mg

Where u_k is the coefficient of static friction, m is the mass of the penny, and g is the gravitational constant.

The centripetal force = mv^2/r

For the penny to not slide we must satisfy this condition

u_k* mg + mv^2/r = 0

canceling the masses and solving for radius allows us to find the maximum radius for a motionless penny.

u_s * g = -v^2/r

r = v^2/u_s *g

At this radius is where you will have the maximum static frictional force. Any further and the penny will begin to slide.

This is a tricky question because the static friction force is zero at the center and will increase in magnitude according to our equation until at a certain radius when the centripetal acceleration is larger than ug, at which point the penny will begin to slide.

So the answer is, it depends...on two things the speed of the penny and the coefficient of static friction.

The best answer in this case is (d).




By the way someone stated the centripetal force = rw^2, this is not the centripetal force, it is the centripetal acceleration. Hope that didn't confuse you.

Answer 2

Yap, the answer is at the edge of the turntable. Because the platter is a round plate and rotates as one system, the center and the edge of the platter rotates at the exact time (try drawing a straight line from the center to the edge. Count the time interval required for the edge to make a full circular motion. It should and would be the exact time interval as the time interval required for the center to make a full circular motion). Now the equation for counting speed (not velocity, as velocity in this case will vary because the platter is going in circular motion. Velocity is direction dependant and can have negative value) is:

v = s/t

where as v=speed, s=distance, t=time
From explanation above, clearly we can see that the time is the same between the edge and the center of the platter. The distance however is very different. The edge would've to travel more distance compared to the center in order to make a full circular motion. So according to the equation, v has the greatest value on the edge. Greatest speed means greatest centripetal force (force that's trying to throw the penny off the platter). To cope with this, the penny need greatest centrifugal force (force that's trying to hold the penny from throwing off the platter).

Answer 3

The centrifugal force on the penny will be F = w^2*R, where w = angular velocity ("RPM") and R is distance from the center. The force is greatest where R is greatest, at the edge. That is where the greatest frictional force is required.

Answer 4

Edge of the turntable. At the edge, the velocity is greatest and centrifugal force is greatest. Therefore, the friction needs to be greatest to hold the coin.

Answer 5

The answer is D

It requires more force to keep the penny in place on the outer edge. Less force the closer to the center.

Answer 6

on the outer edges of the turntable, the force that moves the penny is stronger here, less stability

Answer 7

the edge of the turntable

Mv2/R

Answer 8

d the maximum velocity is there so the maaximum amount of friction is required there

Answer 9

d... on the edge...