Physics Question

[Marty]

"A block of mass m rests on a horizontal circular turntable, a distance R from the origin, as shown below. The table is rotating at a frequency of f revolutions per second. The coefficient of static friction is u. If the block is not slipping, what is the magnitude and direction of the force of static friction? Your answer may contain R, u, m, f, and physical or numerical constants."

Am I right in saying that the magnitude of the frictional force is just (m*g*u)? My roomate told me that the answer was supposed to be 4(pi)^2*m*R*f^2, but I believe this is inaccurate, because we are not told that the block is at the furthest point it can be placed without slipping. We know that the force of friction is >=4(pi)^2*m*R*f^2, but not that it is equal.

Could someone clarify this for me?

Marty

 

[Handle]

If the table is moving at f = 0 revolutions per second, then the magnitude of the frictional force is zero (your roommates equation supports this intuitive conclusion). The answer should be what your roommate said (at least, my result matched his when I worked it out quickly on a scrap piece of paper). As for the direction, the direction is pointing to the centre of the circle... it is therefore a force in the normal direction.

You cannot say that the magnitude is simply m*g*u. That is the MAXIMUM frictional force. The actual frictional force is given by your roommates equation. If 4 * PI^2 * m * R * f^2 > m * g * u then the block will begin to slip and the frictional force is indeed m * g * u, but the question states that the block is at rest on the turntable.

So, if I'm not mistaken, your roommate is right. Feel free to request further clarification.