Mass m1 rests on a rough horizontal surface while mass m2 hangs over a massless,
ID: 1966554 • Letter: M
Question
Mass m1 rests on a rough horizontal surface while mass m2 hangs over a massless, frictionless ideal pulley.
Explain in detail how this setup could be used to determine the coeficient of static friction u-s between m1 and the table. (Remember, this is static friction, so what is the acceleration?) That is, explain carefully
what quantities must be measured,
with what instruments quantities are to be measured (only measuring instruments that you have used previously in this course),
what procedures are to be used, in particular how the maximum value of m2 is determined,
and derive an equation for u-s in terms of the quantities above.
Explanation / Answer
Since the system is in static equilibrium, it is not moving and the acceleration is zero. The only quantities that need to be measured are the mass of each object and you just need a regular scale to do that. After you have the mass of each object, find the weight of M2 (W-M2) by multiplying it's mass in kilograms (m2) by the acceleration due to gravity (9.8m/s^2). This value is also the maximum value of M2. If you add up the forces in the y-direction, you find that the tension in the cable holding M2 in place is equal to the weight of M2, since the system is in static equilibrium. Next, find the weight of M1 (W-M1) the same way you did with M2. Add the forces in the y-direction again and you find the normal force acting on M1 is equal to W-M1. If you add the forces in the x-direction, you'll find that static friction equals tension, which also equals W-M2. Friction equals u-s times the normal force acting on M1, which also equals W-M1. Divide by W-M1. Now you should have the expression u-s = (W-M2)/(W-M1). This answers actually simplifies since the weight of each object was the mass divided by the acceleration due to gravity. You can cancel out the acceleration so you get: u-s = m2/m1