Question

Three objects are connected by weightless flexible strings as shown in the figure. The pulley has no appreciable mass or friction, and the string connected to theblock on the horizontal bench pulls on it parallel to the bench surface. The coefficients of friction between the bench and the block on it areμ_s = 0.660 and μ_k = 0.325. You observe that this system remains at rest. Find (a) the mass of and (b) the friction force on theblock on the bench.

Answer 1

Okay so for part A, you must balance the forces between the blockon the right side, and the tension in the pulley.

So, you know that mg block=9.8*35=343N. Since the pulley must havethe same tension on both sides, you know that the chord holding Aup has the same tension.

However, it is the y-component of the pulley that is holding A up,so m(A)g=343cos(51).

m(A)=22.03kg

For part B, since the whole system is at rest, the block must bebeing held back by static friction which is equal to the horizontalcomponent of the tension before. (I'm not entirely sure if this istrue or not, because the explanation is not descriptive enough ofthe system, but if all of those are connected, this should betrue)

So, the horizontal component would just be 343sin(51) = 266.561

Hope that helps!

***Note: If part B is wrong, then the only other way to do it wouldbe to do μ*N where μ is the coefficient of staticfriction and N =mg. I'm pretty sure the first answer is rightthough because you can never be sure that static friction is at itsmax unless it says so.