Wednesday, May 7, 2025

SIN Bin: 2006, Problem 4

By Department Faculty

Problem

Diagram of problem showing the block of mass against a wall being pushed slightly upwards by a force at an angle.

A block of mass m = 2.25kg is pushed against a vertical wall by a force F which makes an angle (θ) of 36.9 degrees to the horizontal. If the coefficient of static friction between the block and the wall is µs = 0.25 what is the minimum force necessary to keep the block statio0nary?

  1. 11.6
  2. 13.8
  3. 16.5
  4. 27.6
  5. 110

Solution SIN Bin: 2006, Problem 4

(d) 27.6 N

We are seeking the minimum force necessary to keep the block stationary so the frictional force will be directed upwards and will be equal in magnitude to µsFN where FN is the magnitude of the normal force. Newton's second law will give for the vertical and horizontal components:

0 = FN - Fcosθ & 0 = Ff - mg + Fsinθ

Eliminating the frictional and normal froces with the help of Ff = µsFNgives:

mg - fsinθ = µsFcosθ --> F = mg/(sinθ + µscosθ) = 27.6 N