A block of mass M is placed on a rough horizontal surface. The coefficient of static friction between the block and the surface is . The block is to be pulled by applying a force to it. Determine the minimum force required to slide the block, and the direction in which this force should act.

Step-by-step solution

Let the force F be applied at an angle with the horizontal. The normal reaction N from the surface is given by equating vertical forces: N + F = Mg N = Mg - F The maximum static frictional force is: f = N = (Mg - F ) For the block to just slide, the horizontal component of the applied force must be equal to the maximum static friction: F = (Mg - F ) F + F = Mg F ( + ) = Mg F = Mg + To find the minimum force, the denominator + must be maximum. The maximum value of a + b is a^2 + b^2 . Maximum value of + = 1 + ^2 Thi