If you assume in advance that the block will not move, then the equations you wrote down are correct. But they are not written down in a convenient coordinate system. Let's work with your equations first.

The assumption that the block will not move can be incorrect. However, this is not a problem, because you can use your equations to solve for both the normal force N and the friction force f. The value for f you get must then be interpreted as the friction force that is necessary for the block to remain at rest. You then calculate the ratio of f and N to see if it exceeds us. If not, then the block will indeed remain at rest. If the ratio exceeds us, then the block will accelerate. The friction force of f you ...

Solution Summary

The friction force acting on a block is determined. A free-body diagram is provided for the question.

SEE ATTACHMENT #1 for a diagram with parameters.
Block B whose weight B= 22 nt, is placed on top of Block A whose weight is A= 44 nt.
The coefficient of friction for all surfaces is f= .20. A horizontal force P is applied to A to slide both objects across the horizontal table.
Find the maximum force P such that block B d

One block rests upon a horizontal surface. A second identical block rests upon the first one. The coefficient of static friction between the blocks is the same as the coefficient of static friction between the lower block and the horizontal surface. A horizontal force is applied to the upper block, and its magnitude is slowly in

Please see attached file for full problem description.
A 4.40-kg block is placed on top of a 5.50-kg slab. If the slab is held fixed, the block can be made to slip only if a minimum force of 12.0 N is applied to it. The assembly is now placed on a horizontal, frictionless surface, as shown in the diagram.
a) What is th

Find the force P necessary to push a 50.6 kg block down an incline of 32.4 degrees with an acceleration of 1.78 m/s^2. P is parallel to the incline and the coefficient of friction between the block and the incline surface is 0.805.
Picture is attached.

1. A file cabinet weighing 1500 N is at rest on the floor. The coefficient of static friction between the floor and the cabinet is 0.5. What is the minimum force required to make the file cabinet move horizontally?
2. A force of 10 N applied to a block of ice with a mass of 10 kg moves it over a factory floor with a constant

Two blocks, of weights 3.6 N and 7.2 N, are connected by a mass-less string and slide down a 30 degree inclined plane. The coefficient of kinetic friction between the lighter block and the plane is 0.10; that between the heavier block and the plane is 0.20. Assuming that the lighter block leads, find a) the magnitude of the acce

ABCD is a cross-section of a uniform rectangular block of mass 20kg. AB is 0.75m and BC is 1m. The block rests with A on rough horizontal ground with AB at 20 degrees to the horizontal. It is held in place by a horizontal force P N applied at C. Given that the block is on the point of slipping, find the value of P and the coeffi

To measure the static friction coefficient between a 1.9 kg block and a vertical wall, the setup shown in the drawing is used.
A spring (spring constant = 418 N/m) is attached to the block. Someone pushes on the end of the spring in a direction perpendicular to the wall until the block does not slip downward. If the spring i

A block of mass m1 = 4.70 kg sits on top of a second block of mass m2 = 16.3 kg, which in turn is on a horizontal table. The coefficients of friction between the two blocks are µs = 0.300 and µk = 0.100. The coefficients of friction between the lower block and the rough table are µs = 0.600 and µk = 0.500. You apply a consta