Question

The desk as a weight of 75 lb and a center of gravity at G.

The desk has a weight of 75 lb and a center of gravity at G. Determine its initial acceleration if a man pushes on it with a force F = 60 lb. The coefficient of kinetic friction at A and B is mu k = 0.2.

Answer 1

Concepts and reason

When all the supports are removed by replacing them with forces that prevents the translation of body in a given direction that diagram is called free body diagram. When their resultant force and couples becomes equal to zero then the body is said to be in equilibrium.

To apply these equilibrium equations, we need to know the known and unknown forces that act on the body.

Frictional force which opposes the motion of a body. Here, the type of friction is dry friction which opposes the relative lateral motion between two solid surfaces in contact. Dry friction is of two types; static friction between stationary surfaces and kinetic friction between moving surfaces.

In this problem, draw the free body diagram and apply force equilibrium equations and find the least horizontal force applied on the top box in order to cause motion.

Fundamentals

Write the equations of motion.

Here, I is moment of inertia and is the angular acceleration.

The static friction is the friction that always keeps the body in rest, there is some limiting maximum value of this force up to which this frictional force keeps on increasing as the applied force increases.

The maximum value of the frictional force that keeps a body at rest is the static friction.

Here, is the coefficient of static friction.

The frictional force acting on the body when it moves on a surface is:

Here, is the coefficient of static friction and N is the normal reaction force.

Impending motion is defined as the state just before the body starts to move or slip, in case of impending the frictional force acting on the body is:

General sign convention for bending moment: The bending moment is considered positive in counter-clockwise direction and negative in clockwise direction.

General sign convention for vertical force: Forces in the upward direction are considered positive and in the downward direction are considered negative.

General sign convention for horizontal force: Forces towards the right direction are considered positive and towards the left direction are considered negative.

Draw the free body diagram of the desk.

Here, mg is the weight of the desk acting at point G, are the frictional forces acting at point A,B, are the normal reaction at points A,B, is the acceleration acting along the x direction.

Apply force equilibrium equation along y direction.

Substitute for , for , for , and for .

…… (1)

Apply force equilibrium equation along the horizontal direction.

Substitute for , for , for and for .

Substitute for from equation (1).

Ans:

The initial acceleration of the desk is