# Determine the force p required to maintain equilibrium in case (a).

Determine the force P required to maintain equilibrium in cases a, b, & c. The block weighs 100 lb.

## General guidance

Concepts and reason
The external force and couple moment acting on a body can be reduced to an equivalent resultant force and resultant couple moment. When this resultant force and resultant couple moment is both equal to zero then the body is said to be in equilibrium.

The major assumption for applying these equilibrium equations is that the body remains rigid.

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

Fundamentals

Write the equilibrium equations.

Here, the resultant force is and the resultant moment about any arbitrary point is .

For the calculation of force P, we must use force equilibrium equation in vertical direction mentioned above.

Sign Convention for force: Force acting upward is positive and downward weight is negative.

## Step-by-step

### Step 1 of 3

a)

Draw the system which is used to lift a load of as shown below.

Draw the free body diagram of pulley D as shown below.

Consider the equilibrium of vertical forces.

…… (1)

Here, the force required is and the tension is .

Draw the free body diagram of pulley B as shown below.

Consider the equilibrium of vertical forces.

…… (2)

Here, W is the weight.

Substitute equation (1) in equation (2).

The force required to maintain the equilibrium is 25 lb.

Draw the free body diagram to see the internal forces and use equilibrium equation in vertical direction and balance the pulley using the block weights.

### Step 2 of 3

b)

Draw the system which is used to lift a load of as shown below.

Draw the free body diagram of pulley A as shown below.

Consider the equilibrium of vertical forces.

The force required to maintain the equilibrium is 33.3 lb.

Draw the free body diagram to see the internal forces and use equilibrium equation in vertical direction and balance the pulley using the block weights.

### Step 3 of 3

c)

Draw the system which is used to lift a load of as shown below.

Draw the free body diagram of pulley A as shown below.

Consider the equilibrium of vertical forces.

…… (1)

Draw the free body diagram of pulley B as shown below.

Consider the equilibrium of vertical forces.

…… (2)

Substitute equation (1) in equation (2).

The force required to maintain the equilibrium is 11.1 lb.

Draw the free body diagram to see the internal forces and use equilibrium equation in vertical direction and balance the pulley using the block weights.