Chapter 8, Problem 1CQ

To determine

To sketch: The force at point P to make the rod to be in the static equilibrium.

Explanation of Solution

Given data:

Refer to the Figure Q8.1 in the textbook for the force that acts at the tip of the rod.

Explanation:

The following are the conditions for an object to be in static equilibrium condition.

• The net force in the x-component (horizontal direction) must be zero.
• The net force in the y-component (vertical direction) must be zero.
• The net torque about every point must be zero.

The conditions are expressed mathematically as follows:

Write the expression for static equilibrium condition of the force in the x-component as follows:

${\displaystyle \sum F_x}=0$

Here,

${\displaystyle \sum F_x}$ is the sum of the forces acting on the object in the x-component (horizontal direction).

Write the expression for static equilibrium condition of the force in the y-component as follows:

${\displaystyle \sum F_y}=0$

Here,

${\displaystyle \sum F_y}$ is the sum of the forces acting on the object in the y-component (vertical direction).

Write the expression for static equilibrium condition of the torques as follows:

${\displaystyle \sum \tau }=0$

Here,

${\displaystyle \sum \tau }$ is the sum of the torques acting on the object.

All the three conditions must be satisfied in order for the object to be in the static equilibrium condition.

Calculate the torques about the pivot point in Figure Q8.1 in the textbook. The sum of the torques must be zero in order to bring the rod in the static equilibrium condition. The net torque is required to make zero by applying the force at the point P in the rod. The following are the three possible cases to make the net torque to zero and subsequently bring the rod in the static equilibrium.

Draw the possible forces at the point P in the rod in order to bring the rod to the static equilibrium condition as shown in Figure 1.

From Figure 1, the three possible cases to bring the rod in static equilibrium condition are shown.

Conclusion:

Thus, the force at the point P is drawn to bring the rod in the static equilibrium condition.