# Worksheet: Equilibrium of Extended Objects

In this worksheet, we will practice analyzing the net effect of the forces and torques acting on objects that have extension in one or two dimensions.

**Q1: **

A 3.8 m long uniform density ramp with a weight of 20 N is at rest at an angle of above the horizontal, as shown in the diagram. A box is dragged up the ramp. At the point where the box is 0.65 m from the top end of the ramp, it exerts a downward force of 32 N on the ramp.

What is the magnitude of ?

What is the magnitude of ?

**Q2: **

A uniform-density plank is at rest at an angle above the horizontal. The plank is supported by a pivot at a point directly below its center of mass. Which of the following diagrams correctly shows the forces acting on the plank due to the pivot? The weight of the plank is shown in orange and the forces due to contact with the pivot are shown in blue.

- A
- B
- C
- D
- E

**Q3: **

A perfectly rigid disk of uniform density has three forces acting on it at different points on its upper surface, as shown in the diagram. The center of mass of the disk does not move.

Find the angle .

Find the magnitude of the force .

Can the disk be in rotational equilibrium if no other forces act on it?

- AThe disk cannot be in rotational equilibrium.
- BIt is not possible to tell from the information in the question.
- CThe disk can be in rotational equilibrium.

**Q4: **

A ladder stands between a wall and a floor at an angle of above the horizontal, as shown in the diagram. A horizontal applied force of 44 N is acting on the ladder at a point 1.3 m along its length from the position of its center of mass.

What is the magnitude of the torque on the ladder around the point due to the horizontal applied force?

What is the magnitude of the torque on the ladder around the point due to its weight?