Lesson: Equilibrium of Extended Objects Physics • 9th Grade

In this lesson, we will learn how to analyze the net effect of the forces and torques acting on objects that have extension in one or two dimensions.

Lesson Plan

Students will be able to

determine the torque due to a force that does not act perpendicularly to the direction in which an object’s extension is considered,
determine the net torque on a one-dimensional object that forces act on nonperpendicularly to the length of the object,
determine the magnitudes of the forces acting on an object that are required for equilibrium of the object, both rotationally and translationally.

Lesson Worksheet

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 ?

Q2:

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?

Q3:

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.