Question

A large crate sits on the floor of a warehouse. Paul and Bob apply constant horizontal forces to the crate. The force applied by Paul has a magnitude of 60.0 N and a direction of 61.0° south of west. What is the magnitude and direction of the force applied by Bob?

1) Cannot be determined
2) 60.0 N, 61.0° south of west
3) 60.0 N, 61.0° north of east
4) 60.0 N, 61.0° south of east

Answer 1

The forces applied by Paul and Bob must cancel each other out, and by using trigonometry, we can determine that Bob's force is 60.0 N at an angle of 61.0° north of east, balancing Paul's force (Option 3).

Step-by-step explanation:

The question involves resolving forces and understanding vector addition.

Given that Paul applies a force at an angle of 61.0° south of west, and we have a free-body diagram showing a northward force of 64 N and a westward force of 38 N, we can infer that the forces applied by Paul and Bob must balance each other out for the crate to be stationary.

Since Paul's force has a southward component, Bob must be applying a force with a northward component to balance it.

To find the magnitude and direction of Bob's force, we can use trigonometric functions.

Paul's force breaks down into two components: a horizontal (westward) component and a vertical (southward) component.

Given the angles and the magnitude of Paul's force, we can use trigonometry to find these components:

• The westward component (Fw) is 60.0 N × cos(61.0°)
• The southward component (Fs) is 60.0 N × sin(61.0°)

To balance the forces, Bob must apply a force equal in magnitude but opposite in direction to Paul's force. This would suggest option 3: 60.0 N, 61.0° north of east.

This balances the southward component with a northward component and the westward component with an eastward component.

Hence, the correct answer is Option 3.