College Physics I – Step-by-Step Guidance for Midterm Review Problems

Q4. Three forces, $F_1 = 20.0$ N, $F_2 = 40.0$ N, and $F_3 = 10.0$ N act on an object with a mass of $2.00$ kg which can move along a frictionless inclined plane as shown in the figure. The questions refer to the instant when the object has moved through a distance of $0.600$ m along the surface of the inclined plane in the upward direction. Calculate the amount of work done by (a) $F_1$, (b) $F_2$, (c) $F_3$.

Background

Topic: Work and Energy

This question tests your understanding of how to calculate the work done by different forces acting on an object moving along an inclined plane. You need to consider the direction of each force relative to the displacement.

Key Terms and Formulas

• Work ($W$): The energy transferred by a force acting over a distance.

• Formula: $W = F d \cos\theta$

• $F$ = magnitude of the force

• $d$ = displacement (distance moved along the plane)

• $\theta$ = angle between the force and the direction of displacement

Step-by-Step Guidance

1. Identify the direction of displacement: The object moves $0.600$ m upward along the inclined plane.

2. For each force, determine the angle $\theta$ between the force and the direction of displacement using the diagram.

3. Set up the work formula for each force: $W = F d \cos\theta$.

4. Plug in the values for $F_1$, $F_2$, and $F_3$, the displacement $d = 0.600$ m, and the appropriate angle for each force.

Try solving on your own before revealing the answer!

Final Answer:

(a) $W_{F_1} = 12.0$ J

(b) $W_{F_2} = -20.8$ J

(c) $W_{F_3} = 3.0$ J

Each answer is found by applying $W = F d \cos\theta$ for the respective force and angle.