Chapter 6: Problem 12
A boxed 10.0-kg computer monitor is dragged by friction 5.50 m upward along a conveyor belt inclined at an angle of 36.9\(^\circ\) above the horizontal. If the monitor's speed is a constant 2.10 cm/s, how much work is done on the monitor by (a) friction, (b) gravity, and (c) the normal force of the conveyor belt?
Short Answer
Step by step solution
Identify the forces involved
Calculate the work done by friction
Calculate the work done by gravity
Calculate the work done by the normal force
Calculate numerical values
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Inclined Plane Problems
Key things to consider for inclined plane problems include:
- Identifying the incline angle: This affects the gravitational force component along the plane.
- Analyzing forces: Typically involve gravity, the normal force, and friction.
- Calculating displacement parallel to the incline, which helps determine work done by various forces.
Frictional Force Calculations
Points to remember when calculating frictional forces include:
- Friction opposes motion, thus the work done is generally negative.
- Net work is zero when speed is constant, meaning frictional and other forces balance out.
- The work-energy principle can assist in identifying frictional forces by aligning with known energy changes.
Gravitational Work
Consider the following when calculating gravitational work:
- The gravitational force (\( F_{\text{gravity}} = m \cdot g \)) depends on the mass and gravitational acceleration.
- The angle affects the cosine component in the work equation, where\( \cos(126.9^\circ) \) indicates the direction opposing movement.
- Negative work illustrates gravity acting against the upward motion.