Work And Power Worksheet Answer Key

Work and Power Worksheet Answer Key: A Comprehensive Guide

This comprehensive guide provides answers and explanations to common work and power worksheet questions. Understanding work and power is crucial in physics, and mastering these concepts lays a solid foundation for more advanced topics in mechanics and energy. We'll cover various scenarios, from simple calculations involving force and displacement to more complex problems involving efficiency and energy transformations. This guide aims to clarify common misconceptions and provide a step-by-step approach to solving these problems.

Understanding Work and Power: Key Definitions

Before diving into the answers, let's solidify our understanding of the fundamental definitions:

Work: In physics, work (W) is done when a force (F) causes an object to move a certain distance (d) in the direction of the force. The formula for work is:

W = Fd cos θ

where θ is the angle between the force and the displacement. Work is measured in Joules (J), where 1 Joule is equal to 1 Newton-meter (Nm). It's crucial to remember that work is only done if there's movement in the direction of the force. If the force is perpendicular to the displacement (θ = 90°), no work is done.

Power: Power (P) is the rate at which work is done. It measures how quickly work is performed. The formula for power is:

P = W/t

where W is work and t is time. Power is measured in Watts (W), where 1 Watt is equal to 1 Joule per second (J/s). A higher power rating indicates that the same amount of work is done in a shorter time.

Sample Worksheet Problems and Solutions

Let's tackle several example problems, explaining the steps involved in finding the solutions.

Problem 1: Simple Work Calculation

A force of 10 N is applied to push a box 5 meters across a floor. Calculate the work done. Assume the force is applied parallel to the displacement.

Solution:

In this case, θ = 0°, and cos θ = 1. Therefore, the formula simplifies to:

W = Fd = (10 N)(5 m) = 50 J

The work done is 50 Joules.

Problem 2: Work with an Angle

A person pulls a sled with a force of 50 N at an angle of 30° above the horizontal. The sled moves 10 meters horizontally. Calculate the work done.

Solution:

Here, we need to use the complete formula:

W = Fd cos θ = (50 N)(10 m) cos 30°

Since cos 30° = √3/2 ≈ 0.866:

W ≈ (50 N)(10 m)(0.866) ≈ 433 J

The work done is approximately 433 Joules.

Problem 3: Calculating Power

A crane lifts a 2000 kg weight 15 meters in 30 seconds. Calculate the power of the crane. (Assume g = 9.8 m/s²)

Solution:

First, we need to calculate the work done:

1. Calculate the force (weight) acting on the weight: F = mg = (2000 kg)(9.8 m/s²) = 19600 N

2. Calculate the work done: W = Fd = (19600 N)(15 m) = 294000 J

3. Calculate the power: P = W/t = (294000 J) / (30 s) = 9800 W

The power of the crane is 9800 Watts or 9.8 kW.

Problem 4: Efficiency and Power

A motor has a power output of 500 W. It lifts a 100 kg mass to a height of 10 meters in 25 seconds. Calculate the efficiency of the motor.

Solution:

1. Calculate the work done by the motor: W = mgh = (100 kg)(9.8 m/s²)(10 m) = 9800 J

2. Calculate the theoretical power required: P_theoretical = W/t = 9800 J / 25 s = 392 W

3. Calculate the efficiency: Efficiency = (P_output / P_theoretical) * 100% = (500 W / 392 W) * 100% ≈ 127%

This result (over 100%) indicates an error in the problem statement or measurements. Efficiency cannot exceed 100%. This might point to an issue in the given power output or time taken.

Problem 5: Combined Work and Power

A horse pulls a cart with a force of 200 N for 5 minutes at a speed of 2 m/s. Calculate the power exerted by the horse.

Solution:

1. Calculate the distance: Distance = speed x time = 2 m/s x (5 min * 60 s/min) = 600 m

2. Calculate the work done: W = Fd = (200 N)(600 m) = 120000 J

3. Calculate the power: P = W/t = 120000 J / (5 min * 60 s/min) = 400 W

The power exerted by the horse is 400 Watts.

Advanced Concepts and Problem-Solving Strategies

1. Conservative vs. Non-Conservative Forces:

• Conservative forces: The work done by a conservative force is independent of the path taken. Examples include gravity and elastic forces. The work done is only dependent on the initial and final positions.
• Non-conservative forces: The work done depends on the path taken. Examples include friction and air resistance.

2. Kinetic and Potential Energy:

Understanding the relationship between work, kinetic energy (KE = 1/2mv²), and potential energy (PE = mgh) is crucial for solving more complex problems. The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.

3. Energy Conservation:

In systems where only conservative forces are acting, the total mechanical energy (KE + PE) remains constant. This principle is essential for solving problems involving energy transformations.

4. Problem-Solving Approach:

1. Draw a diagram: Visualizing the problem helps clarify the forces and displacements involved.
2. Identify the knowns and unknowns: List the given values and the quantities you need to find.
3. Choose the appropriate formula: Select the relevant equations based on the given information and the unknown variables.
4. Solve the equations: Perform the necessary calculations, being careful with units and significant figures.
5. Check your answer: Ensure that your answer is reasonable and consistent with the problem statement.

Common Mistakes to Avoid

• Forgetting the cosine term: Many students forget to include the cosine of the angle between force and displacement when calculating work.
• Incorrect unit conversions: Always ensure that you use consistent units (e.g., meters for distance, seconds for time).
• Confusing work and power: Remember that work is the amount of energy transferred, while power is the rate at which this energy is transferred.
• Neglecting friction: In real-world scenarios, friction often plays a significant role, and neglecting it can lead to inaccurate results.

Conclusion

Mastering work and power requires a solid understanding of the underlying concepts and a systematic approach to problem-solving. By practicing various problems and understanding the nuances of these concepts, you can build a strong foundation in physics and tackle more challenging problems with confidence. This guide provides a solid foundation; continue practicing different types of problems to improve your understanding and skills. Remember to always double-check your work and ensure your units are consistent throughout your calculations. With consistent effort, you will become proficient in solving work and power problems.