work energy and power worksheet answer key

Lemon

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04-02-2025

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Work, Energy, and Power Worksheet: Answer Key

This answer key provides solutions to a common Work, Energy, and Power worksheet. Note that specific numerical values might vary slightly depending on the worksheet version and rounding practices. Always double-check your calculations and units!

Understanding the Fundamentals:

Before diving into the answers, let's briefly review the key concepts:

• Work (W): Work is done when a force causes an object to move a certain distance in the direction of the force. The formula is: W = Fd cosθ, where F is force, d is displacement, and θ is the angle between the force and displacement vectors. The SI unit for work is the Joule (J).

• Energy (E): Energy is the capacity to do work. Different forms of energy exist (kinetic, potential, thermal, etc.), and energy can be transferred and transformed. The SI unit for energy is also the Joule (J).

• Power (P): Power is the rate at which work is done or energy is transferred. The formula is: P = W/t or P = E/t, where t is time. The SI unit for power is the Watt (W), which is equal to one Joule per second (J/s).

Worksheet Problem Solutions (Example Problems):

The following are example solutions, tailored to commonly found problems in work, energy, and power worksheets. Your specific worksheet might have different numerical values.

Problem 1: Calculating Work

• Question: A 10 kg box is pushed across a frictionless floor with a force of 20 N over a distance of 5 m. Calculate the work done.

• Solution: Since the floor is frictionless, the angle between force and displacement is 0 degrees (cos 0° = 1). Therefore, W = Fd = (20 N)(5 m) = 100 J.

Problem 2: Calculating Kinetic Energy

• Question: A 2 kg ball rolls at a speed of 4 m/s. What is its kinetic energy?

• Solution: The formula for kinetic energy is KE = (1/2)mv², where m is mass and v is velocity. KE = (1/2)(2 kg)(4 m/s)² = 16 J.

Problem 3: Calculating Potential Energy

• Question: A 5 kg object is lifted 3 m above the ground. What is its potential energy? (Assume g = 9.8 m/s²)

• Solution: The formula for potential energy is PE = mgh, where m is mass, g is the acceleration due to gravity, and h is height. PE = (5 kg)(9.8 m/s²)(3 m) = 147 J.

Problem 4: Calculating Power

• Question: A machine lifts a 100 kg weight 20 m in 5 seconds. What is the power output of the machine? (Assume g = 9.8 m/s²)

• Solution: First, calculate the work done: W = mgh = (100 kg)(9.8 m/s²)(20 m) = 19600 J. Then, calculate the power: P = W/t = 19600 J / 5 s = 3920 W.

Problem 5: Combined Work and Energy Problem

• Question: A 500 N force is applied to a cart, causing it to accelerate from rest across a frictionless surface. After traveling 10 meters, the cart's velocity is 5 m/s. Calculate the work done and the cart's mass.

• Solution:

  • Work: W = Fd = (500 N)(10 m) = 5000 J.
  • Kinetic Energy: The work done is equal to the cart's change in kinetic energy (since the surface is frictionless). Therefore, KE = 5000 J.
  • Mass: Using the kinetic energy formula, KE = (1/2)mv², we can solve for mass: m = 2KE/v² = (2 * 5000 J) / (5 m/s)² = 400 kg

Remember: This is an example. Your worksheet may contain different problems and require application of these principles to varied scenarios. Always show your work clearly, including formulas and units, for full credit. If you have specific problems from your worksheet, provide them, and I will gladly help solve them.