This worksheet provides a comprehensive overview of work, energy, and power, three fundamental concepts in physics. We'll explore the definitions, formulas, and relationships between these concepts, followed by practice problems to solidify your understanding. This is designed for students studying introductory physics, but can serve as a refresher for anyone needing a review.
Understanding Work
Work, in physics, is defined as the energy transferred to or from an object via the application of force along a displacement. It's a scalar quantity, meaning it only has magnitude, not direction.
Formula: Work (W) = Force (F) x Distance (d) x cos(θ)
Where:
- W is work, measured in Joules (J)
- F is the force applied, measured in Newtons (N)
- d is the displacement, measured in meters (m)
- θ is the angle between the force and the displacement.
Important Note: Work is only done if there's a displacement in the direction of the applied force. If the force is perpendicular to the displacement (θ = 90°), no work is done.
Types of Work:
- Positive Work: Work done in the direction of motion (0° ≤ θ < 90°).
- Negative Work: Work done opposite to the direction of motion (90° < θ ≤ 180°). Examples include friction or braking forces.
- Zero Work: Work done when the force is perpendicular to the displacement (θ = 90°).
Understanding Energy
Energy is the capacity to do work. It exists in various forms, including:
- Kinetic Energy (KE): The energy of motion. Formula: KE = ½mv² (where m is mass and v is velocity)
- Potential Energy (PE): Stored energy. Several types exist, including:
- Gravitational Potential Energy (GPE): Energy stored due to an object's position relative to a gravitational field. Formula: GPE = mgh (where m is mass, g is acceleration due to gravity, and h is height)
- Elastic Potential Energy: Energy stored in a stretched or compressed spring or elastic material.
- Mechanical Energy: The sum of kinetic and potential energy.
Understanding Power
Power is the rate at which work is done or energy is transferred. It's a scalar quantity.
Formula: Power (P) = Work (W) / Time (t) or Power (P) = Force (F) x Velocity (v)
Units: Power is measured in Watts (W), where 1 Watt = 1 Joule/second.
Practice Problems
Problem 1: A 50 N force is applied to push a box 10 m across a floor. If the force is applied parallel to the floor, calculate the work done.
Problem 2: A 2 kg object is lifted 5 m vertically. Calculate the change in gravitational potential energy. (Assume g = 9.8 m/s²)
Problem 3: A 1000 kg car accelerates from rest to 20 m/s in 10 seconds. Calculate the power output of the car's engine.
Problem 4: A person pushes a 20 kg cart with a force of 10 N at an angle of 30 degrees to the horizontal. If they push the cart 5 m, how much work do they do?
Problem 5: A crane lifts a 1000 kg load vertically at a constant speed of 2 m/s. What is the power output of the crane? (Assume g = 9.8 m/s²)
Solutions (To be added after student attempts)
This worksheet provides a foundation for understanding work, energy, and power. Remember to always include units in your calculations and consider the direction of forces when calculating work. Further exploration into more complex scenarios and energy transformations is encouraged.
