This worksheet provides a comprehensive overview of work, energy, and power, including definitions, formulas, and solved examples to help you master these fundamental physics concepts. We'll explore the relationships between these quantities and delve into various scenarios to solidify your understanding.
What is 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. It's crucial to understand that the force must be applied in the direction of movement for work to be done. If the force is perpendicular to the displacement, no work is done.
Formula: W = Fd cosθ
Where:
- W represents work (measured in Joules, J)
- F represents force (measured in Newtons, N)
- d represents displacement (measured in meters, m)
- θ represents the angle between the force and the displacement.
Important Note: If the force and displacement are in the same direction, θ = 0°, and cosθ = 1, simplifying the formula to W = Fd.
Example 1: Calculating Work
A person pushes a box with a force of 50 N across a floor for a distance of 10 m. Calculate the work done if the force is applied parallel to the floor.
Solution:
Since the force is parallel to the displacement, θ = 0°, and cosθ = 1.
W = Fd = (50 N)(10 m) = 500 J
The work done is 500 Joules.
What is Energy?
Energy (E) is the capacity to do work. It exists in various forms, including:
- Kinetic Energy (KE): The energy of motion. Formula: KE = 1/2mv² (where m is mass and v is velocity)
- Potential Energy (PE): Stored energy due to position or configuration. This includes gravitational potential energy (PE = mgh, where g is acceleration due to gravity and h is height) and elastic potential energy (PE = 1/2kx², where k is the spring constant and x is the displacement from equilibrium).
What is Power?
Power (P) is the rate at which work is done or energy is transferred. It measures how quickly work is accomplished.
Formula: P = W/t = ΔE/t
Where:
- P represents power (measured in Watts, W)
- W represents work (measured in Joules, J)
- t represents time (measured in seconds, s)
- ΔE represents the change in energy.
Example 2: Calculating Power
A machine lifts a 100 kg object to a height of 5 m in 2 seconds. Calculate the power of the machine. (Assume g = 9.8 m/s²)
Solution:
First, calculate the work done:
W = ΔPE = mgh = (100 kg)(9.8 m/s²)(5 m) = 4900 J
Then, calculate the power:
P = W/t = 4900 J / 2 s = 2450 W
The power of the machine is 2450 Watts.
Practice Problems
- A horse pulls a cart with a force of 200 N for a distance of 50 m. What is the work done by the horse?
- A 0.5 kg ball is thrown upward with a velocity of 20 m/s. What is its kinetic energy at the highest point of its trajectory?
- A 50 kg person climbs a 10 m high ladder in 5 seconds. What is the power exerted by the person? (Assume g = 9.8 m/s²)
- A spring with a spring constant of 100 N/m is compressed by 0.2 m. What is its potential energy?
This worksheet provides a solid foundation for understanding work, energy, and power. Remember to always consider the units and ensure you are using the appropriate formulas for each scenario. Further exploration of these concepts will enhance your understanding of fundamental physics principles.
