Work, energy, and power

Define key terms:
- Work
- Energy
- Mechanical energy
- Potential energy
- Kinetic energy
- Power
Relate work to force and the distance over which force is applied.
Outline the work-energy theorem.
State the law of conservation of energy.
Explain how mechanical energy can be converted between potential and kinetic forms.
State the SI units of energy and power.
Integrate concepts of acceleration, force, inertia, momentum, impulse, work, energy, and power in discussing stationary and moving objects.
Perform simple calculations involving force, acceleration, momentum, impulse, work, energy, and power (Week 2 Learning Goals 1, 5 – 11).

Definition: In physics, "work" has a very specific meaning. It is the ability to move an object against a force.
Formula: Work (W) is defined as the product of the force (F) on an object and the distance (d) through which the object is moved by that force:
- W = F imes d
Key Concept: When work is done on an object, it changes the object's energy situation. If the object does not change location as a result of an applied force, no work is done.

Work is done against another force, such as lifting an object upward against the downward force of gravity.
Example: Lifting an object proves work was done as the position of the object changes relative to what it would have otherwise been.
Work can also change the speed of an object, either increasing or decreasing it. The proof of work is the change in the object's position.

Work Formula: W = F imes d
The right side of the equation has units of Newtons (N) multiplied by meters (m), meaning the left side also must have the same unit.
Derived Unit: Joule (abbreviated as "J") is the derived unit for work.
Definition of Joule: 1 Joule = 1 Newton x 1 meter.

Test Questions:
- Question A: If we push a chair and slide it along a floor for 1 meter at a steady speed, is work being done?
- Answer: Yes, because the position of the object changes while the force is applied.
- Question B: You lift a box over your head, then hold it in position for 5 seconds. Is work done on the box?
- Answer: Work is done on the box ONLY during the lift. There is no work done during the hold as neither the position nor the speed of the box changes.

Definition: Energy is the ability to do work. When energy is acquired by an object, it can do work on another object if conditions allow.
Work transfers energy from one system to another.
Forms of Energy: Energy takes many forms, which will be studied in the course.
Unit of Energy: Energy is measured in Joules.

Definition: Mechanical energy is related to motion.
Forms of Mechanical Energy:
- Potential Energy: Energy due to relative position.
- Kinetic Energy: Energy due to motion.

When work is done on an object to position it relative to another location, it stores energy as potential energy.

Stretching an elastic band applies a force to move one end further from the other end of the band:
- Work is done upon applying this force through a distance.
- Energy is stored while the band is held in that stretched position.
- If released, the band returns to its relaxed state, showcasing the presence of potential energy.

Potential energy is stored by virtue of an object's position while restrained in a location.

Question: If you lift a ball 1 meter above the ground, does it have potential energy? What happens if it is raised to a height of 2 m?
- The potential energy increases as more work is done to raise the ball to a greater height.

An object in motion has kinetic energy, which enables it to do work as it interacts with other objects.
The energy comes from the interaction that put the object in motion.
While in motion, kinetic energy can be transferred when colliding with another object.
Kinetic Energy is also the work that the object can do when brought to rest.

Calculate Kinetic Energy: For a 1.0 kg ball moving at 10 m/s:
- KE = rac{1}{2} (1.0 ext{ kg}) (10 ext{ m/s})^2
- This equals 50 Joules.
To reach this speed, the ball needs 50 Joules of work done on it.

An external force must be applied to change an object's state of motion, which involves doing work on it.
The quantity of work required depends on the change in the object's velocity:
- ext{Work} = ext{Force} imes ext{Distance}

Work Calculation for Increased Speed:
- Doubling the speed from 10 m/s to 20 m/s:
- KE ext{ at 20 m/s} = rac{1}{2} mv^2 ext{ where } v = 20 ext{ m/s}
- This leads to:
- KE = 4 imes 50 ext{ Joules} = 200 ext{ Joules} ext{ (when v doubles)}

Equating kinetic energy with work done:
- ext{Work} = ext{Change in KE}
- ext{Work} = KE_{ ext{final}} - KE_{ ext{initial}}
- Thus, F imes d = KE_{ ext{final}} - KE_{ ext{initial}}

Mechanical energy relates to an object's position and movement.
When an object moves, its potential energy and kinetic energy change.
The sum of potential and kinetic energy remains constant until work is done on another system.

Scenario: Pick up a ball and hold it 1 m above the ground:
- Work done is F imes d (with d = 1 m).
- As the ball is held stationary, it possesses potential energy equal to the work done.
- When the ball is dropped, potential energy decreases while kinetic energy increases, approaching 100% kinetic energy just before it hits the ground.
- The total energy equals the initial work done lifting the ball.

The falling ball has kinetic energy, capable of doing work on any objects it collides with (e.g., another ball).
Upon collision, the first ball transfers energy to the second, leading to a redistribution of energy while conserving total energy.