notes/physics-work

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Work.

Amount of energy transferred by a force, measured in joules (J).
Work formula: W = Fdcosθ
- θ is the direction of the acting force F relative to the displacement d
- Horizontal work: cosθ = 1
- Vertical work: cosθ = 0
  - No work is done as Fdcosθ = 0
Net work is the work of all forces on an object added up.
Work-energy principle says that the net work done on a object is equal to the change in KE of the object.
- W(net) = KE(f) - KE(i)
- If the object started at rest, the initial KE is zero.
- This means that the net work done is equal to the the final KE.
Things to remember:
- Forces acting perpendicular to displacement do zero work.
- The sign of the work means something.
  - Positive work (+) means it receives energy from surroundings.
  - Negative work (-) means it gives energy to surroundings.
    - Negative work occurs when force is opposite the direction of displacement.

The energy an object has because of its motion.
- KE = (1/2)mv^2
Change in kinetic energy is the net work done on an object.
- KE(f) - KE(i) = W(net)

Given a spring that moves d meters when a net force F newtons is applied:
- The spring constant is k = F/d
- The restoring force is F(r) = -kx
  - The negative sign refers to the reversal of the spring.
- This is Hooke's Law, which states the the restoring force of a spring is proportional to its displacement.
Relating springs to work:
- W = (1/2)kx^2
- Once the spring is at rest, its potential energy is equal to the work done.
  - PE = (1/2)kx^2

Energy due to position of an object in a gravitational field.
Formula is U = mgh:
- U is the gravitational potential energy.
- m is the object's mass.
- g is the gravitational acceleration.
- h is the change in height.
When finding U, the specific measures of height (aka where h = 0) is unnecessary as the gravitational potential energy only depends on change in height.
- To find the change in height just do h(f) - h(i)

Energy is neither created nor destroyed, but can only be transformed from one form to another or from one system to another.
- KE(i) + PE(i) = KE(f) + PE(f)
  - Assuming no dissipative forces.

Power is the amount of work done over time.
- P = W/t
- Measured in J/s, called a watt (W)
This is technically average power, as we measure the power over a time interval.
- Instantaneous power would be power at a specific instance of time, rather than over an interval.
- P = Fvcosθ, where v is the instantaneous velocity at the desired point in time.