AP Physics: Work and Energy

open system

a system for which matter and energy are allowed to enter or leave the system

• work is done

closed system

a system for which matter and mechanical energy do not cross the system boundary

• energy is not transferred by work but can transform

conservative forces

a mechanical force that transforms energy from one mechanical form to another mechanical form. They ‘conserve’ or keep energy in the mechanical forms of Ug, Us, and K

• force of gravity and spring force

kinetic energy

• “K”

• energy of motion

• higher mass/speed = more K

• scalar quantity (speed)

  • cannot be negative

• K = ½ m v²

gravitational potential energy

• ‘Ug’

• energy stored in a gravitational field

• associated with weight and distance above a reference line

• Ug = mgh

• is a scalar quantity

• g = gravitational field strength so use universal law when in space (g=GM/r²)

  • general form of Ug is Ug = -Gm1m2/r

• only systems containing a planet, not objects, can have Ug

elastic potential energy

• ‘Us’

• energy stored in the elastic nature of an object

• energy of position

• Us = ½ k ∆x²

• scalar quantity

how to define systems

define systems to include all objects interacting by a ‘conservative force’ (Fg/Fs)

• these forces transform energy

• exclude objects that apply force that transforms energy in/out of the system

work

work is a force applied over a displacement parallel to the displacement

• W = Fdcosθ = ∆E

• only the parallel component of F to the displacement does the work

• changes the energy of an object/system

• is a scalar quantity

  • F+d in same direction —> work is in

  • F+d in opp direction —> work is out

conservation of mechanical energy

• total energy of an isolated system does not change (∆E = 0)

• Ki +Ugi + Usi = Kf +Ugf + Usf

• energy can transform from one to another by conservative forces

work energy principle

work is done by a push or pull on an open system to tranfser energy in/out of the system - changes E

• W = ∆E

• Ki + Ugi + Usi + W = Kf + Ugf + Usf

power

the rate at which work is done

• P = W/t = Fd/t = F d/t = Fv = ∆E/t

• measured in watts —> J/s

• scalar quantity

common misconceptions

1. energy is used up or recycled

2. something not moving has no energy

3. force acting on an object does work even if it doesnt move

4. energy is destroyed in transformations

5. Ug is the only potential energy

6. a single object can have Ug

7. the same types of energy exist regardless of system

8. when an object is released the Ug immediately becomes K

9. energy isnt related to newtons laws

10. energy is a force

11. Ug lost always equals K gained

F vs position

• area under the curve is workm

  • area above x axis is positive

  • area below x is negative