Topic 8: Work, energy and power
Work done on an object by a force ~ the product of the displacement and the
component of the force parallel to the displacement
W = FΔxcosθ
W - work done (J) (energy transferred - scalar ∴ no direction)
F - force (N)
Δx - displacement
θ - the angle between the force and the displacement
Positive work: force increases the energy of object
Negative work: force decreases the energy of object
Work at an angle
cosθ: positive
horizontal component of F is in same
direction as Δx
cosθ: negative
horizontal component of F is in opposite
direction as Δx (still parallel direction)
, Friction
If there's a rough surface, either look at work done by each force or first calculate Fnet in
the horizontal direction
Net work done:
Wnet = Wa + Wf + WN + Wg
Alternative method to calculate Wnet:
Wnet = FnetΔxcosθ (Fnet in direction 0°)
- Fx = Fcosθ
- Fnet = Fx - Ff
What would happen to the work done if the angle θ decreases?
Decrease θ → increase Fx → increases Fnet → increases Wnet
Slopes
* Component of gravity (Fg||) moves object of mass down the slope
Work done on an object by a force ~ the product of the displacement and the
component of the force parallel to the displacement
W = FΔxcosθ
W - work done (J) (energy transferred - scalar ∴ no direction)
F - force (N)
Δx - displacement
θ - the angle between the force and the displacement
Positive work: force increases the energy of object
Negative work: force decreases the energy of object
Work at an angle
cosθ: positive
horizontal component of F is in same
direction as Δx
cosθ: negative
horizontal component of F is in opposite
direction as Δx (still parallel direction)
, Friction
If there's a rough surface, either look at work done by each force or first calculate Fnet in
the horizontal direction
Net work done:
Wnet = Wa + Wf + WN + Wg
Alternative method to calculate Wnet:
Wnet = FnetΔxcosθ (Fnet in direction 0°)
- Fx = Fcosθ
- Fnet = Fx - Ff
What would happen to the work done if the angle θ decreases?
Decrease θ → increase Fx → increases Fnet → increases Wnet
Slopes
* Component of gravity (Fg||) moves object of mass down the slope
