Alvl P1: work, energy and power (ch6) Cheat Sheet by MostAncientDream

Work done is maximum when cos0 = 0 (the force and distance travelled are therefore parallel)

Work done is minimum when cos0 = 90 (the force and distance travelled are therefore perpen­dic­ular)

types of energy:
- kinetic energy
- potential energy
- thermal energy (not covered in this spec point)

for example:
a ball held at a height will have Ep, when dropped and landing on the ground (assuming there is no energy loss) all the energy will be converted into Ek.

Δ E = W --> change in energy in a system = work done on a system

Gravit­ational Potential Energy:

ΔE = W
ΔE = Fxcos0
(work done is force x distance x angle)

where F = ma (in this case a is g)
and distance is hieght travelled

ΔE = mghcos0

as cos0 where 0 is 0' cos0 = 1 so

ΔE = mgh


Kinetic Energy:

ΔE = W
ΔE = Fxcos0
(work done is force x distance x angle)

ΔE = Fs
(cos0 = 1)
ΔE = mas

as v² = u² + 2as
rearrange where u = 0
as = v²/2

therefore
ΔE = 1/2 mv²

example of findign resistive forces going down hill

--top | v=0
------|
-------|
--------|
--bottom | v=8

a ball is roll down from the top to the bottom
-length of the ramp is 7m
-height is 5m

as ΔE = W
energy at top (Ep no Ek) then energy at bottom (Ek no Ep)

from this we know it is all transf­erred (assuming no loss to heat) therefore
ΔE = mgh - 1/2mv²
mgh - 1/2mv² = Fx
(where x is length of ramp)

then just put in numbers to solve for F