Conservative/Non-conservative

Forces and Work

- A force is conservative if the work it does on an object

does NOT depend on the path the object takes.

- A force is conservative if, when moving an object thru

a closed path (starting/ending at same position), it does

no net work.

Conservative forces

- gravitational

- elastic (spring)

- electric

Non-conservative forces

- Frictional forces

- Air resistance/drag

- Tension, thrust (of engine), pulling/pushing forces

- Normal force

Non-conservative Work

The work done by all non-conservative forces acting on an object is equal to the change in the KE plus the change in the PE of the object.

W_nc = ΔKE + ΔPE

If there are NO non-conservative forces acting, W_nc = 0,

and

0 = KE_f - KE_i + PE_f - PE_i

0 = (KE_f + PE_f) - (KE_i + PE_i)

0 = E_f - E_i

E_f = E_i

This is the principle of conservation of mechanical energy.

Power

- Power is the (time) rate at which work is done.

- Power is work done per unit time.

- High output power is associated with being able to do

a large amount of work (output a lot of energy) in a

short amount of time.

P = W / t

where W is work done and t is the elapsed time.

Units will be energy per time units. In SI, that will be

joules/second (J/s). This unit has the special name of

watts (W). Note that a watt also = N m/s or kg (m²/s³).

Engine power is commonly rated in horsepower.

1 horsepower = 550 ft lb/s = 746 W

Power can also be determined from force and speed:

P = F v note the units will be N m/s…