- Find the work done to lift a mass of 10 kg through a height of 5 m.
If this takes 15s what is the power?
W= Fx = (10kg)(9.8Nkg-1) (5m) = 490J
P = W/t = 490 J / 15s = 32.67 W
2
A mass of 5 kg is pulled along a surface at a
constant speed. Frictional force between the mass and the surface is 4N what
work is done in moving the mass 2 m along the surface? Find the power if this
takes 2 s.
W = Fx = (4N) (2m) = 8J
P = W/t = 8J/ 2s = 4 W
3
A girl of mass 50 kg runs up a flight of steps 4.5
m high in 5 s. What power does she develop?
W = Fx F = 50kg x 9.8 =
490.5 N x = 4.5m
W = 490.5 x 4.5 = 2207.25 J
P = W/t = 2207.25 J / 5s = 442w
4
2 x 106 kg of water per second flow over
a large waterfall of height 50 m.
W = Fx
F = 2 x 106 kg x 9.8 = 1.96 x10+7N x=50m
W= (1.96 x10+7N) (50m) = 9.8 x10+8
J
What power is available?
As 1W = I J per second the water falling over the fall transfers 9.8 x10+8
J of GPE per second the available power is 9.8 x10+8 W (ignoring
losses due to friction)
5
The first-stage rocket motors of Saturn 5 burnt
fuel at the rate of 13600 kg per second. The work done by the pumps to drive
the fuel into the combustion chambers is the same as that necessary to lift the
fuel through 1680 m.
W= Fx F
= 13600kg x 9.8= 1.3328 x 10+5 N x
= 1680m
W = (1.3328x 10+5 ) (1680) = 2.24 x 10+8
J
What power is needed to do this? (Your answer is about twice the engine
power of the largest ocean liner.)
As this mass of fuel is burnt in 1 second then 2.24 x 10+8 J
of work is done in 1 second so the power is 2.24 x 10+8 W
6
A gas turbine locomotive developing 6330 kW pulls a
train at a steady velocity of 108 kmh- 1. What is the total force in
Newtons resisting the motion?
At a steady velocity all work done by the engine is against friction or
gravity.
The engine does 6.33 x106 J of work every second
As W = Fx the force exerted by the engine is equal Work done per second
divided by the distance travelled per second
F = W/x 108 kmh-1
= (108000m)/(60 min x 60 sec) = 30 ms-1
F = 6.33 x106 J/ 30m = 211 000N = 2.11 x 105 N
