or
If
the work is done in a time
then
we can divide both sides byto
obtain
A Level Maths Notes: M2 – Force and Power
One of the basic equations
of physics is
orIf
the work is done in a timethen
we can divide both sides byto
obtain
or
where
and
We can generalise this
equation: If a body is travelling at a velocity
against
a force
then
the power needed to overcome the force is
It
should be noted that at any instant the body may be accelerating or
decelerating, so that v is an instantaneous, not necessarily a
constant, speed. If a force is applied greater than the force needed
to over come the resistive forcethen
the body may accelerate, or the potential energy of the body may
increase in some way. Given a power
and
a velocitywe
may find the driving force also using
Example
A lorry of mass 1500 kg moves along a straight horizontal road. The resistance to the motion of the
lorry has magnitude 750 N and the lorry’s engine is working at a rate of 36 kW.
a) Find the acceleration of the lorry when its speed is 20 m/s.
The lorry comes to a hill inclined at
an angle
to
the horizontal, where
The magnitude of the resistance to motion from non-gravitational forces remains 750 N.
The lorry moves up the hill at a constant speed of 20 m/s.
b) Find the rate at which the lorry's engine is now working.
a)
The resultant force=1800-750=1050N
Now use
for
the lorry – note thathere
is the resultant force and not the 750N force in the question.
b) The lorry does work to overcome the force of friction and to increase the gravitational potenital energy by travelling up the hill.
