Transcript 1.1.6 impulse

The rate of change of momentum is directly
proportional to the resultant force acting on an
object and takes place in the direction of the
resultant force.
..and we therefore get the maths bit!!!
Force = Change in Momentum/Time Taken
Force = (Final Momentum – Initial Momentum)/Time Taken
Force = (mv – mu)/t = m(v-u)/t
F = ma
F = kma
k=1.
is used to define the Newton and so
Therefore a Force of 1N applied to a 1Kg mass,
causes it to accelerate at 1ms-2.
So …
F = ma
Note that this is not Newton’s second law.
F  dp/dt is!
Impulse
Generally we say that impulse is the product of the applied
force and the time over which it is acting or the change in
momentum
Impulse = Ft = p
Considering a car crash we all know how violent they are but how
can we make them safer for the passengers?
If the impact is made to last longer by slowly crushing the car
the impulse will be less. In other words the impact will be less
violent and therefore less damaging to the frail humans inside
the car.
Unfortunately the car will be smashed! Look at the simulations on
multimedia motion looking at the graphs of car crashes, tennis
balls being hit and air track collisions.
If we consider catching a
cricket ball we all know there
good ways and bad. You can
really smack your hand or not.
What is the difference – the
impulse!!
Which catch would hurt your
hands the most is the balls
were all traveling at the same
speed??
If a ball hits a wall we can say the average force
that the ball exerts on the wall is F1.
According to Newton’s Third Law there should be
an equal and opposite force exerted on the ball
F2
Wall
F2
F1
So
Wall
F1 = - F2
If the force acts for a short
period of time t then
F2
F1 t = - F2 t
F1
Newton’s second law tells us that F= p/t
And so p = F1t
This implies that the units of IMPULSE are the same
as MOMENTUM. Using your training in Base units and
Quantities you should be able to prove that
Ns = Kgms-1
Force
The impulse can also be calculated from the
area under a force time graph.
Time
Questions
1. A ball has a mass of 150g and is travelling at 20ms-1.
It is caught and brought to rest in 75ms.
What is the average force on the ball which brings it
to rest?
1.
Ft = p
F x 75X10-3 = 20x0.150
F = 20x0.150 / 75X10-3
F = 20x0.002x103
F = 40N
2.Over what distance did the force act?
Work Done = Force * distance
In this case the work done is in slowing the ball
down to zero velocity so Work done = ½ mv2
½ mv2 = F*d
0.5*0.150*202 = 40*d
d = 0.075*400/40
d = 0.75m
Remember the discussion about catching cricket
balls and how to avoid hurting your hand!
Force
The following graph represent the force
acting on a floor as a ball bounces on it.
The ball changes direction because the
force on the floor changes direction Newton’s third law will show that this
force acts on the ball too in the
opposite direction.
Time
Explain what you can deduce about the motion of
the ball and why.
The change of momentum as it speeds up (second part of
graph) is less that than the change in the first part. This
means the ball leaves
the floor travelling more slowly than
it hit the floor.
Force
Time
The area under the
second part is less than
the area in the first part.
(area = impulse = p)