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Lesson 5 notes – Impulse
Objectives
Be able to define impulse of a force;
Be able to recall that the area under a force against time graph is equal to
impulse;
Be able to recall and use the equation impulse = change in momentum.
Outcomes
Be able to define the impulse of a force in words.
Know the equation impulse=Ft=(mv-mu)=change in momentum.
Know that the area under a force against time graph is equal to impulse.
Be able to use the equation impulse=Ft=(mv-mu)=change in momentum.
Be able to find the impulse of a force graphically from a force against time graph.
Impulse is the concept we use to describe the effect of a force acting on an
object for a finite amount of time.
It is defined as the product of the force and the time interval over which the
force acts.
The equation for the calculation of impulse is:
Impulse = FaveΔt
Fave is the magnitude of the average force and Δt is the time over which the force
acts. J is a vector with the same direction as the force.
We must use the average force since the magnitude of the force can vary during
the time interval when it is applied.
Since impulse is the product of the force and the time interval over which the
force acts its units are Ns.
In the graphic, the force applied by a
bat on a ball is plotted on the Y axis
against the corresponding time on the
X axis. During the time of contact, the
force rises to a maximum value, then
rapidly falls to zero as the ball leaves the bat.
Since impulse is the product of the force and the time interval over which the
force acts it can be found graphically from the area underneath a Force – time
graph like the one above.
The relationship between impulse and momentum comes from Newton's second
law.
F = ma
F = m(v-u)/Δt
F = (mv-mu)/Δt
Therefore FΔt = mv-mu (Impulse = the change in momentum)
This equation is called the Impulse - Momentum Theorem and states that the
impulse equals the change in momentum.
Very often it is not possible to determine the force acting on an object, especially
if the time interval is very short. In these cases if the initial and final masses and
velocities can be measured and the time of contact determined, the average
force can be found.
Example
A golfer gives a ball a velocity of +38.0 m/s. The mass of the ball is 0.045 kg and
the time of impact is 0.00300 s.
(a) Find the change in momentum of the ball.
(b) Determine the average force applied to the ball.
a)
p=mv-mu
p=0.045 x 38.0 (initial velocity equals zero)
p= 1.71 Ns
b)
F = p/t
F = 1.71/0.00300
F = 570N