Momentum
-Momentum
-Impulse
-Problems
Physics 1D03 - Lecture 25
Definition: The linear momentum p of a particle
is its mass times its velocity:
p  mv
Momentum is a vector, since velocity is a vector.
Units: kg m/s
Physics 1D03 - Lecture 25
Impulse
dp
 F , or dp = F dt
Newton #2:
dt
For a constant force, Dp = F Dt . The vector quantity F Dt is
called the Impulse:
J = FΔt = Δp
(change in p) = (total impulse from external forces)
(Newton’s Second Law again)
(Extra) In general (force not constant), we integrate:

J 
 Fdt
where the integral gives the area under a curve…
Physics 1D03 - Lecture 25

F

F
ti
tf
t

Area = F (Dt )
ti
tf
t
Impulse is the area under the curve. The average force
is the constant force which would give the same impulse.
Compare with work: W = F Dx ; so the work-energy theorem
(derived from Newton #2) is DK = F Dx.
Physics 1D03 - Lecture 25
Example
A golf ball is launched with a velocity of 44 m/s. The
ball has a mass of 50g. Determine the average force
on the ball during the collision with the club, if the
collision lasted 0.01 s.
Physics 1D03 - Lecture 25
Example
Use the impulse-momentum theorem to find how long a
falling object takes to increase its speed from 5.5m/s
to 10.4m/s.
Physics 1D03 - Lecture 25
Example
• A 150 g baseball is thrown with a speed of 20m/s. It
is hit straight back toward the pitcher at a speed of
40m/s. The interaction force is shown by the graph:
Fmax
What is the maximum force Fmax that the bat exerts
on the ball ?
Physics 1D03 - Lecture 25
Example: the fire extinguisher
How can we calculate the backwards force a fire extinguisher
exerts on the operator?
Plan: Calculate the momentum
transferred to the gas in an
arbitrary time Dt; this is equal to
the impulse the gas gets from
the extinguisher nozzle.
gas
From Newton’s Third Law, the nozzle gets an equal but opposite
impulse (somehow) from the gas. Since impulse is FDt, divide by
Dt to get the force.
Result: F = (speed of gas) x (mass of gas ejected per unit time)
Physics 1D03 - Lecture 25
Concept Quiz
A 100g rubber and a 100g clay ball are thrown at a wall
with equal speed. The rubber ball bounces back
while the clay ball sticks to the wall.
Which ball exerts a larger impulse on the wall ?
a)
b)
c)
d)
the clay bass b/c it sticks
the rubber ball b/c it bounces
they are equal because the have equal momenta
neither exerts an impulse b/c the wall doesn’t move
Physics 1D03 - Lecture 25