Momentum
• Momentum is a measure of how hard it is
to stop or turn a moving object.
• What characteristics of an object would
make it hard to stop or turn?
– Mass
– Velocity
Momentum
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ρ=mv
ρ – momentum (greek letter rho)
m – mass (kg)
v – velocity (m/s)
Momentum is a vector
The units are kg m/s OR Ns
Example
• Calculate the momentum of a 65-kg
sprinter running east at 10 m/s.
Example
• Calculate the momentum of a system composed of a
65-kg sprinter running east at 10 m/s and a 75-kg
sprinter running north at 9.5 m/s.
Change in momentum
• Like any change, change in momentum
is calculated by looking at final and
initial momentums.
• Dρ = ρf – ρi
– Dρ: change in momentum
– ρf: final momentum
– ρi: initial momentum
Example
• A 0.50 kg water balloon is thrown against a
wall at 32 m/s. It bursts when it hits the
wall. What is its change in momentum?
• Now a 0.05 kg bouncy ball is thrown against a
wall at 32 m/s and it bounces back with the
same speed. What is its change in
momentum?
Impulse (J)
• Impulse is the product of an external
force and time, which results in a
change in momentum of a particle or
system.
• J = F t and J = Dρ
• Units: N s or kg m/s (same as momentum)
Impulse formula from Newton’s 2nd law
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F=ma
F=m Δv/t
Ft=mΔv
Ft = Δρ
This is called the impulse momentum
theorem
Example
• A soccer player kicks a 0.45 kg ball at 25
m/s. If the goalie stops it by exerting 215
N of force, how long does it take for the
ball to stop?
• If the goalie stops a 6.5 kg bowling ball
traveling at the same velocity in the same
amount of time, how much force is
required?
Example
• Suppose a 1.5-kg brick is dropped on a
glass table top from a height of 20 cm.
a) What is the magnitude and direction of the
impulse necessary to stop the brick?
b) If the table top doesn’t shatter, and stops
the brick in 0.01 s, what is the average
force it exerts on the brick?
c) What is the average force that the brick
exerts on the table top during this period?
Impulse (J) on a graph
F(N)
3000
2000
area under curve
1000
0
0
1
2
3
4
t (ms)
Example
F(N)
2,000
1,000
0.20
0.40
0.60
0.80
t(s)
• This force acts on a 1.2 kg object moving at 120.0 m/s.
The direction of the force is aligned with the velocity.
What is the new velocity of the object?
Real-world connection
Collision time affects the amount of force that an
object experiences during a collision. From the
impulse equation we can see that force and time are
inversely proportional. That means that the longer
the amount of time to bring an object to a stop in a
collision, the less force is experienced.
Real-world connection (write theorem
for each to explain)
Air bags
Wearing pads in sports
Catching water balloons
Bending knees when landing from jumping
Follow through in sports
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it change in equation?)
• “Rebound” in collision result in large change
of momentum so what do car manufacturers
do to lessen chance of rebound?
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