Download Momentum

 Momentum 
A.K.A. The difference between
moving and standing still.
Definition
Mathematical
Momentum = Mass (kg) x Velocity (m/s)
Or
p=mv
The units for momentum are kgm/s
Verbal
Momentum is “inertia in motion”.
Remember Newton’s 1st law. It’s analogous to
Inertia.
Momentum = mass x velocity
• Momentum is a true measure of how
difficult it is to stop something.
– A charging hippo can do some damage, a hippo
charging twice as fast can do twice the damage.
– Calculating momentum is easy, just find the
mass and the velocity and multiply.
p = mv
– Notice that mass and velocity both affect
momentum equally.
Impulse – where momentum comes
from!
• Only a force can “give” something momentum (or take it
away).
– Lets say you are a member of a bobsled team. You push the
sled to speed it up. The longer the you push the sled the greater
the velocity and the greater the momentum you give it so time is
also a factor.
– Or think about the airbags in your car. They give you more time
to slow down so less force is applied to your body.
• So… a force applied for a certain time leads to a
change in momentum.
• Δp = (Force) x (time) This is called an impulse (J)
J = Favg ∆ t
• Impulse is a change in momentum (∆mV)
∆(mV) = Ft
J = m∆V = Favg ∆ t
• The units for impulse are the same as momentum (kgm/s)
Constant Force IMPULSE
F
Dt
Impulse J is a force
F acting for a small
time interval Dt.
Impulse:
J = Favg Dt
Example 1: The face of a golf club exerts
an average force of 4000 N for 0.002 s.
What is the impulse imparted to the ball?
Impulse:
J = F Dt
F
J = (4000 N)(0.002 s)
J = 8.00 kg m/s
Dt
The unit for impulse is the kg m/s
Impulse from a Varying Force
Normally, a force acting for a short interval is
not constant. When force is not constant you
need to look at a Force vs Time graph.
Impulse is the area of a
Force vs Time graph.
This is similar to the area
of a Force vs Position
Graph
Example 2: Two flexible balls collide. The
ball B exerts an average force of 1200 N
on ball A. How long were the balls in
contact if the impulse is 5 N s?
A
B
J
-5 N s
Dt 

Favg -1200 N
J  Favg D t
Dt = 0.00420 s
The impulse is negative; the force on ball
A is to the left. Unless told otherwise, treat
forces as average forces.
Impulse Changes Velocity
Consider a mallet hitting a ball:
F  ma; a 
v f  vo
 v f  v0 
F  m

 Dt 
F
Dt
F Dt  mv f  mvo
Impulse = Change in “mv”
Momentum Defined
Momentum p is defined as the product of
mass and velocity, mv. Units: kg m/s
p = mv
m = 1000 kg
Momentum
p = (1000 kg)(16 m/s)
p = 16,000 kg m/s
v = 16 m/s
Impulse and Momentum
Impulse = Change in momentum
F Dt = mvf - mvo
F
Dt
mv
A force F acting on a ball
for a time Dt increases its
momentum mv.
Example 3: A 50-g golf ball leaves the
face of the club at 20 m/s. If the club
is in contact for 0.002 s, what average
force acted on the ball?
Given: m = 0.05 kg; vo = 0;
+
F
Dt
mv
Dt = 0.002 s; vf = 20 m/s
Choose right as positive.
0
F Dt = mvf - mvo
F (0.002 s) = (0.05 kg)(20 m/s)
Average Force:
F = 500 N
Vector Nature of Momentum
Consider the change in momentum of a
ball that is dropped onto a rigid plate:
+
vf
vo
A 2-kg ball strikes the plate with
a speed of 20 m/s and rebounds
with a speed of 15 m/s. What is
the change in momentum?
Dp = mvf - mvo = (2 kg)(15 m/s) - (2 kg)(-20 m/s)
Dp = 30 kg m/s + 40 kg m/s
Dp = 70 kg m/s
Directions Are Essential
1. Choose and label a positive direction.
v0
+
vf
vf = +10 m/s
v0= -30 m/s
2. A velocity is positive when
with this direction and
negative when against it.
Assume v0 is 30 m/s to
the left and vf is 10 m/s
to the right. What is the
change in velocity Dv?
vf – v0 = (10 m/s) – (-30 m/s)
Dv  40 m/s
Example 4: A 500-g baseball moves to
the left at 20 m/s striking a bat. The bat is
in contact with the ball for 0.002 s, and it
leaves in the opposite direction at 40 m/s.
What was average force on ball?
+
m = 0.5 kg
- 20 m/s
F Dt = mvf - mvo
F
+ 40 m/s
Dt
vo = -20 m/s; vf = 40 m/s
F(0.002 s) = (0.5 kg)(40 m/s) - (0.5 kg)(-20 m/s)
Continued . . .
Example Continued:
+
m = 0.5 kg
F
- 20 m/s
+
40 m/s
Dt
F Dt = mvf - mvo
F(0.002 s) = (0.5 kg)(40 m/s) - (0.5 kg)(-20 m/s)
F(0.002 s) = (20 kg m/s) + (10 kg m/s)
F(0.002 s) = 30 kg m/s
F = 15,000 N
Summary of Formulas:
Impulse
J = FavgDt
Momentum
p = mv
Impulse = Change in momentum
F Dt = mvf - mvo
Impulse and Momentum