Transcript 1.1 _ 1.2 - Impulse and Momentum

MOMENTUM
• the product of mass and velocity
p  mv
•Units are kg•m/s, or any mass velocity combo
•Example: Which has more momentum, a 8000-kg hippo
trotting at 1.5 m/s or a 150-g bullet whizzing by at 1500 m/s?
IMPULSE
Change in momentum


impulse  p  mv
The second Law of Motion says any unbalanced force
acting on an object will change its motion:


F  ma


mv
Ft 
t
t


Ft  mv
So…..

impulse  Ft
•Units of impulse are Ns or kgm/s
•Momentum, impulse and velocity are vectors: magnitude
and direction must be considered
•A small force for a long period of time can cause the
same change in momentum as a large force acting for a
very short period of time
•The area under a force-time graph is the impulse acting
on the object
F
impulse
t
Two Types of Collisions:
1) Elastic collisions: kinetic energy is conserved.
2) Inelastic
collisions:
kinetic energy is
not conserved.
•The bulls are moving slower after the
collision, so kinetic energy is not
conserved (inelastic)
• Momentum is conserved. (approx 0
kg•m/s before and after)
2) Inelastic
collisions:
kinetic energy
is not
conserved.
•The bulls are moving slower after the collision, so kinetic
energy is not conserved (inelastic)
• Momentum is conserved. (approx 0 kg•m/s before and after)
Examples
1.Determine the magnitude of the impulse required to stop
a 1000 kg car moving at 21.0 m/s.
1. A 0.120 kg ball moving at 11.0 m/s strikes a solid massive
steel wall. The ball bounces straight back at 8.9 m/s.
a.If the ball was in contact with the wall for 0.17 s, what is
the magnitude of the force acting on the ball?
b. An identical ball with the same initial speed strikes a
glass window. The window cracks and the ball stops in
0.17 s. Using principles of physics, explain which ball
experiences the greater force.
The force multiplied by the change in time = change in momentum. Since both
collisions occur in the same amount time, the ball that has the larger force
acting on it is the ball in part “a” because it had the greatest change in
momentum since it changed direction.
3. An object experiences a varying force as shown below.
Which graph shows the largest change in momentum?
CONSERVATION OF MOMENTUM
Collisions:
momentum is always conserved in collisions
momentum before = momentum after
p
before
 p after
Example
1. A 900 kg car is moving at 20.0 m/s when it collides with a
50.0 kg bale of hay at rest on the road. If the two objects remain
together, determine their speed after the collision.
p
before
 p after
p car  p hay  p 'car  hay

(900kg)( 20.0m / s )  0  (950kg) v '

v '  18.9m / s
2. A 5.30 kg wagon is moving at 2.00 m/s to the right. A 0.180 kg
blob of putty moving at 32.0 m/s also to the right strikes the wagon
and sticks to it. With what speed will the wagon and the putty move
after the collision?
Explosions:
• Remember: if the momentum before the explosion is
zero, then the momentum after the explosion is zero.
• When a gun fires, the bullet goes one way, the gun
goes in the opposite way (recoil). The momentum adds
up to zero.
p
before
 p after  0
 0
pgun  pbullet
   pgun
pbullet
Example
1.A 600 kg cannon fires a 35.0 kg person
horizontally at 250 m/s, left. Determine the
recoil velocity of the cannon.
v
v
p

 before  pafter  0
 0
pgun  pbullet
p gun   pbullet

mgunvgun   mbulletvbullet

 mbulletvbullet
vgun 
mgun
 35.0kg 250m / s 
vgun 
600kg
vgun  14.6m / s