Transcript 1a-Momentum and Impulse - MrD-Home

Momentum and Collisions
Momentum
►
From Newton’s laws: force must be present to change an
object’s velocity (speed and/or direction)
Golf ball initially at rest, so
some of the KE of club
transferred to provide motion
of golf ball and its change in
velocity

Method to describe is to use concept of linear momentum
Linear momentum = product of mass
scalar
 velocity
vector
Momentum
p  mv
►
►
Vector quantity, the direction of the momentum is
the same as the velocity’s
Applies to two-dimensional motion as well
p x  m v x and p y  m v y
Size of momentum: depends upon mass
depends upon velocity
Impulse
order to change the momentum of an object
(say, golf ball), a force must be applied
► In
F net
 p m (v f  v i )


 ma
t
t
or : p  F net t
Impulse Cont’d
D p = F net Dt
 Gives an alternative statement of Newton’s second law
 (F Δt) is defined as the impulse
 Impulse is a vector quantity, the direction is the same
as the direction of the force
Finding Impulse using F-t Graph
► Usually
force is not
constant, but timedependent
► If
the force is not
constant, use the
average force
applied
Graphical Interpretation of Impulse
►
The average force can be
thought of as the constant
force that would give the
same impulse to the object
in the time interval as the
actual time-varying force
gives in the interval
If force is constant: impulse = F t
Example: Impulse Applied to
Auto Collisions
► The
most important factor is the collision time or
the time it takes the person to come to a rest
► Ways
to increase the time
 Seat belts
 Air bags

The air bag increases the time of the collision and
absorbs some of the energy from the body
To Do….
In the first section of the Momentum chapter
in your SNAP (Impulse and Momentum):
► Read
Example problems
► Do Practice Exercises (odds)
► Next:
2-D collisions; Elastic vs. Inelasctic
Collisions
ConcepTest1
Suppose a ping-pong ball and a bowling ball are rolling toward
you. Both have the same momentum, and you exert the same
force to stop each. How do the time intervals to stop them
compare?
1. It takes less time to stop the ping-pong ball.
2. Both take the same time.
3. It takes more time to stop the ping-pong ball.
ConcepTest1
Suppose a ping-pong ball and a bowling ball are rolling toward
you. Both have the same momentum, and you exert the same
force to stop each. How do the time intervals to stop them
compare?
1. It takes less time to stop the ping-pong ball.
2. Both take the same time. 
3. It takes more time to stop the ping-pong ball.
Note: Because force equals the time rate of change of
momentum, the two balls loose momentum at the same
rate. If both balls initially had the same momenta, it
takes the same amount of time to stop them.
Problem: Teeing Off
A 50-g golf ball at rest is hit by “Big
Bertha” club with 500-g mass.
After the collision, the golf ball
leaves with velocity of 50 m/s.
a) Find impulse imparted to ball
b) Assuming club in contact with
ball for 0.5 ms, find average force
acting on golf ball
Problem: teeing off
1. Use impulse-momentum relation:
Given:
impulse = Dp = mv f - mvi
= ( 0.050 kg) (50 m s - 0)
mball = 50 g
= 0.050 kg
v = 50 m/s
Find:
Impulse = ?
Faverage = ?
= 2.50 kg × m s

2. Having found impulse, find the average
force from the definition of impulse:
p 2.50 kg  m s

t
0.5 10 3 s
 5.00 103 N
p  F  t , thus F 

Note: according to Newton’s 3rd law, that is also a reaction force to club hitting the ball:
F × Dt = -F R × Dt, or
(
of club
)
mv f - mvi = - MV f - MV i , or
mv f + MV f = mvi + MV i
CONSERVATION OF MOMENTUM