Download Lecture 8: Forces & The Laws of Motion

Lecture 13:
Momentum
Questions of Yesterday
1) A mass with speed v hits a horizontal spring and compresses it a
distance d. If the the speed of the mass were doubled (2v)
what would the compression distance be?
a) 4d
b) 2d
c) d
d) d/2
2) A mass on a spring is oscillating back and forth from x = -d to x =
d? At what point in the oscillation is the speed of the mass the
greatest?
a) x = d
b) x = -d
c) x = 0
d) x = d and x = -d
Momentum
Which ball do you want to have a game of toss with? Why?
So, would you rather catch a speeding bullet? Why?
MASS and VELOCITY
affect force needed to stop
a moving object in a given time interval
Momentum
Linear Momentum (p)
of a moving object is the product of
its mass m and velocity v
UNITS
kg*m/s
p = m*v
px = m*vx
p is a vector!
Vector Equation!
py = m*vy
The more momentum an object has
the more force you need to apply
to stop it in a given time interval
Momentum & Newton’s 2nd Law
Force is required to change an object’s momentum
Fnet = ma
Dv
Dt
Dv
D(mv)
Fnet = m
=
Dt
Dt
Fnet =
Dp
Dt
The net force acting on an object is equal to the object’s
change in momentum divided by the elapsed time of the force
Momentum & Newton’s 2nd Law
Force is required to change an object’s momentum
Fnet = ma
Dv
Dt
Dv
D(mv)
Fnet = m
=
Dt
Dt
Fnet =
Dp
Dt
MOMENTUM of an object is CONSERVED if Fnet = 0
Impulse
IMPULSE (I)
The change in an object’s momentum (Dp) caused by a
constant force (F) applied to the object
over a given time interval (Dt)
Units
kg*m/s
I = FDt
I acts in
same direction
as F
If F is only force acting on an object…
Impulse = change in total momentum of the object
FDt = Dp = mvf - mvi
Impulse & Varying Force
Dp = FDt
F
t
Impulse & Varying Force
Dp = FDt
F
F
A=
Dp
Fav
A=
FavDt
t
Impulse =
Area under F vs t curve
t
Impulse =
Average Force * time interval
Dp = FavDt
Momentum & Impulse Concepts
If a Mack truck and a Ford Escort have a head-on collision,
which vehicle will experience…
the greater force of impact?
the greater impulse?
the greater change in momentum?
the greater acceleration?
Momentum & Impulse Concepts
Would you rather get punched in the face
with a bare fist or a boxing glove?
In which case is the impulse delivered to your face greater?
In which case is force on your face greater?
Momentum: Practice Problem
A ball of mass 0.10 kg is dropped from rest from a height of 1.5 m.
It rebounds from the floor to reach a height of 1.0 m.
What impulse (magnitude and direction) was given to the ball by
the floor?
If the ball was in contact with the floor for 0.5 s, what was the
force (magnitude and direction) exerted by the ball?
What fraction of kinetic energy is lost in the collision?
Momentum: Practice Problem
A 100-kg stuntman jumps from a balcony and falls 10.0 m before
colliding with a pile of mattresses. If the mattresses are
compressed 1.0 m before he is brought to rest…
what is the average force exerted by the mattresses on the
stuntman?
Momentum Conservation
MOMENTUM of an object is CONSERVED if Fnet = 0
What happens in a collision?
pi1 = m1vi1
pi2 = m2vi2
Momentum Conservation
MOMENTUM of an object is CONSERVED if Fnet = 0
What happens in a collision?
pi1 = m1vi1
pf1 = ?
pf2 = ?
F21Dt = Dp1 = mvf1 - mvi1
F12Dt = Dp2 = mvf2 - mvi2
mvi1 + mvi2 = mvf1 + mvf2
pi2 = m1vi2
3rd law:
F21 = -F12
Momentum Conservation
MOMENTUM of an object is CONSERVED if Fnet = 0
What happens in a collision?
If no net external force acts on a system of objects…
The total momentum of the system remains constant in time
pi = pf
mvi1 + mvi2 = mvf1 + mvf2
Momentum: Practice Problem
A rifle with a weight of 30 N fires a 10.0 g bullet with a speed of
300 m/s.
-Find the recoil speed of the rifle
-If a 700 N man holds the rifle firmly against his shoulder,
find the recoil speed of the man and the rifle
Momentum: Practice Problem
A 50-kg girl is standing on a 100-kg plank. The plank, originally at
rest, is free to slide on a frozen lake, which is a flat, frictionless
surface. The girl begins to walk along the plank at a constant
velocity of 2 m/s to the right relative to the plank.
-What is her velocity relative to the surface of the ice?
-What is the velocity of the plank relative to the surface of the ice?
Questions of the Day
A 50-kg object is traveling with a speed of 100 m/s and a 100-kg
object is traveling at a speed of 50 m/s.
1a) Which object has more momentum?
1b) Which object has more kinetic energy?
a) 50-kg object
b) 100-kg object
c) they are equal
2) Would a head-on collision between two cars be more
damaging to the occupants if the cars stuck together or if the
cars rebounded upon impact?
a) if the cars stuck together
b) if the cars rebounded
c) both collisions would be equally damaging
d) it depends on the relative masses of the cars