Download ch6 momentum

Momentum and Collisions
Review
Chapter 6(all)
Overview
Momentum (p=mv) Vector quantity of motion equal to an object’s mass
times its velocity.
Impulse (Dp=FDt)- is equal to the change in momentum
Conservation of Momentum Since every action creates an EQUAL and
opposite reaction (F12Dt= -F21Dt) the total momentum in an
isolated system is constant. pinit=pfinal
Collisions-(recognize and give examples of each)
Elastic (both momentum & kinetic energy conserved)
Inelastic (momentum conserved, kinetic energy is not)
Perfectly Inelastic (two objects collide & stick together)
Linear Momentum
Mass x Velocity
Vector Quantity
Measured in Kg x m/s, direction matches
velocity
Object A, with mass a moves to the right
at velocity a
Object A has a momentum of mava
Impulse
Defined as: change in momentum, also FDt
Newton’s Second Law: Originally written as
F=Dp/Dt, instead of F=ma
Force x Time Graph: On a F x T graph the area
between the graph and the x-axis is the impulse.
Reducing Impulse: To reduce force of impact,
cars are designed to crumple like an accordion,
increasing Dt and thus reducing the force on the
driver in a car crash
Conservation of Momentum
Momentum is always conserved: m1v1i + m2v2i = m1v1f +
m2v2f
The total momentum of an isolated system of objects is
conserved regardless of the nature of the forces
between the objects.
m1
v1i
v2i
Before Collision
m2
v1f
m1
m2
After Collision
v2f
Collisions
Inelastic-Example: A rubber ball collides with a hard
surface, kinetic energy is lost because ball is deformed
during contact with the surface transforming some of the
energy into heat.
Elastic-(m1v1i + m2v2i = m1v1f + m2v2f) Example: Billiard
balls collide without losing any of their energy.
Perfectly Inelastic- (m1v1i + m2v2i=(m1+m2)vf) (two
objects stick together creating single mass) Two
snowballs collide, and create one larger snowball and
final velocities of snowballs are the same.
Explosions- Something flies apart into two or more
pieces. (mvo=m1v1+m2v2) Of course, m1 and
m2 will add up to the original mass.
Glancing Collisions
When objects do not collide on the same path line, they
make glancing collisions.
To solve this type of problem, break it into components!!
v1i
q
f
After Collision
Before Collision
X: m1v1i = m1v1fcosq + m2v2fcosf
Y: 0 = m1v1fsinq - m2v2fsinf
What are the two basic types of
collisions?
Elastic and Inelastic
Explain the formula p=mv,
describe what each variable is
Momentum is equal to the mass of the object times
the velocity, p=momentum m=mass v=velocity
What was Newton’s second law
originally expressed as?
HINT: not F=ma
F= change in momentum = Dp
time interval
Dt
Why is it safer to bend your knees
when you land from a relatively
large height?
HINT: F= Dp/Dt
Bending your knees increases
the time in which the impact
occurs,thus reducing the force
If ball a is stationary and has a
mass of m, what will it’s velocity
be when it is hit by ball b (mass
2m, velocity v) assuming a
perfectly inelastic collision?
mava+mbvb=(ma+mb)vfinal
0 + 2mv = (m+2m)vfinal
Vfinal= 2/3 v
The total momentum of an
isolated system of objects is
_________ regardless of the
nature of the forces between the
objects.
Conserved
An _________ collision is one in which
both momentum and kinetic energy are
conserved
Elastic
An __________ collision is one in
which momentum is conserved
but kinetic energy is not
Inelastic
What is indicated by the area
under a graph of force vs. time?
Impulse
What are some examples of
things that are designed to
increase the Dt of an impact?
Boxing Gloves, Cars, baseball
gloves
m1v1i + m2v2i = m1v1f + m2v2f
What does this equation demonstrate?
Conservation of Momentum (in
one dimension)
If a 3000 kg object traveling at 22 m/s
collides with a 60 kg object traveling the
opposite direction at 30 m/s, which
object experiences the most force?
They experience the same
force
In golf, novice players are often
advised to be sure to “follow
through” with their swing. Why
does this make the ball travel a
longer distance?
Following through allows the club
to remain in contact with the ball
longer. This means the ball
experiences a greater impulse
which results in a larger change of
its momentum.
Impulse is given by the formula:
Impulse= FDt
Is momentum conserved in a
glancing collision?
Yes!!! It is conserved in both
the x and y directions. Break
problem into components to
solve!
Momentum is conserved in all
collisions when no
_____________ are acting.
External Forces
The time rate of change of
momentum of an object is equal
to the ____________ acting on
the object
Net Force
When holding a hose fire-fighters need to
ensure that they are not pushed
backwards, especially if the water is
ejected at a high speed.
Explain why the fire-fighters experience a
backwards force.
The water is pushing against the firefighters so that it can
project in the opposite direction. This is a good example of
Newton’s third Law (action-reaction), but can also be
explained in terms of conservation of momentum.
Is momentum a vector or scalar
quantity?
Vector. (So always pay
attention to DIRECTION when
working with momentum!)
Which has more momentum;
a semi-truck or a Mini Cooper, if they
are both going 10 mph?
The semi-truck
Which has more momentum;
a parked semi-truck or a Mini Cooper
moving at 10 mph?
The Mini Cooper
What units are used to define
momentum?
Kg m/s (also N s)
If a force of 12 N is applied to a 66 kg
object for 11 seconds, what is the
impulse?
If the object was originally traveling in the
positive direction at 1.0 m/s, what is its
speed at the end of this time?
Impulse=FDt =12x11=132 Ns
Pinit=mv=66Ns
Dp=impulse=132Ns
Pfinal=pinit+Dp=198Ns
vfinal=pfinal/m=3.0 m/s
An object experiences an impulse of 40.51
N-s for a time period of 19.32 s. What was
the average force on the object during
this time?
A) 782.65 N
B) 0.47 N
C) 0.62 N
D) 3.76 N
E) 2.09 N
E) 2.09 N
Could you select the correct answer
without a calculator? Estimate!! (answer
~40/20=2 only one answer is close to this)
A squid propels itself by expelling
water at a high velocity. How is
this possible?
The squid increases the
momentum of the water in the
backward direction, therefore
increasing the momentum of
the squid in the forward
direction
Four billiard balls, each of mass .5 kg, all
are traveling in the same direction on a
billiard table, with speeds 2 m/s, 4 m/s, 8
m/s and 10 m/s. What is the linear
momentum of this system?
What is the linear momentum if the last ball
was traveling in the OPPOSITE direction at
10m/s?
12 kg m/s
2 kg m/s
Two balls, each with mass 2 kg, and
speeds of 2 m/s and 3 m/s collide head
on. They rebound at speeds of 2 m/s and
1 m/s, respectively. Is this collision
elastic or inelastic?
Inelastic.
Kinit=½(2)22+½(2)32=13Joules
Kfinal=½22+½(2)12=5Joules
8Joules of energy was lost.
A car of 500 kg, traveling at 30 m/s rear
ends another car of 600 kg, traveling at
20 m/s. in the same direction The
collision is great enough that the two
cars stick together after they collide.
How fast will both cars be going after the
collision?
24.5 m/s use
m1v1i + m2v2i = (m1+ m2)vf
A bat exerts a force on a ball of 100 N for a
period of .1 seconds. What is the impulse
provided by the bat?
Impulse=FDt=100(.1)=10 Ns
What is the momentum of a 4.0 kg object
that has a kinetic energy of 50 J?
K = ½mv2  v=5m/s
p = mv = 20 kg m/s
What is the linear momentum of a system
of two particles with equal mass m
traveling in opposite directions with
speed v?
Zero
Two cars of equal mass collide head on
and both come to a stop. What can be
said about the cars before the crash?
They were moving with equal
speeds in opposite directions
Could you conclude the same thing if the
cars were not of equal mass?