Momentum and Collisions Review

1
Momentum and Collisions Review

• Chapter 6(all)

2
Overview

• Momentum (pmv) Vector quantity of motion equal
  to an objects mass times its velocity.
• Impulse (DpFDt)- 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. pinitpfinal
• 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)

3
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
4
Impulse

• Defined as change in momentum, also FDt
• Newtons Second Law Originally written as
  FDp/Dt, instead of Fma
• 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

5
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.

v2f
v1i
v2i
v1f
m2
m1
m2
m1
Before Collision
After Collision
6
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(m1m2)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. (mvom1v1m2v2) Of course, m1 and
  m2 will add up to the original mass.

7
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!!

v1f
v1i
q
f
After Collision
Before Collision
v2f
X m1v1i m1v1fcosq m2v2fcosf
Y 0 m1v1fsinq - m2v2fsinf
8

• What are the two basic types of collisions?

Elastic and Inelastic
9

• Explain the formula pmv, describe what each
  variable is

Momentum is equal to the mass of the object times
the velocity, pmomentum mmass vvelocity
10

• What was Newtons second law originally expressed
  as?

HINT not Fma
F change in momentum Dp time interval Dt
11

• 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
12

• If ball a is stationary and has a mass of m, what
  will its velocity be when it is hit by ball b
  (mass 2m, velocity v) assuming a perfectly
  inelastic collision?

mavambvb(mamb)vfinal 0 2mv
(m2m)vfinal Vfinal 2/3 v
13

• The total momentum of an isolated system of
  objects is _________ regardless of the nature of
  the forces between the objects.

Conserved
14

• An _________ collision is one in which both
  momentum and kinetic energy are conserved

Elastic
15

• An __________ collision is one in which momentum
  is conserved but kinetic energy is not

Inelastic
16

• What is indicated by the area under a graph of
  force vs. time?

Impulse
17

• What are some examples of things that are
  designed to increase the Dt of an impact?

Boxing Gloves, Cars, baseball gloves
18

• m1v1i m2v2i m1v1f m2v2f
• What does this equation demonstrate?

Conservation of Momentum (in one dimension)
19

• 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
20

• 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.
21

• Impulse is given by the formula

Impulse FDt
22

• Is momentum conserved in a glancing collision?

Yes!!! It is conserved in both the x and y
directions. Break problem into components to
solve!
23

• Momentum is conserved in all collisions when no
  _____________ are acting.

External Forces
24

• The time rate of change of momentum of an object
  is equal to the ____________ acting on the object

Net Force
25

• 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 Newtons third Law
(action-reaction), but can also be explained in
terms of conservation of momentum.
26

• Is momentum a vector or scalar quantity?

Vector. (So always pay attention to DIRECTION
when working with momentum!)
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• Which has more momentum a semi-truck or a Mini
  Cooper, if they are both going 10 mph?

The semi-truck
28

• Which has more momentum a parked semi-truck or
  a Mini Cooper moving at 10 mph?

The Mini Cooper
29

• What units are used to define momentum?

Kg m/s (also N s)
30

• 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?

ImpulseFDt 12x11132 Ns Pinitmv66Ns Dpimpulse
132Ns PfinalpinitDp198Ns vfinalpfinal/m3.0
m/s
31

• 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
40/202 only one answer is close to this)
32

• 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
33

• 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
34

• 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. Kinit½(2)22½(2)3213Joules Kfinal½
22½(2)125Joules 8Joules of energy was lost.
35

• 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
36

• 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?

ImpulseFDt100(.1)10 Ns
37

• What is the momentum of a 4.0 kg object that has
  a kinetic energy of 50 J?

K ½mv2 ? v5m/s p mv 20 kg m/s
38

• What is the linear momentum of a system of two
  particles with equal mass m traveling in opposite
  directions with speed v?

Zero
39

• 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?