Physics 30
Unit 1: Momentum
Physics 30 Self-Assessment Checklist
Upon completion of Unit 1, I will explain how momentum is conserved when objects
interact in an isolated system
To meet an acceptable standard I will be able
to:
state that momentum is equal to the product of
mass times velocity
define “vector”
define “scalar”
define “magnitude”
classify momentum and velocity as vector
quantities
classify mass as a scalar quantity
𝑝⃗ = 𝑚𝑣⃗

relate SI units to physics quantities: p in N.s or

kg.m/s; m in kg; v in m/s or in km/h
state that the impulse of an object is equal to the
change in its momentum
classify impulse as a vector quantity
classify force as a vector quantity
classify acceleration as a vector quantity
classify time as a scalar quantity
define “time interval”
classify speed as a scalar quantity
solve for the magnitude of any variable in

impulse = Δ p

impulse = mΔ v (vi or vf = 0 m/s)

impulse= Fnet Δt (ti = 0 s)
relate SI units to physics quantities:
impulse in N.s or in kg.m/s
F in N or in kg.m/s2 or in mJ
a in m/s2
t, Δt in s, or in h, or in min, or in a
state that area under a Fnet vs t graph is equal to
the impulse
calculate simple areas (two rectangles or two
triangles or a trapezoid; also all positive area or
all negative area)
use delta notation appropriately
follow instructions and collect data using available
equipment or computer simulation measure
distances and calculate speed and momentum
from timed images (strobe photography, motion
sensors, ticker-tape timer, etc.)
identify a situation in which impulse is important
To meet an excellent standard I will also
be able to:
derive formulas for impulse from Newton’s
third law (FAB = –FBA ) and Newton’s second
law (F =ma ) and kinematics formulas for
acceleration
solve for any variable, both vi and vf ≠ 0, in
impulse = Δ p impulse = mΔv
impulse =F Δt
calculate complex areas
show understanding of what positive area
and negative area mean
explain analysis of experimental observations
design an experiment
unit derivations
explain STS/safety applications that address
the importance of impulse
define “isolated system”
define “conserved”
state that momentum is conserved in an isolated
system
follow instructions and collect data using available
equipment or a computer simulation for
collisions:
linear hit and bounce
linear hit and stick
linear explosions
two objects moving toward each other at 90°,
and hit and stick
one object scattering off a stationary object with
the angle between the paths after the collision
being 90°
define perpendicular components
calculate any variable in a linear conservation of
momentum situation
calculate one speed in a 2-D conservation of
momentum 90° situation
calculate one rectilinear component or the
resultant given one or more sides and/or angle
draw vector addition diagrams for linear or 2-D
interactions
classify energy as scalar
define “elastic collision”
define “inelastic collision”
calculate Ek = 12 mv2
calculate ΣEki, ΣEkf for up to two moving objects
use Ek values to classify collisions
ΣEki= ΣEkf means elastic
ΣEki> Ekf means inelastic
relate SI units to physics quantities: E in J or in
kg.m2/s2 or in N.m
use delta notation appropriately
 work cooperatively in a group
predict whether or not momentum will be
conserved given a description of a system
design an experiment or investigation to
investigate the conservation of momentum
in a 2-D hit and bounce where one or both
vi ≠ 0
explain the analysis of experimental
observations
evaluate quality of experimental results
including discrepant or unexpected results
analyze 2-D interactions
-two objects moving toward each other at
an angle other than 90°, and hit and stick,
or hit and bounce
-one object scattering off a stationary object
with the angle between the paths after the
collision being other than 90°
-explosions involving three objects
draw scale vector diagrams
explain vector analysis
solve for any variable (not needing systems of
equations or the quadratic formula) using
the concept that in an elastic collision,
ΣEki = ΣEkf
explain what has happened in terms of the
work done by non-conservative forces to the
Eki in an inelastic collision
compare and contrast the conservation of
momentum and kinetic energy during any
collision
take a positive leadership role in group
activities
volunteer a connection between the real
world and classroom activity
Physics 30
Unit A: Forces and Fields
General Outcome 1: Students will explain how momentum is conserved when objects interact in an isolated
system.
define momentum as a vector quantity equal to the
product of the mass and the velocity of an object
Explain, quantitatively, the concepts of impulse and
change in momentum, using Newton’s laws of motion
1. A compact car, with mass 725 kg, is moving at
115 km/h toward the east.
a. Sketch the moving car.
3. The driver of a truck with a weight of 1.47 x 104 N
suddenly applies the brakes hard for 2.0 s. As a
result, an average force of 5.0 x 103 N is exerted
on the car to slow it down. The initial velocity of
the truck is 110 km/h, South.
a. What is the change in momentum; that is, the
magnitude and direction of the impulse, on the
car?
b.
Find the magnitude and direction of its
momentum. Draw an arrow on your sketch
showing the momentum.
b.
c.
A second car, with a mass of 2175 kg, has the
same momentum. What is its velocity?
2. A car with mass 1500 kg moving 110 km/h North
has the same momentum as a motorcycle with
sidecar of mass 750 kg. What is the velocity of the
motorcycle?
Complete the "before" and "after" sketches, and
determine the momentum and the velocity of the
car now.
4. A 7.0 kg bowling ball is rolling down the alley with
a velocity of 2.0 m/s. For each graph shown below,
find the resulting speed and direction of motion of
the bowling ball.
Graph A
Graph B
6. Suppose a 60.0 kg person was in a 1.25 x 103 kg
vehicle that hit a concrete wall travelling 110
km/h, west. The velocity of the person equals that
of the car both before and after the crash, and the
velocity changes in 0.20 s.
a. What is the average force exerted on the person?
b.
5. The driver accelerates a 240.0 kg snowmobile,
which results in a force being exerted that speeds
up the snowmobile from 6.00 m/s to 28.0 m/s
over a time interval of 60.0 s.
a. Sketch the event, showing the initial and final
situations.
b.
7. The graph shows the relationship between the
force on a 0.801 kg football and the time a kicker’s
foot is in contact with the ball. As a result of the
kick, the football, which was initially at rest, has a
final speed of 28.5 m/s:
What is the snowmobile's change in momentum?
What is the impulse on the snowmobile?
a.
c.
Some people think that they can stop their bodies
from lurching forward in a vehicle that is suddenly
braking by putting their hands on the dashboard.
Find the mass of an object that has a weight equal
to the force you just calculated. Could you lift such
a mass? Are you strong enough to stop your body
with your arms?
What is the magnitude of the average force that is
exerted on the snowmobile?
What is the magnitude of the maximum force,
Fmax, exerted on the ball during the kicking
process?
b.
What is the magnitude of the average force
exerted on the ball during the kick?
explain, quantitatively, that momentum is conserved in
one dimensional interactions in an isolated system
9. A 1575 kg car, initially travelling at 10.0 m/s,
collides with a stationary 2 250 kg car. The
bumpers of the two cars become locked together.
What is the speed of the combined cars
immediately after impact?
c.
How fast was the ball moving after 0.15 s?
10. Two freight cars, each with a mass of 3.0 X 105 kg,
collide and stick together. One was initially moving
at 2.2 m/s, and the other was at rest. What is
their final speed?
explain, qualitatively, that momentum is conserved in
an isolated system
8. Which of the following are isolated systems?
Explain why.
Initial
11. The two objects shown collide head on:
Final
A
The velocity of the 9.5 kg object after the collision
is 5.4 m/s to the left. What is the velocity of the
2.4 kg object after the collision?
B
C
D
12. A 105 g hockey puck moving at 24 m/s is caught
and held by a 75-kg goalie at rest. With what
speed does the goalie slide on the ice?
13. A 35.0-g bullet strikes a 5.0-kg stationary piece of
lumber and embeds itself in the wood. The piece of
lumber and bullet fly off together at 8.6 m/s. What
was the original speed of the bullet?
14. A 115 g arrow travelling east at 20 m/s imbeds
itself in a 57 g tennis ball moving north at 42 m/s.
What is the direction of the ball-and-arrow
combination after impact?
15. A 35.0-g bullet moving at 475 m/s strikes a 2.5-kg
bag of flour that is on ice, at rest. The bullet
passes through the bag and exits it at 275 m/s.
How fast is the bag moving when the bullet exits?
16. The bullet in the previous problem, now moving
275 m/s, strikes a 2.5-kg steel ball that is at rest.
The bullet bounces backward after its collision at a
speed of 5.0 m/s. How fast is the ball moving
when the bullet bounces backward?
17. A 0.50 kg ball that is traveling at 6.0 m/s collides
head-on with a 1.00-kg ball moving in the opposite
direction at a speed of 12.0 m/s. The 0.50 kg ball
bounces backward at 14 m/s after the collision.
Find the speed of the second ball after the
collision.
explain, quantitatively, that momentum is conserved in
two dimensional interactions in an isolated system
18. A 925 kg car moving north at 20.1 m/s collides
with a 1865 kg car moving west at 13.4 m/s. The
two cars are stuck together. In what direction and
at what speed do they move after the collision?
19. A 1383 kg car moving south at 11.2 m/s is struck
by a 1732 kg car moving east at 31.3 m/s. The
cars are stuck together. How fast and in what
direction do they move immediately after the
collision?
20. A stationary billiard ball, with a mass of 0.17 kg, is
struck by an identical ball moving at 4.0 m/s. After
the collision, the second ball moves 60.0° to the
left of its original direction. The stationary ball
moves 30.0° to the right of the moving ball's
original direction. What is the velocity of each ball
after the collision?
21. A 1345 kg car moving east at 15.7 m/s is struck
by a 1923 kg car moving north. They are stuck
together and move with an initial velocity of 14.5
m/s at E63°S. Was the north-moving car
exceeding the 20.1 m/s speed lmit?
22. A stationary bomb explodes into 3 pieces of equal
mass. If piece A moves at 4.5 m/s to the east and
piece B moves at 6.0 m/s, 30° west of North, what
is the velocity of piece C?
23. A spring loaded child’s toy (m=300g) moving 2.3
m/s 45° South of West explodes into 3 pieces.
Following the explosion one piece of mass 150g
moves 1.1 m/s South and another piece with mass
100g moves West. What is the velocity of the final
piece?
b.
Is this collision elastic or inelastic (Prove
mathematically)?
25. A 10 g ball moves at a velocity of 25 cm/s to the
right. This ball collides with a stationary 30 g ball.
After the collision the velocity of the 10 g ball is
8.0 cm/s to the left.
a. What is the velocity of the 30 g ball after the
collision?
define, compare and contrast elastic and inelastic
collisions, using quantitative examples, in terms of
conservation of kinetic energy
24. A 450 g ball moves at a velocity of 60 cm/s to the
right. This ball collides with a 225 g ball moving at
a velocity of 20 cm/s to the right. After the
collision the velocity of the 225 g ball is 35 cm/s to
the right.
a. What is the velocity of the 22g ball after the
collision?
b.
Is the collision elastic or inelastic (Prove
mathematically)?
Unit A: Momentum and Impulse
Review
1. Determine the momentum of a 5.0 kg bowling ball
rolling with a velocity of 3.5 m/s, North toward a
set of bowling pins.
2. What is the mass of a car that is travelling with a
velocity of 28 m/s, West and a momentum of 4.2 x
104 kg·m/s, West?
3. The momentum of a 55.0 kg in-line skater is 66.0
kg m/s, South. What is his velocity?
4. How fast would a 5.0 x 10-3 kg golf ball have to
travel to have the same momentum as a 5.0 kg
bowling ball that is rolling at 6.0 m/s, forward?
5. Calculate the impulse for the following
interactions.
a. A person knocks at the door with an average force
of 9.1 N, East, over a time interval of 2.5 x 10-3 s.
b. A wooden mallet strikes a large iron gong with an
average force of 4.2 N, South over a time interval
of 8.6 x 10-3 s.
6. A volleyball player spikes the ball with an impulse
of 8.8 kg·m/s over a duration of 2.3 x 10-3 s. What
was the average applied force?
7. If a tennis racquet exerts an average force of 55
N, West, and an impulse of 2.0 N·s, West, on a
tennis ball, what is the duration of the contact?
8. What is the impulse of a 0.300 kg hockey puck
slapshot that strikes the goal post at a velocity of
44 m/s North and rebounds straight back with a
velocity of 9.2 m/s, South? If the average force of
the interaction was -2.5 x 103 N, what was the
duration of the interaction?
9. A 2.5 kg curling stone is moving down the ice at
3.5 m/s West. What force would be needed to stop
the stone in a time of 3.5 x 10-4 s?
10. At an automobile test facility, a car with a 75.0 kg
crash-test dummy is travelling 28 m/s, forward
when it hits a wall. Calculate the force that the
seat belt exerts on the dummy on impact. Assume
that the car and dummy travel about 1.0 m as the
car comes to rest and that the acceleration is
constant during the crash.
11. A 0.0120 kg bullet is fired horizontally into a
stationary 5.00 kg block of wood and becomes
embedded in the wood. After the impact, the block
and bullet begin to move with an initial velocity of
0.320 m/s, East. What was the velocity of the
bullet just before it hit the wood?
12. A 48.0 kg skateboarder kicks his 7.0 kg board
ahead with a velocity of 2.6 m/s, East. If he runs
with a velocity of 3.2 m/s, East and jumps onto
the skateboard, what is the velocity of the
skateboard and skateboarder immediately after he
jumps on the board?
13. Astrid, who has a mass of 37.0 kg, steps off a
stationary 8.0 kg toboggan onto the snow. If her
forward velocity is 0.50 m/s, what is the recoil
velocity of the toboggan? (Assume that the snow is
level and the friction is negligible.)
14. A 60.0 t submarine, initially travelling forward at
1.5 m/s, fires a 5.0 x 102 kg torpedo straight
ahead with a velocity of 21 m/s in relation to the
submarine. What is the velocity of the submarine
immediately after it fires the torpedo?
15. Suppose that a 75.0 kg goalkeeper catches a 0.40
kg ball that is moving at 32 m/s. With what
forward velocity must the goalkeeper jump when
she catches the ball so that the goalkeeper and the
ball have a horizontal velocity of zero?
16. In billiards, the 0.165 kg cue ball is hit toward the
0.155 kg eight ball, which is stationary. The cue
ball travels at 6.2 m/s forward and, after impact,
rolls away at an angle of 40.0° counterclockwise
from its initial direction, with a velocity of 3.7 m/s.
What are the velocity and direction of the eight
ball?
17. Consider a nuclear reaction in which a neutron
travelling 1.0 x 107 m/s in the +x direction collides
with a proton travelling 5.0 x 106 m/s in the +y
direction. They combine at impact to form a new
particle called a "deuteron." What is the magnitude
and direction of the deuteron velocity? Assume for
simplicity that the proton and neutron have the
same mass.
18. A ball of mass m1 strikes a stationary ball of mass
m2 in a head-on, elastic collision.
a. Show that the final velocities of the two balls have
the form:
𝑚 −𝑚
2𝑚1
𝑣1′ = 1 2 𝑣1
𝑣2′ =
𝑣1
𝑚1 +𝑚2
𝑚1 +𝑚2
b. Examine three cases for the masses
c. Comment on the results.
19. In a demonstration, two identical 0.0520 kg golf
balls collide head on. If the initial velocity of one
ball is 1.25 m/s, North and the other is 0.860 m/s,
South, what is the final velocity of each ball?
20. A 750 g red ball travelling 0.30 m/s, East
approaches a 550 g blue ball travelling 0.50 m/s,
West They suffer a glancing collision. The red ball
moves away at 0.15 m/s, 30.0° S of E, and the
blue ball moves away in a northwesterly direction.
a. What is the final velocity of the blue ball?
b. What percentage of the total kinetic energy is lost
in the collision?
21. You and a colleague are on a spacewalk, repairing
your spacecraft that has stalled in deep space.
Your 60.0 kg colleague, initially at rest, asks you
to throw her a hammer, which has a mass of 3.0
kg. You throw it to her with a velocity of 4.5 m/s,
forward.
a. What is her velocity after catching the hammer?
b. What impulse does the hammer exert on her?
c. What percentage of kinetic energy is lost in the
collision?