Transcript document

Momentum and
Collision
Practice Problems and
Answers
PROBLEM 1
A 2250 kg pickup truck has a velocity
of 25 m/s to the east. What is the
momentum of the truck?
m  2250kg
v  25m / s
p  mv  2250kg  25m / s
 56250kg * m / s east
PROBLEM 2
What velocity must a car with a mass
of 1210 kg have in order to have the
same momentum as the pickup truck?
m  1210kg
v  ?m/ s
p  56250kgm / s
p 56250kgm / s
v

 46.49m / s east
m
1210kg
PROBLEM 3
A baseball of mass 0.14 kg is
moving at 35 m/s. A) Find the
momentum of the baseball.
B) Find the velocity of a bowling
ball, mass 7.26 kg, would have if
its momentum is the same as the
baseball.
m  0.14kg
v  35m / s
p  mv
 .14  35
 4.9kgm / s
p  4.9kgm / s
m  7.26kg
v ?
p 4.9
v 
 .67 m / s
m 7.26
PROBLEM 4
A compact car, mass 725 kg, is
moving at 60 m/s. A) Find its
momentum. B) At what
velocity is the momentum of a
larger car, mass 2175 kg,
equal to that of the smaller
car?
m  725kg
v  60m / s
p  mv
p

43500
kgm
/
s
 725  60
m

2175
kg
 43500kgm / s
v ? pm
 43500  2175
 20m / s
PROBLEM 5
A snowmobile has a mass of
250 kg. A constant force is exerted
on it for 60 s. The snowmobile’s
initial velocity is 6 m/s and its final
velocity is 28 m/s. A) what is the
change in momentum? B) what is
the magnitude of the force exerted?
m  250kg
t  60s
v i  6m / s
p  m ( v f  v i )
 250( 28  6)
 5500kgm / s
v f  28m / s F  t  p

p
p  ?
F
t
F ?
5500kgm / s

60s
 92 N
PROBLEM 6
The brakes exerted a 640 N force on a
car weighing 15689 N and moving at
20 m/s. The car finally stops. A) What
is the car’s mass? B) What is the car’s
initial momentum? C) What is the
change in the car’s momentum?
D) How long does the braking force act
on the car to bring it to a halt?
F
W
t
vi
 640 N
 15689 N
?
 20m / s
v f  0m / s
m?
pi  ?
p  ?
t  ?
W  15689N
v  20m / s
m W g
m  1600.92kg
 15689  9.8
pi  mv i
 1600.92kg
 1600.92  20
 32018.4kgm / s
p i  32018kgm/s
p f  0kgm/s
Δp  p f  p i
 32018.4kgm /s
F  t  p
 32018.4kgm / s
t 
 640N
 50s
PROBLEM 7
What impulse is needed to stop a 45 g
mass traveling at 42 m/s?
m  .045kg
v i  42m/s
v f  0m/s
Impulse  ?
Impulse  change in momentum
 p f  pi
 mv f  mv i
 0  .045(42)
 1.89kgm / s
PROBLEM 8
Which has the greater momentum: a
145 g baseball traveling at 40 m/s or
45 g golf ball traveling at 67 m/s?
baseball
m  .145kg
golfball
m  .045kg
v  40m / s
v  67m / s
p  mv  5.8kgm / s
p  mv  3.015kgm / s
PROBLEM 9
A force of 540 N is used to stop an
object with a mass of 65 kg moving at
175 m/s. How long will it take to bring
the object to a full stop?
F  t  m(v f  vi )
m  65kg
t  ? s
vi  175m / s
v f  0m / s
F   540 N
 540  t  65(0  175)
65(0  175)
t 
 540
 21.06s
PROBLEM 10
In hitting a stationary hockey puck
having a mass of 180g, a hockey
player gives the puck an impulse of
6 N*s. At what speed will the puck move
toward the goal?
Impulse  m (v f  v i )
m  .180kg
impulse  6Ns
v i  0m / s
vf  ?m / s
6  .180(v f  0)
6
vf 
.180
 33.3m / s
Before
Collision
Person
0
Medicine ball 300
Total
300
After
Collision
60 * v
15 * v
300
60v  15v  300
75v  300
v  4 km/hr
Before Collision
After Collision
Granny
80 * 6 = 480
80 * v
Ambrose
0
40 * v
Total
480
480
80v  40v  480
120v  480
v  4m/s
Before Collision
Truck
Car
Total
After Collision
3000 * 10 = 30 000 3000 * v
0
1000 * 15 = 15 000
30 000
30 000
3000v  15000  30000
3000v  15000
v  5m/s
PROBLEM 11
Glider A of mass .355 kg moves
along a frictionless air track with a
velocity of .095 m/s. It collides with a
glider B of mass .710 kg moving in
the same direction at a speed of .045
m/s. After collision glider A continues
in the same direction with a velocity
of .035 m/s. What is the velocity of
glider B after collision?
Glider A
Glider B
ma  .355kg
mb  .710kg
vai  .095m / s
vbi  .045m / s
vaf  .035m / s
vbf  ? m / s
pinitial  pfinal
pai  pbi  paf  pbf
ma vai  mbvbi  ma vaf  mbvbf
m av ai  m bv bi  m av af  m bv bf
.355(. 095)  (. 710)(. 045)  .355(. 035)  .710v bf
.033725  .03195  .012425  .710v bf
.065675  .012425  .710v bf
.05325  .710v bf
v bf  .075m / s
PROBLEM 12
A .105 kg hockey puck moving at 48m/s is
caught by a 75kg goalie at rest. With what
speed does the goalie slide on the ice?
puck
ma  .105kg
Goalie
v ai  48m / s
v bi  0m / s
v af  x
v bf  x
m/s
m b  75kg
m/s
m a v ai  m b v bi  m a v af  m b v bf
(.105  48)  0  .105 x  75 x
5.04  75.105 x
5.04
x
75.105
 .0672m / s
PROBLEM 13
A 35 g bullet strikes a 5 kg stationary
wooden block and embeds itself in the
block. The block and the bullet fly off
together at 8.6m/s. What is the original
velocity of the bullet?
bullet
m a  .035kg
block
m b  5kg
v ai  ? m / s
v bi  0m / s
v af  8.6m / s
v bf  8.6m / s
ma vai  mb vbi  ma vaf  mb vbf
(.035  vai )  0  (.035  8.6)  (5  8.6)
vai  1237.17m / s
PROBLEM 14
A 35 g bullet moving at 475m/s strikes a
2.5 kg wooden block. The bullet passes
through the block, leaving at 275 m/s.
The block was at rest when it was hit.
How fast is it moving when the bullet
leaves ?
ma  .035kg
mb  2.5kg
vai  475m / s
vbi  0m / s
vaf  275 m / s
vbf  x m / s
m av ai  m bv bi  m av af  m bv bf
(.035  475)  2.5  0  .035  275  (2.5 x )
x  2.8m / s
PROBLEM 15
An astronaut at rest in space with
mass 84kg fires a thruster that
expels 35g of hot gas at 875m/s.
What is the velocity of the astronaut
after the firing shot?
Astronaut
ma  84kg
mb  .035kg
vai  0m / s
vbi  0m / s
vaf  ? m / s
vbf  875m / s
Thruster
m av ai  m bv bi  m av af  m bv bf
84(0)  .035(0)  84v af  .035(875)
0  84v af  .035(875)
v af
 .035(875)

 .365m / s
84
PROBLEM 16
A 4 kg model rocket is launched, shooting
50g fuel from its exhaust at an average
velocity of 625 m/s. What is the velocity of
the rocket after the fuel has burned?
(Ignore effects of gravity and air
resistance)
Rocket
Fuel
ma  3.95kg mb  .050kg
vai  0m / s
vbi  0m / s
vaf  ? m / s
vbf  625 m / s
0  m a v af  m b v bf
v af
 m b v bf

ma
x  7.815m / s
PROBLEM 17
Two campers dock a canoe. One
camper steps on the dock. This
camper has a mass of 80 kg and
moves forward at 4 m/s. With what
speed and direction do the canoe
and the other camper move if their
combined mass is 110 kg?
Camper
Camper and Canoe
m a  80kg
m b  110kg
v ai  0m / s
v bi  0m / s
v af  4 m / s v bf  ? m / s
pai  pbi  paf  pbf
0  m a v af  m bv bf
v bf
 m a v af

mb
x  2.9m / s
PROBLEM 18
Two students on roller skates stand
face to face, then push each other
away. One student has a mass of 90
kg, the other 60 kg. Find the ratio of
their velocities just after their hands
lose contact. Which student has the
greater speed?
ma  90kg
vai  0m / s
vaf  ? m / s
pi  pf
pai  pbi  paf  pbf
0  m av af  m bv bf
mb  60kg
v af
 mb

v bf
ma
vbi  0m / s
v af
 .66
v bf
vbf  ? m / s
The smaller mass has the larger vel ocity.
Their velo city are in opposite directions .
PROBLEM 19
Block A with a mass 12 kg
moving at 2.4 m/s makes a
perfect elastic head-on
collision with a block B,
mass 36 kg, at rest. Find the
velocities of the two blocks
after collision. Assume all
motion is in one dimension.
ma  12kg
mb  36kg
vai  2.4m / s
vbi  0m / s
vaf  x
vbf  y
ma vai  mbvbi  ma vaf  mbvbf
12( 2.4)  36(0)  12 x  36 y
12( 2.4)  12 x  36 y
2.4  x  3 y
3 y  2.4  x
1
vai  vbi  (v af  vbf )
2.4   x  y
2. 4  x  3 y
2. 4   x  y
y  1.2m / s
x  1.2m / s
2
PROBLEM 20
A 2575 kg van runs into the
back of a 825kg compact
car at rest. They move off
together at 8.5 m/s.
Assuming no friction with
the ground, find the initial
speed of the van.
m a  2575kg
m b  825kg
v ai  ? m / s
v bi  0
v af  8.5m / s
v bf  8.5m / s
m a v ai  m bv bi  m av af  m bv bf
2575v ai  825(0)  2575(8.5)  825(8.5)
2575v ai  21887.5  7012.5
2575v ai  28900
v ai  11.2m / s
PROBLEM 21
A 5g bullet is fired with a
velocity of 100 m/s toward a
10 kg stationary solid lock
resting on a frictionless
surface. What is the change
in momentum of the bullet if
it becomes embedded in the
block?
m a  .005kg
m b  10kg
v ai  100m / s
v bi  0
v af  x
v bf  x
m a v ai  m bv bi  m av af  m bv bf
.005(100)  10(0)  .005( x )  10( x )
.5  10.005x
x  .05m / s
Change in Momentum of Bullet
 ma (v af  v ai )
 .005(.05  100)
 0.5kgm / s
PROBLEM 22
A 50 g ball is struck with a club. The
force on the ball varies from zero
when contact is made up to some
maximum value (when the ball is
deformed) and then back to zero
when the ball leaves the club.
Assume the ball leaves the club
face with a velocity of +44 m/s.
Estimate the impulse due to the
collision.
Impulse  Change in Momentum
 .050( 0  44)
 2.2kgm / s
PROBLEM 23
In a particular car test, a 1.50 x 103
kg automobile collides with a
wall. The initial and final
velocities of the automobile are –
15 m/s and 2.6 m/s respectively.
If the collision lasts for 0.150s,
find the impulse due to collision
and the average force exerted on
the automobile.
F  T  pf  p i
F  .15  1500(2.6  15)
F  .15  26400
 176000N
PROBLEM 24
A baseball player attempts to use a
pitching machine to help him
improve his batting average. He
places the 50 kg machine on a
frozen pond. The machine fires a
0.15 kg baseball horizontally with a
speed of 36 m/s. What is the recoil
velocity of the machine?
machine
m a  50kg
baseball
m b  .15kg
v ai  0m / s
v bi  0m / s
v af  x
v bf  36m / s
m av ai  m bv bi  m av af  m bv bf
0  50 x  .15(36)
50 x  5.4
x  .11m / s
PROBLEM 25
An 1800 kg luxury sedan stopped at a
traffic light is struck from the rear by
a compact car with a mass of 900 kg.
The two cars became entangled as a
result of the collision. If the compact
car was moving at a velocity of +20
m/s before the collision, what is
velocity of the entangled mass after
the collision?
compact  car
m a  900kg
sedan
mb  1800kg
v ai  20m / s
v bi  0
v af  x
v bf  x
m av ai  m bv bi  m av af  m bv bf
900  20  1500(0)  900x  1800x
18000  2700x
x  6.67m / s
Ball
ma  1kg
Block
m b  2kg
v ai  6.3m / s
v bi  0m / s
v af  x
v bf  x
m av ai  m bv bi  m av af  m bv bf
1(6.3)  2(0)  1 x  2 x
6.3  3 x
x  2.1m / s