Name
Date
Pd
Impulsive Force Model Worksheet 4:
Conservation of Momentum II
(All units of momentum in the momentum conservation diagrams are kgsm .)
1. Old cannons were built on wheeled carts, both to facilitate moving the cannon and to allow the
cannon to recoil when fired. When a 150 kg cannon and cart recoils at 1.5 m/s, at what velocity
would a 10 kg cannonball leave the cannon?
a. Complete a conservation of momentum diagram for firing one of these cannons.
event:
Explosive interaction where two objects at rest push off each other.
initial
object/mass/velocity
final
object/mass/velocity
10 kg at 0 m/s
10 kg at ? m/s
150 kg at 0 m/s
150 kg at -1.5m/s
–
150
+
-150
0
–
b. Momentum conservation equation:
0  0  m150 f v150 f  m10 f v10 f
c. Find the velocity of the cannonball.
0
+
225 kgsm
 22.5 ms  22 ms
10kg
2. On an icy road, a 5000 kg truck rear-ends a 1200 kg car that had been traveling at 13 m/s, causing
the truck to slow from 14 m/s to 12 m/s and the car to speed up.
a. Complete the momentum conservation diagram for the accident.
0  0  10kg(v10f )  150kg( 1.5 ms )  v10f 
event: Two moving objects collide but do not stick together.
initial
object/mass/velocity
final
object/mass/velocity
5000 kg at 14 m/s
5000 kg at 12 m/s
1200 kg at 13 m/s
1200 kg at ? m/s
+
–
0
40,000
0
40,000
–
+
b. Momentum conservation equation
m5000 iv 5000i  m1200iv1200i  m5000f v 5000f  m1200f v1200f
c. Find the final velocity of the car.
5000kg (14 ms )  1200kg (13 ms )  1200kg (v1200 f )  5000kg (12 ms )
v1200 f 
70,00 kgsm  15,600 kgsm  60,000 kgsm
 21 ms
1200kg
©Modeling Instruction – AMTA 2013
1
U9 Momentum – ws 4 v3.1
3. When radium-226 decays, it becomes radon-222 by ejecting an alpha particle - two protons and
two neutrons (a helium nucleus).
 decay occurs 
226
222
4
Ra
Rn
He
a. Complete a qualitative momentum conservation diagram for the radioactive decay of radium-226.
(Recall from chemistry that the isotopic number of an element is related to its mass.)
event: Interaction where one object splits into two and the objects push off each other.
initial
object/mass/velocity
final
object/mass/velocity
226 mass units at 0 m/s
222 mass units at ? m/s
4 mass units at ? m/s
–
0
+
–
0
+
b. Momentum conservation equation:
0  0  m222f v 222f  m4 f v 4 f
c. How many times larger will the final velocity of the alpha particle be compared to the final
velocity of the radon-222?
v
222m
0  0  222mv 222f  4mv 4f  4f  
 v 4f  55.5v 222f
v 222f
4m
4. An apple falls from a tree.
a. Complete a qualitative conservation of momentum diagram where the apple is initially
attached to the tree and the final situation is just before the apple hits the ground.
event:
Interaction where two stationary objects pull on each other and move toward each other.
initial
object/mass/velocity
final
object/mass/velocity
apple at 0 m/s
apple at ? m/s
earth at 0 m/s
earth at ? m/s
–
0
+
–
0
+
b. Momentum conservation equation:
0  0  mearthf vearthf  mapplef vapplef
©Modeling Instruction – AMTA 2013
2
U9 Momentum – ws 4 v3.1
5. Airplanes maneuver on the
ground by using thrust from their
jets or propellers. A fully loaded,
396,900 kg Boeing 747-400 gets
a total of 1100 kilonewtons of
thrust from its jet engines. (Data
from Boeing's website.) Takeoff
speed depends on a number of
factors like air temperature,
airplane weight, and airport
elevation, but let us say that
liftoff will occur at 170 mph.
a. Determine the time the plane takes to go from 0 to 170 mph. (1 mile = 1600 meters)
F t  mv  t 
1600 m
1hr
m
396,900kg 170 mi
hr ( 1mi )( 3600 s )   (0 s )

1,100,000N

396,900kg (75.6 ms )
 27s
1,100,000N
b. Complete a conservation of momentum diagram showing how the initially stationary airplane
gets to takeoff speed.
event: Interaction where airplane and ejected gases push off each other.
initial
object/mass/velocity
final
object/mass/velocity
396,900 kg at 0 m/s
396,900 kg at 76 m/s
? kg of gases at 0 m/s
? kg gases at -? m/s
–
0
3.0x108
+
-3.0x108
0
–
c. Momentum conservation equation:
0  0  mplanef v planef  mgasesf v gasesf
+
d. Determine the momentum of the airplane at takeoff.
p  mv  396,900kg(75.6 ms )  3.0  107 kgsm
e. Calculate the impulse the plane receives from the exhaust gases during takeoff.
Using the answer from d. it must be 3.0x107 Ns since the impulse and change in momentum
are numerically equal. One could also multiply the force times the time and get the same
answer.
f. What additional information would be needed to calculate the velocity of the exhaust gases
from the engines?
Need to know the mass of the exhaust gases.
©Modeling Instruction – AMTA 2013
3
U9 Momentum – ws 4 v3.1