Conservation of Momentum & Collisions – Class Notes (KEY)
In-Class Practice:
1. Two figure skaters (of mass 50 kg and 75 kg) stand next to each other on the
ice. They push off each other, and head off in opposite directions. If the more
massive skater moves with a velocity of 10 m/s, find the velocity of the less
massive skater.
mv  mv  mv  mv
50(0)  75(0)  50v  75(10)
v  15 ms (opposite direction as the more massive skater)
2. A 1200 kg car barrels down a city street at 40 m/s. It hits a stationary 4000 kg
truck. If the two vehicles, stick together, find the velocity of the “car pile”.
mv  mv  MV
1200(40)  4000(0)  5200V
V  9.23 ms (still moving forward)
3. Another 1200 kg car barrels down a city street at 40 m/s. It rear-ends a 4000 kg
truck that is moving at 20 m/s in the same direction. If the two vehicles do not
stick together, and the truck attains a speed of 25 m/s, find the velocity of the
car.
mv  mv  mv  mv
1200(40)  4000(20)  1200v  4000(25)
v  23.33 ms (still moving forward)
4. A 1,000 kg car, which is heading East at 40 m/s, collides head-on with a 2,200
kg car heading West at 25 m/s. The force of the collision causes enough heat to
weld the cars together. Find the velocity of the car pile.
mv  mv  MV
1000(40)  2200(25)  3200V
V  4.69 ms (since East is  and West is -, the final velocity of the pile is West)
5. Another 1,000 kg car, which is also heading East at 40 m/s, collides head-on
with another 2,200 kg car heading West at 25 m/s. COINCIDENCE? ……
Maybe. After the collision, the cars move separately. The 1,000 kg car moves
West at 10 m/s. Find the velocity of the 2,200 kg car.
mv  mv  mv  mv
1000(40)  2200(25)  1000(10)  2200v
v  2.27 ms (since East is  and West is -, the final velocity of larger car is also West)
Homework:
1. A boy holds a 1 kg rifle loosely and fires a pellet of mass 1 gram. The pellet’s velocity is 150 m/sec. With
what velocity does the gun recoil?
(1kg)(0 ms )  (.001kg)(0 ms )  (1kg)(v)  (.001kg)(150 ms )
 (1kg)(v)  (.001kg)(150 ms )
v  .15 ms
Since the sign is negative, this implies that the gun recoils in the opposite direction as the bullet.
2.
(1+48+.001)(0) = (49)v + (.001)(150)
v = -.003 m/s
3. A shell of mass 25 kg is fired horizontally eastward from a cannon of mass 1200 kg. The velocity of the shell is
500 m/sec. What is the magnitude and direction of the recoil?
(25kg)(0 ms )  (1200kg)(0 ms )  (25kg)(500 ms )  (1200kg)(v)
 (1200kg)(v)  (25kg)(500 ms )
v  10.4 ms
Since the sign is negative, this implies that the gun recoils in the opposite direction as the bullet.
4. A 1 kg ball moving forward at 5 m/sec hits a second ball which is at rest. After the collision, the 1 kg ball
reverses its direction and moves at 1 m/sec. The second ball moves forward at 2 m/sec. What is the mass of
the second ball?
forward is POSITIVE
reverse is NEGATIVE
(1kg)(5 ms )  (m)(0 ms )  (1kg)( 1 ms )  (m)( 2 ms )
6 N  s  (2 ms )m
m  3kg
5. A 2 gram ball is moving at 4 cm/sec. It collides with a target ball of unknown mass. After the collision, the
ball continues to move forward at 2 cm/sec while the target ball moves forward at 3 cm/sec. What is the mass
of the target ball?
Need to convert ve locity from cm/s to m/s.
(.002kg)(.04 ms )  (m)(0 ms )  (.002kg)(.02 ms )  (m)(.03 ms )
m  .0013kg  1.3g
6. An astronaut of mass 80 kg carries an empty oxygen tank of mass 10 kg. He pushes the tank away from
himself with a velocity of 2 m/sec. What is the velocity of the astronaut?
(80kg)(0 ms )  (10kg)(0 ms )  (80)(v)  (10kg)( 2 ms )
v  .25 ms
Since the sign is negative, this implies that the astronaut goes in the opposite direction as the tank.
7. A train is being made up in a freight yard. An empty box car coasting at 10 m/sec strikes a loaded car that is at
rest, and the cars couple together. Each car has a mass of 3000 kg empty, and the loaded car contains
12,000 kg of bottled soft drinks. What is the new velocity of the pair?
STICK!!!
(3000kg)(10 ms )  (3000kg  12000kg)(0 ms )  (18,000kg)(v)
v  1.67 ms
8. An 82 kg fullback moving at 6.67 m/sec is tackled by a 100 kg linebacker approaching him at 3.34 m/sec.
What is the speed and direction of the players after the tackle?
STICK !!!
(82kg)(6.67 ms )  (100kg)( 3.34 ms )  (82kg  100kg)(v)
v  1.17 ms [in the fullbacks original direction]
9. A toy railroad car of mass 0.5 kg is moving on a straight track at 0.1 m/sec. It collides with a similar car
traveling in the same direction at 0.06 m/sec. The cars lock together on impact. What is the velocity of the
pair?
STICK!!!
(0.5kg)(0.1 ms )  (0.5kg)(0.06 ms )  (0.5kg  0.5kg)(v)
v  .08 ms [forward]
10. A life raft of mass 200 kg carries two swimmers of mass 50 kg and 80 kg, respectively. The raft is initially at
rest, then the swimmers dive off opposite ends at 4 m/sec. What is the velocity and direction of the raft?
STICK !!!
(200kg)(0 ms )  (50kg)(0 ms )  (80kg)(0 ms )  (200kg)(v)  (50kg)( 4 ms )  (80kg)( 4 ms )
v  .6 ms
Since the 80 kg boy had the negative velocity, the raft must move in the opposite direction of thic boy.
Therefore, v  .6 ms [in the direction that the 50kg boy jumped]