Henry Ford Community College
Science Division
Winter 2014
Physics 131, Section 70
Conservation of Linear Momentum and Collision
The Law of Conservation of Linear Momentum
The Law of Conservation of Momentum states that “If the net external force acting on a system
of objects is zero (in other words if there are no outside forces acting on the system of moving
objects), the total momentum of the objects in the system will remain constant”.
Questions on Law of Conservation of Linear Momentum
Question 1 (To be solved in class)
A bullet of mass 65 g is fired with an initial velocity of 550 m/s from a gun with mass 4.50 kg.
What is the speed of recoil of the gun?
Question 2 (To be solved in class)
A cannon is mounted on a railroad car. The cannon shoots a 1.75 kg ball with a muzzle velocity
of 300 m/s. The cannon and the railroad car together have a mass of 4500 kg. If the ball, cannon
and railroad car are initially at rest, what is the recoil velocity of the car and cannon?
Question 3 (To be solved in class)
An astronaut is floating in space near her shuttle when she realizes that the cord that is
supposed to attach her to the ship has become disconnected. Her total mass (body, suit and
equipment) is 90 kg. She reaches into her pocket and finds a 1 kg metal tool and throws it out
into space with a velocity of 6 m/s, directly away from the ship. If the ship is 10 m away, how
long will it take her to reach it?
Collision
Conservation of Linear Momentum is used to analyze collisions. The objects whose collisions we
will analyze form a system, and although the objects exert forces on each other during impact,
these forces are internal. They occur within the system. The system’s total linear momentum is
conserved.
Collisions are classified as either Elastic or Inelastic.
Elastic Collision
A collision is said to be elastic if kinetic energy is conserved and the two colliding objects return
to their original shape without being permanently deformed. An example of such a collision is
when two billard balls collide. The loss of kinetic energy is small enough to be ignored.
Example of Elastic Collision (To be solved in class)
Two balls roll toward each other. The red ball has a mass of 0.5 kg and a speed of 4 m/s just
before impact. The green ball has a mass of 0.3 kg and a speed of 2 m/s. After a head-on
collision, the red ball continues forward with a speed of 2 m/s. Find the speed of the green ball
after the collision. Was the collision elastic?
Inelastic Collision
Inelastic collisions are collisions in which the total kinetic energy is different after the collision.
During a perfectly inelastic collision, two objects collide and become entangled or coupled
together.
Example of Perfectly Inelastic Collision (To be solved in class)
Two balls roll toward each other. The red ball has a mass of 0.5 kg and a speed of 4 m/s just
before impact. The green ball has a mass of 0.3 kg and a speed of 2 m/s. The two balls stick
together after colliding. What will be the velocity of the composite objects after collision?
Questions on Collision
Question 1 (To be solved in class)
A 2275 kg car traveling at 28 m/s rear ends an 875 kg compact car traveling at 16 m/s on ice in
the same direction. The two cars stick together. How fast does the wreck move immediately
after the collision?
Question 2 (To be solved in class)
A 0.105 kg 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?
Question 3 (To be solved in class)
An 8 g bullet is fired horizontally into a 9 kg block of wood on an air table and is embedded in it.
After the collision, the block and the bullet slide along a frictionless surface together with a
speed of 0.1 m/s. What was the initial speed of the bullet?
Question 4 (Student Practice)
A hockey puck, mass 0.115 kg moving at 35 m/s, strikes an octopus thrown on the ice by a fan.
The octopus has a mass of 0.265 kg. The puck and octopus slide off together. Find their velocity.
Question 5 (Student Practice)
A 95 kg fullback running at 8.2 m/s collides in midair with a 128 kg defensive tackle moving in
the opposite direction. Both players end up with zero speed.
a.
b.
c.
d.
e.
What was the fullback’s momentum before the collision?
What was the change in the fullback’s momentum?
What was the change in the tackle’s momentum?
What was the tackle’s original momentum?
How fast was the tackle moving originally?
Question 6 (To be solved in class)
A 92 kg fullback, running at 5 m/s attempts to dive across the goal line for a touchdown. Just as
he reaches the goal line, he is met head-on in mid-air by two 75 kg line backers, one moving at
2 m/s and the other at 4 m/s. If they all become entangled as one mass, with what velocity do
they travel? Does the full back score?