PlanningGuide

Module 4

Lesson 1.13
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. Examples
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Lesson 1.13
Lesson 1.14
Lesson 1.15
Lesson 1.16
Lab 1.13
Lab 1.14
Lab 1.15
Lab 1.16
Project 4


LESSON 1.13 - COLLISIONS

Overview
This lesson deals with the conservation of momentum when two or more objects interact. On completion of the lesson, you should be able to calculate the velocities of objects after elastic and inelastic collisions. You should also be able to describe typical elastic and inelastic collisions and discuss the vectors involved in collisions.


ACTIVITIES

  1. Match Projectiles: Use a drinking straw as a blowpipe to launch matches at a target. Shorten the straw by cutting a piece off the straw and see how this affects the range of the blowpipe.
  2. Use marbles or pool balls to illustrate how momentum is conserved during collisions.

Systems
A system is a defined collection of objects. It is common to define a system in terms of a boundary around the system. In dealing with collisions, the system usually consists of the objects that collide. Another system could be a rifle that is at rest before a projectile is fired from it. The rifle and the projectile make up the system. After the item is fired both the rifle and the bullet move.

Conservation of Momentum
The net momentum of a system does not change. If a moving object collides with a stationary object, the combined momentum of the two objects after collision is the same as the momentum of the moving object before collision. If a rifle is fired, the momentum of the bullet in one direction cancels the momentum of the rifle as it moves in the opposite direction.

Types of Collisions
Collisions can be elastic, inelastic or a combination of the two. In an elastic collision, no energy is lost during the collision. In an inelastic collision, some energy is coverted to other forms but momentum is conserved. If a bullet hits a sandbag that is hanging on a piece of rope, the sand will absorb some of the bullet’s energy but the combined momentum of the bag and the bullet will be nearly the same as the momentum of the bullet before collision.

Momentum Vectors
If objects collide in such a way that their directions differ after collision from the directions of the colliding objects, the net momentum an any direction will be the same as before the collision. For example, if a moving pool ball collides with a stationary pool ball and both move off at an angle, the components of their momenta in different directions will either be the same as the momentum of the first moving ball or they will cancel out.

Example 1.13.1 Collision
A freight car with a mass of 9000 kg moving along a track at 2 m/s collides elastically with a stationary freight car with a mass of 10,000 kg and stops.

  1. Assuming that no momentum is lost during the collision, what will be the speed of the second railcar after the collision?
  2. If the cars hook together during the collision and the collision can be regarded as inelastic, what will be the speed of both cars after the collision?

Solution

a) The momentum of the first freight car = 9000 x 2 = 18000 kg-m/s

If it stops on collision, the second railcar must absorb a momentum of 18000 kg-m/s

The second car’s velocity must therefore be = (18000 kg-m/s) / (10000 kg)
= 1.8 m/s

b) The momentum of the freight car = 9000 x 2 = 18000 kg-m/s

The combined momentum after the collision must be = 18000 kg-m/s

The combined mass of the two cars is 19000 kg.

The velocity must therefore be = (18000 kg-m/s) / (19000 kg) = 0.947 m/s

Review Questions

  1. If two glass marbles collide, is the collision likely to be elastic or inelastic?
  2. If a railcar moving along a track collides with a second railcar and the couplings join during the collision, is the collision regarded as elastic or inelastic?
  3. A system consists of a person standing on a skateboard holding a large rock. If nothing in the system moves, what is the momentum of the system?
  4. If the person throws the rock away from the skateboard in a direction in line with the wheels, will the skateboard move?
    If it moves, in what direction will it move?
  5. If the rock has a mass of 20kg and it leaves the person’s hands with a velocity of 2 m/s, what will be the combined momentum of the person and the skateboard as the rock leaves the person’s hands? Why?
  6. A marble with a mass of 15 grams moving at 2 m/s collides with an identical marble that is at rest. After the collision, the first marble is at rest. What is the speed of the second marble after the collision?
  7. A marble with a mass of 15 grams swinging on the end of a piece of string and moving at 2.5 m/s collides with a lump of putty that is attached to the end of a second piece of string. The putty has a mass of 20 grams and is stationary prior to the collision. What is the combined momentum of the putty and marble after the collision?
  8. A marble rolls down a chute and collides with a stationary marble with the same mass at the edge of a table. If the arrow, A, in the diagram below indicates the velocity of the marble prior to collision and B indicates the velocity of the stationary marble after collision, draw an arrow that roughly indicates the direction of the first marble after collision.


ACTIVITIES

  1. Match Projectiles: Use a drinking straw as a blowpipe to launch matches at a target. Shorten the straw by cutting a piece off the straw and see how this affects the range of the blowpipe.
  2. Use marbles or pool balls to illustrate how momentum is conserved during collisions.

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HANDS-ON HOMEWORK
Select one or more of the recommended activities for Lesson 1.14, collect the items needed and test the procedure before demonstrating the activity during the next theory lesson.

Lesson 1.13 Collisions

  1. Mainly elastic.
  2. Inelastic.
  3. Zero
  4. Yes. In the opposite direction to the rock.
  5. The momentum of the person and the skateboard will be the same as that of the rock but in the opposite direction. The net momentum must be the same after the rock has been thrown as it was before the rock was thrown because nothing outside of the system (consisting of the person, the rock and the skateboard) has influenced the system. The momentum of the person and the skateboard will be equal to 20kg x 2 m/s = 40 kg-m/s.
  6. 2 m/s. All of the momentum from the first marble will have been transferred to the second marble.
  7. Momentum before collision = 0.015kg x 2 m/s = 0.03 kg-m/s. The momentum of the system after collision must be the same. the combined mass is 0.015kg + 0.02kg = 0.035 kg.
    The velocity just after impact will be = 0.03 / 0.035 = 0.857 m/s
  8.