Welcome to practical physicsPracticle physics - practical activities designed for use in the classroom with 11 to 19 year olds
 

Elastic collisions with bodies of equal mass

Demonstration

This is a useful demonstration to help students understand the shape of the tracks when an alpha particle collides with the nucleus of an atom (particularly a helium atom) in a cloud chamber.

Apparatus and materials

Photograph of Alpha particle tracks including a collision with a helium nucleus

Steel balls

Steel balls with hooks, 5 cm diameter, 2


Floating pucks

Edinburgh CO2 pucks kit (2 or 3 magnetic pucks and a glass base)

Mass, 500g

Blu-tak or Velcro

Dry ice

OR CO2 cylinder and dry ice attachment

Flexicam or webcam linked to a projector (OPTIONAL)

Leather gloves and eye protection 

Health & Safety and Technical notes


If the pendulums are attached to the ceiling, ensure that an adult is available to hold the step-ladder while another one works at a height. 

Remember to wear leather gloves and eye protection when handling dry ice.

Read our standard health & safety guidance

You can use either method.  

Although the pucks require specialist apparatus and take a bit more setting up, they show the paths of the pucks very clearly in a single plane. 
 
The dry ice provides a cushion of carbon dioxide gas to make the pucks float. You have some dry ice available from cloud chamber experiments. 
 
You could set up a flexicam underneath the pendulums (facing upwards) and project it onto a screen. This will show their motion in the horizontal plane. Similarly, you could set up a flexicam above the pucks to watch their motion. 
 
In either experiment, you could capture short movie clips of collisions. You could use interactive whiteboard software to draw lines over the motion and measure the angles between the paths. 
 
The pucks can also be recorded using multiflash photography (see guidance note Multiflash photography). You will need a (digital) camera with a shutter that can be held open and a bright strobe light. 

 

Procedure


Steel balls

a Suspend the two massive steel balls from the ceiling to make two very long pendulums. 
 
b Adjust them so that they are at the same height. 
 
c Draw one of the pendulums aside and release it so that it makes an oblique collision with the other stationary ball. 
 Elastic collisions with bodies of equal mass
 
d Draw attention to the directions of the balls after the collision. They should set off at right angles to each other. 
 
e Try a number of collisions with different lines of impact. Show that, although the angles of the paths after the collision change, they are always at right angles to each other. 
 
Floating pucks 
f Make sure that the glass base is level. 
 
g Put some dry ice in the cavity underneath the pucks. They should float on a cushion of CO2
 
h Put one of the pucks in the centre of the base.

 Elastic collisions with bodies of equal mass
 
 
i Gently push the other one towards it so that they make an oblique collision. The metal of the pucks should not come in contact – this will make the collision less elastic. 
 
j Draw attention to the motion of the pucks after the collision. When they have equal mass, they should set off at right angles to each other. 
 
k Try a number of collisions with different lines of impact. Show that, although the angles of the paths after the collision change, they are always at right angles to each other. 
 
l Increase the mass of the target puck (by putting another puck on top or by attaching a 500g mass with some Blu-tak or Velcro). Try some more collisions and draw attention to the angle between the paths after the collision. 
 
m Swap the pucks around and use the less massive one as the target. Try some more collisions and draw attention to the angle between the paths each time. 

 

Teaching notes


1 When the colliding masses are equal, the angle between the paths after the collision is 90°. You can show this in photographs of a cloud chamber filled with helium gas instead of air (see the photograph Alpha particle tracks including a collision with a helium nucleus). This shows that the alpha particle has the same mass as a helium atom and is evidence that it is itself a helium nucleus. 
 
2 Such forks occur so rarely that there is little chance of seeing one of them unless you have a lot of observing time. Human scanners were employed to find interesting photographs which could then be analyzed. Similar triage processes are now used at CERN. Results are analyzed by software and humans to find interesting events. 
 
3 When the alpha particle collides with a more massive nucleus, like nitrogen (see the photograph Alpha particle tracks including a collision with a massive nucleus), then the angle between the forked tracks is more than a right angle. This is modelled in step l of the pucks experiment. 
 
4 When the alpha particle collides with a less massive nucleus like hydrogen (see the photograph Alpha particle tracks including a collision with a hydrogen nucleus), the angle between the tracks is less than a right angle. This is modelled in step m of the pucks experiment.
 
5 Advanced students might appreciate a mathematical proof of the right angle result for equal masses. Using the conservation of momentum, you can draw a closed triangle of vectors. Conservation of kinetic energy produces an equation linking the squares of the velocities (before and after). In the special case where the masses are equal, these two equations give a triangle whose longest side squared equals the sum of the squares of the other two sides. This shows that there is a right angle between the two shorter sides. Further analysis is described in Two dimensional momentum interchanges with pucks
 
This experiment was safety-checked in April 2006

 

Related guidance


Evidence for the hollow atom

Developing a model: the nuclear atom

Alpha particle tracks

Making dry ice

Multiflash photography


Related experiments


Display of cloud chamber photographs

Alpha radiation: range and stopping

Two dimensional momentum interchanges with pucks