Elastic collisions with bodies of equal mass
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 with hooks, 5 cm diameter, 2
Edinburgh CO2 pucks kit (2 or 3 magnetic pucks and a glass base)
Blu-tak or Velcro
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.
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.
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.
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.
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.
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.
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