The speed of a rifle pellet by momentum
A practical application of the law of conservation of momentum to measure the speed of a fast-moving object.
Apparatus and materials
Air rifle and pellets
Lengths of gauge 0 straight railway track, 5
Flat truck, gauge 0
Stopclock or stopwatch
Health & Safety and Technical notes
Make absolutely certain the rifle is unloaded before setting up or adjusting the experiment.
A safety screen should be used, with students standing at a distance behind the rifle.
All present should wear eye protection.
Absorbing material should be used to catch stray pellets.
The rifle must remain fixed to the board at all times. You should check whether a licence is needed. (In the UK you will need a licence if the muzzle energy of the pellet exceeds 16.25 J.)
The rifle is securely bolted on its side to a board near to one end. It is mounted on two blocks of wood of suitable height to ensure the pellet will hit the centre of a 200-300 gramme mass of Plasticine on the truck. The bolts go through the two blocks of wood which act as spacers. The barrel of the gun must be parallel to the track; and the assembly should be such that the loading mechanism can be pulled out sideways.
The straight railway track is laid along the trolley board to take the flat truck with its Plasticine load. The board should be inclined slightly to compensate for friction so that the truck runs down the track at constant speed when given a start. The truck is placed a few centimetres from the muzzle. A metre rule is placed on the board parallel to the track with its end 7-10 centimetres along the track from the end of the truck.
There must be a safety stop at the end of the range to catch pellets. This may be a large block of Plasticine or clay or a large block of polystyrene with wooden backing (at least 2 cm thick). It would be wise to add a metal plate behind that. Alternatively, a large box of sand can be used.
The rifle should be loaded immediately before firing as any delay may produce inconsistent results due to air escaping or weakening of the spring.
a Friction compensate the board. Otherwise the truck may not travel one metre.
b Pull back and then close the loading mechanism in order to insert a pellet and cock the rifle.
c Fire the rifle, after a count-down.
d Start the stop clock when the truck reaches the beginning of the metre rule and stop it when the truck has travelled one metre.
e Use this time to calculate the velocity of the loaded truck assuming the conservation of momentum.
f Calculate the initial kinetic energy of the pellet and the final kinetic energy of the pellet and truck
g The velocity of the pellet can be confirmed by a time-of-fight method.
It is tempting to place the beginning of the metre rule at the truck before firing, and start the stopwatch when the rifle is fired. That procedure, however, is likely to make students associate the measurement with an acceleration from rest. You want the constant velocity of the truck (and pellet) after impact. Therefore, it is better for the sake of appearances to let the impact occur first and then make a measurement of speed at a stage that is clearly later.
Students can calculate the velocity of the pellet assuming the conservation of momentum. The loaded truck is weighed and the average mass of a pellet is also found by weighing, say, a group of 10 or 20 of them.