Apparatus: Metre Rules
Stopwatches
Triple beam balance
Electronic top-pan balance
Light gates attached to Acorn Risc computer (with software for light-gates)
Wheeled trolleys and track
Mass bars
Air track and gliders
Mass discs
Spreadsheet and other software
Calculator (included in Excel)
Method:
- Put air track on firm stable desk or table
- Weight (mass) trolleys separately and record their mass.
- Put 2 trolleys on air track facing each other in opposite directions
- Put bands on each trolley so that they push each other after collision
- Install two light gates and then connect them to computer
- Turn on Acorn Risc computer
- Turn on air glider so that air goes through air glide
- Set software on velocity of 2 trolleys
- Separate manually two trolleys and put at each extremity
- With help of partner push trolleys towards each other at same time
- Repeat two or three times to avoid uncertainties and random errors
- Record velocities of both trolleys before and after collision
- Make appropriate calculations. (show below)
- Repeat calculations for every single trial
Fig 1. diagram of apparatus and experiment set
Momentum of a body of mass m, moving with velocity, is given by p=mv.
The units of momentum are kgms-1
i.e m1v1 + m2v2 = m1v1 + m2v2
E.g. Total momentum= mass x velocity of trolley A + mass x velocity of trolley B
200 g . + 200g .
Law of conservation of momentum, the momentum after the collision is equal to the momentum before collision.
Calculation of Momentum: eg1
Total momentum before = 0.2 x 45.4 + 0.2 x 39.5
= 16.98 kgms-1
Total momentum after = 0.2 x 39.5 + 0.2 x 44.8
= 16.86 kgms-1
% change = - 0.7
-0.707 and -0.629
Calculation of K.E
K.E = ½ mv² (but energy is a scalar, not a vector).
Total K.E before = ½ (0.2 x 45.4 + 0.2 x 39.5) ^2
= 72.4 Joules
Total K.E after = ½ (0.2 x 44.8 + 0.2 x 39.5)^2
= 71.3 Joules
% Change in kinetic energy = -1.5 % ± 1%
-1.515 and 1.485
Uncertainties and errors in experiment:
Systematic errors: In computer software, might be a lack of precision in measuring equipment. Stopwatch might have systematic error as well.
Random uncertainties caused by computer software:
Quantization, may be caused when converting continuous analogue data into individual digital numbers.
Sampling frequency, the computer can only record a number every x second. If the data changes significantly within this amount x of time, then sampled results will be almost random compared to actual signal.
Friction: the air track is there to avoid any friction however there will always be a small amount of friction.
If we accept that an uncertainty (sometimes called an indeterminacy) of about 1% of the measurement being made is reasonable.
Conclusion:
The laws have been verified and found to be true. The results found were close to 0% although 0 was never reached, it might be due to the significant numbers of uncertainties (random and digitally recorded data) and the systematic errors. Therefore, momentum and kinetic energy are conserved during one-dimensional-elastic collisions (not enough time to try the inelastic collisions with different apparatus). This piece of information is very relevant since it enables us to know the momentum and the kinetic energy after a collision before the collision occurred. Nonetheless, there is a lot of room fro improvement in this experiment, and find below some of them:
- Take uncertainty of 1% in every single piece of data, final result will then be a lot more accurate, but time limits.
- Make more trials to verify laws, more than 4 times at least.
- Take uncertainty in consideration more carefully following rules of finding uncertainties.
- Describe method in more details so that anyone can follow it.
- Make sure there are no time limits next time.
- Draw more diagrams to show apparatus after each step.