SITEMAP School-college Physics Notes: Forces & motion Section 4.
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Forces and Newton's Laws of Motion 4.3 Experiments described to investigate Newton's 2nd law of motion
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4.3 Experiments to investigate Newton's 2nd law of motion (F = ma)
The experiments described below can be used to investigate how force and mass affect acceleration.
These experiments use light gates to measure speed - so they need to be explained!
In version 1, with one light gate, you use an inverted Π shaped card (rectangle with a middle section cut out).
The lengths of the upright sections that cut the light beam are d1 and d2 (which you can make the same).
As the trolley and card pass through the light gate, the first section of card of length d1, cuts light beam for time t1 (for speed 1).
When the second section of the card of length d2 passes through the light gate, the beam is cut for time t2 (for speed 2).
At this point the combined light gate also records the time difference t3 between the two speed measurements (for acceleration a). So for speed s ...
s1 = d1/t1, s2 = d2/t2, acceleration = change in speed / time taken = a = (s2 - s1) / t3
However, all you do is input d1 (= d2) into the computer and the software does the acceleration calculation for you!
Obviously, the computer software system must be set up to suit the way you have set up the experiment.
In version 2, with two light gates, you use a rectangular shaped card [ ] of length d.
You set up two light gates a suitable distance apart.
When the trolley and card pass through the first light gate, the beam is cut for t1.
After passing through the 2nd light gate, time t2 is recorded.
At this point the combined light gates also record the time difference t3 between the two speed measurements.
Its now a similar data situation to version 1 of the experiment, so for speed s ....
s1 = d/t1, s2 = d/t2, acceleration = change in speed / time taken = a = (s2 - s1) / t3
Again, the computer software system must be set up to suit the way you have set up the experiment and will do the acceleration calculation for you.
Example of calculation for experiment version 2
Investigation version 1 using one light gate
Error correction NOT shown in the diagram above
The experiment is conducted on a smooth bench on which a trolley can freely run.
You need to mark on a start line to keep things consistent.
The total mass of the trolley and extra weights (m) is measured and can be altered by adding extra weights.
On the trolley is fixed a 'rectangular' Џ shaped card, whose two arms will block the light beam twice when the trolley passes through the light gate when it measures the time taken twice.
The trolley is connected by wire or string to the weights via the pulley wheel, that on falling, provide the downward force to accelerate the trolley along the 'runway'
The time measured by the light gate system is recorded electronically and passed to the connected data logger or computer.
As the Џ card passes through the light gate, the light beam is cut off twice, so two velocities are measured and the time interval between them.
The principles of the F = ma calculations for version 1.
The accelerating force F is given by the falling weight: mass in kg x 9.8 N/kg
The mass being accelerated = total mass of trolley plus weights (m)
The acceleration is given by the light gate velocities divided by the time interval between them: a = v2 - v1 / Δt
You can do a series of experiments with constant trolley mass m, and varying the accelerating force F by varying the falling weights on the end of the hook.
Sources of error
Investigation version 2 using two light gates
Error correction NOT shown in the diagram above
As the [ ] card goes past the light gates, the two time intervals for blocking the light give you an initial and final velocity, and the time interval between these two events can be used to calculate the acceleration of the trolley.
The investigations, calculations and graphs you can do are described above in method 1.
Version 3 of acceleration experiments.
You can run the trolley down an inclined ramp onto the level running board and then past two light gates (2 and 3) to measure the final velocity.
Keywords, phrases and learning objectives for experiments to show the validity of Newton's 2nd law of motion
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