F=ma using ticker timer
Extracts from this document...
Introduction
Physics Investigation: F = ma using a Ticker Timer
Data Collection and Processing:
Mass of trolley – (496.70±0.01)g
m/g  ML/g  M/(±0.01)g  t/s  s/(±0.05)cm  a/ms2  Δa/ms2  F/N  ΔF/N 
100  300  796.70  0.36  10.20  1.57  ±0.015  1.25  ±0.012 
150  250  746.70  0.36  10.20  1.57  ±0.015  1.17  ±0.011 
200  200  696.70  0.36  12.30  1.90  ±0.015  1.32  ±0.011 
250  150  646.70  0.36  13.60  2.10  ±0.015  1.36  ±0.010 
300  100  596.70  0.36  16.80  2.59  ±0.015  1.55  ±0.009 
Key  Sample Calculations 
m is the mass that hangs from the pulley.   
ML is the load on the trolley.   
M is the total mass of trolley.  M = 496.70 + ML First row: 
Middle
s is the length for 18 ticks.

a is the actual acceleration of the trolley.
s = ut +at2
∴ a =
First row:
a =
= 1.57ms2
Δa is the absolute uncertainty of a.
Δa =
First row:
Δa =
= ±0.015ms2 (2s.f)
F is the net force acting on trolley.
F = Ma
First row:
F =
= 1.25N
ΔF is the absolute uncertainty of F.
ΔF =
First row:
ΔF =
= ±0.012N (2s.f.)
Attached is the graph of a/ms2 against F/N.
The first value, (1.25, 1.57) is rejected as the net force, 1.25N, is larger than the second value of 1.17N.
Gradient =
= 2.69 (3s.f.)
Maximum gradient =
= 2.90 (3s.
Conclusion
These errors result in the value being inaccurate and the graph being deviated from the origin and have a negative intercept. However, due to the scale chosen the graph is not able to accommodate the intercept.
The graph is a straight line, with a constant gradient, indicating the proportional relationship shared by net force and acceleration when mass is constant. When the force increases, the acceleration increases proportionally.
The uncertainty is rather small as only one reading was taken. If time allowed, more reading could be taken ti find the average and the uncertainty would add but would eliminate random error.
Modifying this experiment slightly, by keep the accelerating force constant, varying, instead, the mass on the trolley, the dependent variable acceleration can plotted against mass to show the inverse relationship between mass and acceleration.
This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.
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