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F=ma using ticker timer

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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/ms-2

Δa/ms-2

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:

...read more.

Middle

  = 0.36s.

s is the length for 18 ticks.

-

a is the actual acceleration of the trolley.

s = ut +image00.pngat2

∴ a = image01.png

First row:

a = image08.png

   =   1.57ms-2

Δa is the absolute uncertainty of a.

image09.png

Δa =image10.png

First row:

Δa = image11.png

     =   ±0.015ms-2 (2s.f)

F is the net force acting on trolley.

F = Ma

First row:

F = image12.png

   =   1.25N

ΔF is the absolute uncertainty of F.

ΔF = image13.png

First row:

ΔF = image14.png

      =   ±0.012N (2s.f.)

Attached is the graph of a/ms-2 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 = image15.png

               =   2.69 (3s.f.)

Maximum gradient = image02.png

                               =    2.90 (3s.

...read more.

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.

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.

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