To investigate and prove Newtons law, F=ma.

Percentage error (%)

mass:

0.31089kg

0.00005

0.016

length:

0.02648m

0.00001

0.038

We have to keep the mass of the whole setup constant, which means mass x + mass y has to be constant at all cases. The percentage error of force will be dealt later on during calculation.

Data Processing and Presentation:

Force (N)

Absolute error

Acceleration (m/s2)

Absolute error

0.081

0.0062

0.26

0.000208

0.162

0.0031

0.52

0.000468

0.274

0.0018

0.88

0.000968

0.370

0.0014

.19

0.001428

0.454

0.0011

.46

0.001752

0.516

0.0010

.66

0.002158

0.600

0.0008

.93

0.002509

Our starting formula is: F = ma

Now we have F and a, we can now plot a graph. From the formula, I predict the slope of the graph is m, which is 0.31, due to the fact that a straight line graph has a general formula of y = mx + c.

F = ma

Absolute error

Percentage error (%)

mass:

0.31089kg

0.00005

0.016

Acceleration:

0.26 - 1.93ms2

/

0.07 - 0.13

Percentage error of m: 0.016%

Highest percentage error of a: 0.13%

Highest percentage error of F: 0.016 + 0.13 = 0.146%

Graph please see the graphing paper attached.

Note: Uncertainties are invisible on the graph as the errors are relatively negligible to the scale.

F = ma

y = mx

Slope of graph (mass):

m = ?y/?x

= (0.600 - 0.081) / (1.93 - 0.26)

= 0.31078

We can also calculate the slope of the graph by:

F = ma

m = F/a

Force (N)

Acceleration (m/s2)

F/a

0.081

0.26

0.3115

0.162

0.52

0.3115

0.274

0.88

0.3114

0.370

.19

0.3109

0.454

.46

0.3110

0.516

.66

0.3108

0.600

.93

0.3109

Average of F/a:

(0.3115 + 0.3115 + 0.3114 + 0.3109 + 0.3110 + 0.3108 + 0.3109) / 7 = 0.3111

Overall percentage error:

Percentage error = difference in value / actual value *100%

Measured value of mass: 0.31089kg

Calculated slope (mass): 0.31078kg

Percentage error: (0.31089 - 0.31078) / 0.31089 * 100%

= 0.00011 / 0.31089 * 100%

= 0.035%

As we can see from above, m = F/a which equals 0.31. From measurements taken above, the mass that we used is also 0.31kg. So we can say F = ma is proved in this experiment.

Conclusion:

F = ma, force increases proportionally to acceleration, also it increases proportionally to mass. Acceleration increases inversely to mass, mass increases inversely to acceleration.