Verifying Newton’s Second Law of Motion

Introduction

The aim with this investigation is to verify Newton’s second law of motion by exerting a force on a body and measuring its acceleration. The independent variables in this experiment are the force exerted and the mass of the body. Acceleration is the dependent variable.

Materials and Methods

An object was put on an apparatus which creates a near-frictionless surface. A force was applied to the object. We measured the object’s momentaneous velocity on two points along the surface, as well as the time elapsed during traveling between those two points.

The independent variables, the mass of the weight and the mass of the glider’, are varied throughout the experiment. The experiment was conducted four times with every set of independent variables.

Results

The distance measured on t₁ and t₂ was 1 dm.

Table 1: Glider results
glider mass [kg]	weight mass [kg]	t1 [s]	t2 [s]	t1 to t2 [s]
0.360	0.010	0.35885	0.17230	1.27652
0.360	0.010	0.37776	0.17312	1.31245
0.360	0.010	0.35900	0.17135	1.27624
0.360	0.010	0.42935	0.17702	1.39867
0.522	0.010	0.43511	0.20445	1.53560
0.522	0.010	0.43380	0.20491	1.53196
0.522	0.010	0.41020	0.20373	1.49012
0.522	0.010	0.43690	0.20686	1.155194
0.522	0.030	0.25305	0.12068	0.903039
0.522	0.030	0.25579	0.12127	0.907210
0.522	0.030	0.32114	0.12627	1.02483
0.522	0.030	0.24598	0.12077	0.885258
0.763	0.030	0.40276	0.15211	1.25234
0.763	0.030	0.29374	0.14348	1.05475
0.763	0.030	0.30457	0.14473	1.07882
0.763	0.030	0.31121	0.14616	1.09995
0.360	0.080	0.13825	0.06657	0.49296
0.360	0.080	0.13440	0.06683	0.49534
0.360	0.080	0.12847	0.06568	0.47251
0.360	0.080	0.13646	0.06675	0.49048
0.749	0.080	0.19572	0.09245	0.69013
0.749	0.080	0.18879	0.09160	0.67628
0.749	0.080	0.18645	0.09101	0.67149
0.749	0.080	0.19026	0.09175	0.67893

No anomalous results were recorded.

The acceleration was calculated twice for every set of data: First the estimated acceleration, calculated with Newton’s second law of motion, and then the real acceleration, calculated with the data from the photocells. This is an example calculation for the first set of data:

Acceleration Calculated with Newton’s Second Law of Motion

F_net = m_weight X G = 0.01kg X 9.82ms^-2 = 0.0982N

F_net = a X m => a = F_net / m

=> a = 0.0982N / 0.370kg = 0.265ms^-2

Acceleration Measured

a = (x_change) / t = ( d/t₁ - d/t₂ ) / t

=> a = ( 0.581 - 0.279 )ms^-1 / 1.277s

=> a = 0.236ms^-2

The distance in the first row is the distance that the photocells measured time of. It was equal to 0.1 m.

Calculated Values

Table 2: Calculated and measured results
glider mass [kg]	weight mass [kg]	t1 [s]	t2 [s]	t1 to t2 [s]	calculated acceleration [ms-2]	measured acceleration [ms-2]
0.360	0.010	0.35885	0.17230	1.27652	0.265	0.236
0.360	0.010	0.37776	0.17312	1.31245	0.265	0.239
0.360	0.010	0.35900	0.17135	1.27624	0.265	0.240
0.360	0.010	0.42935	0.17702	1.39867	0.265	0.187
0.522	0.010	0.43511	0.20445	1.53560	0.185	0.170
0.522	0.010	0.43380	0.20491	1.53196	0.185	0.168
0.522	0.010	0.41020	0.20373	1.49012	0.185	0.165
0.522	0.010	0.43690	0.20686	1.155194	0.185	0.220
0.522	0.030	0.25305	0.12068	0.903039	0.534	0.478
0.522	0.030	0.25579	0.12127	0.907210	0.534	0.481
0.522	0.030	0.32114	0.12627	1.02483	0.534	0.437
0.522	0.030	0.24598	0.12077	0.885258	0.534	0.475
0.763	0.030	0.40276	0.15211	1.25234	0.372	0.327
0.763	0.030	0.29374	0.14348	1.05475	0.372	0.340
0.763	0.030	0.30457	0.14473	1.07882	0.372	0.335
0.763	0.030	0.31121	0.14616	1.09995	0.372	0.330
0.360	0.080	0.13825	0.06657	0.49296	1.785	1.557
0.360	0.080	0.13440	0.06683	0.49534	1.785	1.508
0.360	0.080	0.12847	0.06568	0.47251	1.785	1.552
0.360	0.080	0.13646	0.06675	0.49048	1.785	1.592
0.749	0.080	0.19572	0.09245	0.69013	0.948	0.836
0.749	0.080	0.18879	0.09160	0.67628	0.948	0.825
0.749	0.080	0.18645	0.09101	0.67149	0.948	0.836
0.749	0.080	0.19026	0.09175	0.67893	0.948	0.826

Conclusion

The calculated values are clearly related to the measured values: they are around 10% higher in the majority of the cases. This means that Newton’s second law of motion probably is correct, but there might be a systematic error. That error is omission of friction. The so-called frictionless surface was not entirely frictionless, which also explains why the error margin is greater if the glider passed the photocells late in its course rather than early.

Evaluation

This method is fairly viable, but it has one weaknesses: Friction is not accounted for, neither to the surface nor to the air, which affects both the weight and the glider. This could be fixed by performing the investigation on an entirely frictionless surface in vacuum. However, this is difficult to achieve.
The effect of this problem can also be decreased by using a heavier weight and a lighter glider.

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