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Mechanics

Experimental Verification of Newton's Second Law of Motion

It is observed that if a mass, m, causes a given spring to extend x, then 2m causes 2x and 3m causes 3x etc. See diagram below.

We conclude that the force due to gravity exerted by a suspended mass m is proportional to the mass.

Apparatus

The mobile moves without friction on a cushion of air.

As we have three variables, force, mass and acceleration, the investigation must be done in two parts.

Experiment 1

To find the relation between acceleration and force with mass constant.

The force is provided by gravity.

To maintain a constant mass whilst varying the force, masses, m were moved from the mobile to the string as shown below.

In this experiment, the same object was pulled by forces of different magnitudes. The acceleration produced by each force was measured.

The body being accelerated started from rest so we can write

s = ½at2

and

v = at

These two equations can be combined to eliminate t which then gives us

a =

So, to measure the acceleration of the body we measured its velocity, v, after it had been accelerating for a known distance, s.

We did not know the magnitudes of the forces but we did know how the force varied.

Results

Force

Acceleration

F

a

2F

2a

3F

3a

Conclusion

These results show that the acceleration is directly proportional to the force.

This is written as

a SYGMAf

Experiment 2

To find the relation between acceleration and mass with force constant.

In this experiment, an object was pulled with a certain force and the acceleration was measured as before. The mass of the object was then increased and it was pulled again with the same force.

Results

Mass

Acceleration

m

a

2m

a/2

3m

a/3

Conclusion

These results show that the acceleration is inversely proportional to mass.

This is written as

a SYGMA 1/m

The two conclusions can be combined in one statement

 

a SYGMA f/m

so, written as an equation we have

a = (a constant) × f/m

and if we choose the units correctly the constant can be made equal to 1. Therefore, we have

force = mass × acceleration

This is know as Newton’s second law of motion.

The "correct" units are

mass

kg

acceleration

ms-2

force

Newtons (N)

This relation therefore gives us a definition of the unit of force.

1N is the force which can give a 1kg mass an acceleration of 1ms-2

Also, if we rearrange the equation to give

m = f/a

we are reminded that the mass of a body is a measure of its inertia.

This is clear because if m is large, a large force is needed for a given acceleration.

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