8.1 – Investigating Force, Mass and Acceleration Relationships (Leaving Cert Physics): Revision Notes

8.1 – Investigating Force, Mass and Acceleration Relationships

Introduction to the experiment

This experiment is designed to verify Newton's second law of motion through practical investigation. Newton's second law states that the net force acting on an object is directly proportional to its acceleration and inversely proportional to its mass. This can be expressed mathematically as:

$F = ma$

Where:

• F = net force (in Newtons)
• m = mass (in kilogrammes)
• a = acceleration (in metres per second squared)

The experiment has two main parts that investigate different aspects of this fundamental relationship in physics.

Part A: investigating force and acceleration relationship

Aim and theory

Part A aims to demonstrate that acceleration is directly proportional to the applied force when mass remains constant. This relationship can be written as:

$a \propto F$ (when mass is constant)

This means that if you double the force acting on an object, its acceleration will also double, provided the mass stays the same.

Equipment needed

Method overview

The basic principle involves using a trolley on an inclined runway with hanging weights that create an accelerating force. Here's how it works:

Data collection

The results are recorded in a table with the following columns:

Mass of scale pan and contents, m (g)	Force, F (N) = (m × g)/1000	Acceleration, a (m s⁻¹)
[Values recorded during experiment]	[Calculated values]	[Measured values]

Expected results

When the data is plotted on a graph, you should obtain a straight line passing through the origin. This linear relationship proves that acceleration is directly proportional to force when mass remains constant.

Part B: investigating mass and acceleration relationship

Aim and theory

Part B demonstrates that acceleration is inversely proportional to mass when the applied force remains constant. This relationship is expressed as:

$a \propto \frac{1}{m}$ (when force is constant)

This means that as you increase the mass of an object, its acceleration decreases proportionally for the same applied force.

Method modifications

The key difference in Part B is that the accelerating force stays constant while the total mass being accelerated changes:

Data collection for Part B

Acceleration a (m s⁻²)	Total mass of the trolley and weights on it, m (g)
[Measured values]	[Recorded values]

Expected results

The graph of acceleration versus 1/mass should produce another straight line through the origin. This proves the inverse proportionality relationship - as mass increases, acceleration decreases proportionally.

Safety considerations

Sources of experimental error

Understanding potential sources of error helps improve experimental accuracy:

Analysis and conclusions

Both parts of this experiment work together to verify Newton's second law:

• Part A shows that F ∝ a (when m is constant)
• Part B shows that a ∝ 1/m (when F is constant)
• Combined: These relationships confirm that F = ma

The straight-line graphs passing through the origin in both parts provide strong evidence for these proportional relationships. When the experimental data produces linear graphs with zero intercepts, it confirms that the theoretical predictions of Newton's second law are correct.