Required Practical: Investigating Force & Acceleration

Aim of Practical

The main aim of this practical is to investigate the relationship between force and acceleration, testing Newton's Second Law of Motion. You will measure how the acceleration of a trolley changes when different forces are applied. This helps confirm that acceleration is directly proportional to the resultant force acting on an object, provided the mass remains constant. The relationship is described by the formula: Force = mass × acceleration (F = m times a).

Apparatus & Setup

• Trolley (with a known mass) on a low-friction track to reduce resistance
• Pulley system to apply force via hanging masses
• Hanging masses to vary the force applied to the trolley
• Ticker timer or motion sensor to measure acceleration
• Measuring tape or ruler to measure distances travelled

The trolley is placed on the track, connected by a string over the pulley to the hanging masses. The force applied to the trolley is due to the weight of the hanging masses (force = mass times gravitational field strength).

Method

1. Set up the trolley on the low-friction track with the string running over the pulley attached at the end.
2. Attach a known mass to the trolley (which remains constant throughout the experiment) and hang masses from the string over the pulley.
3. Vary the force by changing the hanging mass (e.g., 0.1 kg, 0.2 kg, 0.3 kg, etc.).
4. Release the trolley and measure its acceleration using the ticker timer or motion sensor.
5. Record the force applied (weight of hanging mass) and the corresponding acceleration of the trolley.
6. Repeat each measurement several times for reliability and calculate average acceleration.

Data Analysis

Calculate the acceleration of the trolley from the motion data. If using a ticker timer, acceleration can be found by analysing the spacing of dots. If using a motion sensor, the acceleration can be directly read or calculated from velocity-time data.

Plot a graph of acceleration (y-axis) against force (x-axis). According to Newton's Second Law, force and acceleration should be directly proportional, so the graph should be a straight line through the origin.

The relationship can be written as:

Force $F = m \times a$

where $m$ is the mass of the trolley (including any additional masses on it), and $a$ is the acceleration.

From the graph, the gradient represents the mass of the trolley. This confirms Newton's Second Law that acceleration is proportional to force and inversely proportional to mass.

For instance, if a trolley of mass 0.5 kg is pulled by a force of 1.0 N, the acceleration is:

$$a = \frac{F}{m} = \frac{1.0}{0.5} = 2.0 \text{ m/s}^2$$