In an experiment to investigate the relationship between force and acceleration a student applied a force to a body and measured the resulting acceleration - Leaving Cert Physics - Question 1 - 2005

The student measured the applied force using:

• Electronic Balance: To determine the weight of the force applied, recorded in newtons (N).
• Weights: The student used known weights, confirming they were in the correct position for accurate force measurement. The total mass can be determined by multiplying the mass (in kg) by the acceleration due to gravity (approximated as 9.81 m/s²) to convert to force (in Newtons).

To plot the graph:

1. Label the X-axis as "Acceleration (m/s²)" and the Y-axis as "Applied Force (N)".
2. Mark the points corresponding to each pair of force and acceleration values from the table. For instance:
   • At 0.1 N, the acceleration is 0.10 m/s².
   • At 0.2 N, it is 0.22 m/s², and so forth.
3. Draw a straight line best fit through the points. Ensure the line goes through the origin, indicating proportionality between force and acceleration.

To calculate the slope of the graph:

1. Use the formula for slope:

   $ext{slope} = \frac{\Delta y}{\Delta x} = \frac{F_2 - F_1}{a_2 - a_1}$

   where (F1, a1) and (F2, a2) are any two points on the line.

2. After calculating the slope (e.g. $0.8$), we can find the mass ($m$) using Newton's second law:

   $F = m \cdot a$

   Therefore, the mass of the body can be found by rearranging:

   $m = \frac{F}{a}$

   Based on the slope representing $\frac{F}{a}$, the mass can be derived from the calculated slope.

One precaution the student could take is to ensure that the surface of the track is smooth and free from any obstructions to allow for unimpeded motion of the trolley. Additionally, making sure that the weights do not touch the ground to avoid any erroneous force readings can be crucial.