# Graphical relationship between force and acceleration

### Verifying Newton’s Second Law

Demonstration A trolley experiences an acceleration when an external force is The aim of this datalogging experiment is explore the relationship between the applied force is investigated more precisely by plotting an XY graph of these. To determine the relationship between force, mass, and acceleration using a What are the units of the slope of force vs. acceleration graph?. The slope of an acceleration graph represents a quantity called the jerk. and you would have to keep applying different amounts of force from your muscles to .

Simplify the units of the slope to fundamental units m, kg, s.

### BBC - GCSE Bitesize: Forces, mass and acceleration

What does the slope represent? The units of the slope of force vs. This simplifies to kg. The slope represents the mass of the pulley. What is the total mass of the system both with and without extra weight that you measured? The total mass of the system without the extra weight was 0. How does the slope of your graph compare percent difference with the total mass of the system that you measured?

The slope of the graph without any added weights was 0. The slope of the graph with the added weights was 0. Are the net force on an object and the acceleration of the object directly proportional?

Yes, as the net force is increased, the acceleration is also increased. Write a general equation that relates all three variables: The goal was achieved using a cart and pulley system with varying weights to measure force and acceleration. The forces and accelerations collected were then graphed against each other the construct a linear fit line, whose slope showed the mass of the system the cart, sensor, and any added weights. The difference between these, divided by the time between them, yields the acceleration.

A series of results is accumulated in a table. This should also include a column for the manual entry of values for 'force' in newtons. It is informative to display successive measurements on a simple bar chart.

Pull the trolley back so that the mass is raised to just below the pulley. Position the light gate so that it will detect the motion of the trolley soon after it has started moving.

- Getting Started
- Forces, mass and acceleration
- What are acceleration vs. time graphs?

Set the software to record data, then release the trolley. Observe the measurement for the acceleration of the trolley.

Enter from the keyboard '1' 1 newton in the force column of the table. Release the trolley from the same starting point as before. Repeat this several times. Enter '2' 2 newtons in the force column of the table.

Analysis Depending upon the software, the results may be displayed on a bar chart as the experiment proceeds. Note the relative increase in values of acceleration as the slotted mass is increased.

The relationship between acceleration and applied force is investigated more precisely by plotting an XY graph of these two quantities.

Use a curve-matching tool to identify the algebraic form of the relationship. This is usually of the form 'acceleration is proportional to the applied force'. This relationship is indicative of Newton's second law of motion.

The great advantage of this version is that the software presents acceleration values instantly.

## Verifying Newton’s Second Law

This avoids preoccupation with the calculation process, and greatly assists thinking about the relationship between acceleration and force. Each repetition with the same force gives a similar acceleration. If the force is doubled, this results in a doubling of the acceleration, and so on.