An investigation into the relationship

The aim of this investigation is to see what the relationship between force, mass and acceleration is. We will investigate the law of motion F=ma using a trolley, a runway, light gates and a computer program called a data logger.

Background information

Acceleration: Rate of velocity change over a given time. Acceleration can be measured in m/s/s or m/s2 (distance/time/time)

Velocity: Rate of linear motion (in a straight line) of a body in a particular direction. Since it takes into account Direction and the magnitude of the force, velocity is known as a vector. Velocity can be measured in m/s north (distance/time-direction)

Speed: is a measure of how fast an object is moving, speed is measured in m/s, it is calculated using distance/time. It does not take into account direction and so therefore is not a vector.

The laws of motion

Newton’s third law of motion

For every action (force) there is an equal and opposite reaction (force)

Newton’s second law of motion

If an unbalanced force acts on an object then it will either accelerate or decelerate. Experiments show that F = ma

Where F = unbalanced force in Newtons (N)

m = mass in kilograms (kg)

a = acceleration in metres per second squared (m/s2)

Newton’s first law of motion

An object will stay in a state of rest or in uniform motion unless acted on by an external force.

Friction- the resistance force between two surfaces as they pass over one another. The uneven surfaces of the objects (sometimes only microscopic imperfections) cause them to catch against each other creating a resistance force. The force of friction is at its maximum between two objects when they are at rest.

The angle of friction- the angle to which a surface must be raised for objects placed on the surface to begin to steadily slide, thus the force of friction is removed.

Introduction

In order to investigate this relationship we will vary the force applied to the trolley, this is because force is easy to vary using 100g masses placed on a piece of string run over a pulley whereas, varying the mass of the trolley would involve taping masses to the trolley which would be time consuming. Varying the force also allows us to gain enough measurements to justify our prediction when it comes to drawing graphs

We will use a light gate to measure the acceleration of the trolley; it does this by measuring the length of time between the light being broken by one 3cm wide card prong and it being broken again by another 3cm wide card prong. The computer program the connected to light gate, then calculates the acceleration of the trolley between these two points.

Hypothesis- the relationship between Force, mass and Acceleration will be that the force applied to the trolley is directly proportional to the Mass of the trolley multiplied by its acceleration.

A table to show which variables we will need to control in order

For this to be a fair test and which ones we will measure:

Input variable

Control variables – for a fair test

Outcome variable

Variable

Range

interval

Variable

Value

Variable

Force

3-10 Newtons

(In100g masses)

1 Newton

Weight of trolley

0.831 kg

Acceleration- measured in m/s/s

Length of runway

Length of two card prongs

3cms

Distance of light gate from start line

20cm

Position of card prongs

Fixed by cello-tape to trolley

Preliminary experiment

Doing a preliminary experiment is necessary when doing any investigation because it allows us to plan which variables and ranges will be suitable for use, for our actual experiment to give us reliable results. We need, for example to see if putting a force of 10 Newtons pulling the trolley gives us a result that we are able to plot onto a graph.

Method for preliminary

Preliminary results

Force (N)

Acceleration (m/s/s)

3

2.06

6

3.74

8

4.13

10

3.95

1. set up equipment (as in diagram)

2. set up light gate and computer program

3. hold trolley at start ready to release

4. press green button on computer program

5. release trolley

6. record result

7. repeat with other forces

The gradient of this graph represents mass, so this shallow gradient shows that the mass must be large.

Evaluation of preliminary experiment

Our preliminary experiment shows us that we will be able to use this range of values for our final experiment since they gave us results that were relatively consistent with our hypothesis. One thing to notice on the graph is that the trend line does not pass through the origin, this means that the relationship demonstrated is not directly proportional.

From the graph we can also see that the gradient is much shallower than we would have predicted for this relationship, this fact means that the mass is being falsely made to seem high due to external factors decreasing the acceleration .These external factors are those such as air resistance and friction.

For my final experiment we have decided, as a result, to counteract friction since it is relatively easy to counter using the angle of friction (as mentioned in background information).

I can now see that for the actual experiment keeping the experiment fair is going to be very important if we are going to have any hope of gaining a reliable experiment from which we are able to draw a conclusion supporting our hypothesis. We will make sure that the trolley is always released from the same point and we will keep all other factors, (excepting those to be measured) controlled as well.

Actual experiment-we will base our conclusion on this experiment.

For this experiment we will take multiple results for each force, five in total. These will allow us to calculate an average, and therefore eliminate some of the problems concerning human error and anomalous results.

The way in which I will counteract friction will be to raise the runway up before we begin until is just before the angle of friction (until it is only just stationary). I will do this using many pieces of card stacked at the end of the runway

Equipment needed:

* Runway

* Wooden trolley

* Light gate

* Piece of card with two 3cm wide prongs

* Pieces of card to raise the runway

* String

* 100g masses

* Computer program

* Pulley

Method for final experiment

1. Lift the runway until just prior to the trolley rolling, place card underneath to hold the runway in this position.

2. Set up equipment (pulley, runway, string, trolley, etc- as in diagram) insuring that all variables needing to be controlled are.

3. set up computer program and attach light gate to computer

4. set up computer software

5. one person holds the trolley at the start line, another loads the appropriate number of masses onto the string

6. press green button on computer program

7. simultaneously 1 person releases the trolley

8. record results in a table

9. draw graph to analyse data collected

A table of results from the experiment:

Force (N)

Acceleration repeat 1 (m/s/s)

Acceleration repeat 2 (m/s/s)

Acceleration repeat 3 (m/s/s)

Acceleration repeat 4 (m/s/s)

Acceleration repeat 5 (m/s/s)

Average acceleration

(m/s/s)

3

2.28

2.24

2.17

2.16

2.32

2.234

4

2.84

2.88

2.98

2.70

3.29

2.938

5

3.53

3.38

3.42

3.33

3.13

3.358

6

3.62

3.76

3.55

3.71

3.82

3.692

7

3.81

4.18

3.91

4.19

3.90

3.998

8

4.30

4.54

4.27

4.34

4.47

4.384

9

4.50

5.09

4.86

4.56

4.50

4.702

10

5.13

5.21

5.07

5.01

4.99

5.082

Processing results

Mathematically generating mass; using equation- F/a =m

Preliminary results

force

Acceleration (m/s/s)

Actual mass

Generated mass

Difference

Between 2 masses

3

2.06

0.831

1.456

0.625

6

3.74

0.831

1.604

0.773

8

4.13

0.831

1.937

1.106

10

3.95

0.831

2.531

1.700

Actual results

force

Average acceleration

Actual mass

Generated mass

Difference

Between 2 masses

3

2.234

0.831

1.342

0.511

4

2.938

0.831

1.361

0.530

5

3.358

0.831

1.488

0.657

6

3.692

0.831

1.625

0.794

7

3.998

0.831

1.750

0.929

8

4.384

0.831

1.824

0.993

9

4.702

0.831

1.914

1.083

10

5.082

0.831

1.967

1.136

Analysis

Conclusion: Our experiment has not proved conclusively that there is a proportional relationship between the factors we are investigating and therefore our hypothesis is not categorically correct

We can see, nonetheless that our results can tell us something of the relationship between force acceleration and Mass, there is definitely a positive relationship between these three factors. This relationship may in fact be a proportional relationship with other factors involved since we have seen that removing some of the external factors has made the relationship closer to a proportional one. This is explained below.

We used the equation m = F/a to work out the accuracy of our results and the degree to which our results support our hypothesis. We know that the mass of the trolley has not changed, (it remained at 0.831Kg throughout our experimenting) so if using the equation gives us an artificially high or low result for mass then the result we attained for acceleration must be artificially high or low also, to compensate. When we put our results into the equation (as seen previously) we found that we were given an artificially high mass therefore our acceleration result must have been artificially low in order to balance the equation. The only way our acceleration results could have been too low would be that other external factors were working upon the trolley; the most likely factor to do this is friction.

If we look at our preliminary results using the equation m = F/a we can see that the difference between the mass we mathematically generated and the actual mass is comparatively large. The mass differences when manipulating our actual results were less so (using the same equation). This disparity between the mass differences of the actual and preliminary results is due to our attempts to counteract friction by lifting up the runway (explained in evaluating preliminary results). When we left the runway horizontal for our preliminaries friction was far greater and so this lowered the acceleration consequently to compensate the mass appears higher when you mathematically calculate it. The difference between our findings for our preliminaries and actual experiment shows that we did manage to counteract some of the friction involved between the runway and the trolley. We could never however counteract all of this friction and there are many other external factors lowering the acceleration of the trolley. Friction in the trolley axels air resistance and human error for example. The more of these factors we can remove the truer our results will be to the original equation.

This however does not take away from the fact that the equation works. It however does not take into account external factors and talks of one unbalanced force (see background information) other factors however are involved.

Ideally, in order to investigate the experiment in a fairer fashion we would eliminate all counter forces or work out the amount of these forces working against the trolley so that we could work out the overall unbalanced force. This would mean that the mathematical calculations would reliably correspond to Newton’s second law of motion.

Evaluation

In order to make our experiment more accurate we could do more repeats and try to eliminate more of the counter forces working on the trolley. One way of doing this would be to use an air track; this uses an air cushion to eliminate friction, the price we would have to pay for eliminated friction would be air resistance due to the fact that this method uses air.

A theory we would want to do further experimentation into is that…

Where friction is present, Newton’s second law can be expanded to:

F effective – F friction = ma

We have seen already seen that this rule may in fact be true, as previously mentioned. When we looked at our mathematically generated results for our preliminary and actual results we saw that subtracting some of the friction gave us a more realistic result for our mass (as seen previously). Another way we could continue our experimentation into this law of motion would be to look at it from a different perspective, for example, we could vary the trolley mass instead of varying the force, and we could then measure the acceleration. This would mean that we could manipulate these results to check that our hypothesis is correct whichever way you look at the relationship.