Investigating force and acceleration

In a nutshell

By using a pulley system and a toy car with weight stacks, you will be able to investigate the relationship between force, mass and acceleration. You will do this by conducting two different experiments. One will vary the force and the other will vary the mass.

Equations

The first equation is the one which is being evaluated in your experiment. However you will need the other two equations in order to work out the acceleration.

Word Equation	Symbol Equation
$force = mass \times acceleration$	$F = m \times a$
$acceleration = {change \space in \space velocity\over time}$	$a = {\Delta v\over t}$
$velocity = {displacement \over time}$	$v = {s \over t}$

Variable definitions

Quantity Name	Symbol	Unit Name	Unit
$force$	$F$	$newton$	$N$
$mass$	$m$	$kilogram$	$kg$
$acceleration$	$a$	$metre \space per \space second \space squared$	$m/s^2$
$velocity$	$v$	$metre \space per \space second$	$m/s$
$time$	$t$	$second$	$s$
$displacement$	$s$	$metre$	$m$

Equipment list

The following equipment list can be used to conduct an experiment to evaluate the relationship between force, mass and acceleration.

Equipment	Use
$1 \, m$ ruler	To measure distance
Toy car/trolley	The object which its acceleration is being measured
Chalk	To mark out intervals of distance
Bench Pulley and string	To connect the toy car/trolley to weights
Weight stack and weights	To provide a force to the toy car/trolley
Stop watch	To measure the time of the toy car/trolley between intervals of distance
Blue tac	To attach weights to the toy car/trolley

Experiment 1: Investigating the effect of varying force on acceleration with a constant mass

Experimental variables

The independent variable is the one you change. The dependent variable is the one which depends on what has been changed, therefore it is the one you measure. The control variable is the one which is kept constant.

Independent variable	$force$
Dependent variable	$acceleration$
Control variable	$mass$

Safety precautions

When performing experiments, it is very important you consider safety precautions. This is so you and others do not get hurt.

Hazard	risk	safety measure
Weights	Weights become loose and fall on your feet	Don't stand directly beneath the weights

Method

This is your instructions for how to complete the experiment.

Method diagram

Below is a diagram to show how the experiment should be set up.

Physics; Physics practicals; KS4 Year 10; Investigating force and acceleration

1.	Toy car/trolley
2.	Chalk lines $20 \, cm$ apart
3.	String
4.	Bench
5.	Pulley
6.	Weight stacks and weights

1.	Draw out straight lines using chalk at $20 \, cm$ intervals on a flat table up to $1 \, m$ . This will allow the time between distances to be easily recorded.
2.	Attach the pulley to the end of the table.
3.	Add the weight stack to one end of the string and pull it over the pulley.
4.	Attach the toy car to the other end of the string. You need to make sure the string is in a straight line between the pulley and the toy car.
5.	Hold onto the toy car and attach a weight of $0.2 \, N$ to the weight stack.
6.	Set the stopwatch into 'lap mode'.
7.	When you are ready release the car and start the stopwatch. Every time the toy car reaches a $20 \, cm$ interval you should start a new lap on the stop watch until the toy car reaches $1 \, m$ . Hint: Do not push the toy car as this will not give reliable results, make sure you are just releasing it.
8.	Record the times on a table.
9.	Repeat steps 7 and 8 two more times.
10.	Repeat steps 5 to 9 by adding a weight of $0.2 \, N$ each time until the total weight in $1 \, N$ .

Analysis

This is how you will use your data to be able to form conclusions.

1.	Firstly, calculate the mean time for each interval. $mean \space time = {time_1 + time_2 + time_3\over 3}$
2.	Calculate the velocity of the toy car at each interval for each weight. $velocity = {displacement \over time}$ Hint: The displacement will be $0.2 \, m (20 \, cm)$ each time. The time used is the mean time you have calculated for each interval.
3.	For each weight, you then need to calculate the acceleration. To do this you will need the average velocity of the first interval, and the average velocity of the last interval. $acceleration = {\Delta velocity \over time}$ Hint: The change in velocity is the difference between the average velocities of the first and last interval.
4.	You should then plot acceleration and force onto a graph. Acceleration should be on the $y$ -axis as it is the dependent variable and force should be on the $x$ -axis as it is the independent variable. Draw a line of best fit.
5.	Finally you should comment on what your results show and the relationship between force and acceleration. $force = mass \times acceleration$

Conclusion

Your graph should show a directly proportional relationship between force and acceleration. This means that as force increases, the acceleration will also increase.

Your line of best fit should be a straight line through the origin, and should look like the one below. You can calculate the mass of the toy truck by finding the gradient of the line.

Physics; Physics practicals; KS4 Year 10; Investigating force and acceleration

Evaluation

Once you have completed your experiment, it will be important to consider how well your graph relates to the equation. For example, do all of your results lie on the best fit line. You should make sure you identify any anomalies and not include them in your final results. If you did have anomalous results, you will need to think about why.

Experiment 2: Investigate the effect of varying mass with a constant force

Experimental variables

Independent variable	$mass$
Dependent variable	$acceleration$
Control variable	$force$

Method

You should repeat experiment one, but this time you should keep the same mass on the weight stack. You should then vary the masses on top of the car and make sure you include the toy cars own mass.

Analysis

Repeat the same analysis as experiment one. However, you should now plot mass on your $x$ -axis as this is now the independent variable.

Conclusion

Your line of best fit should be a curve, and should look like the graph below. The graph should show that as mass increases, the acceleration decreases. The acceleration should decrease at a greater rate with smaller masses than with larger masses.

Physics; Physics practicals; KS4 Year 10; Investigating force and acceleration

Evaluation

You should repeat the same evaluation as experiment one on your new set of data.