Summative Practical: Motion down an Incline Plane

In the next lesson, your task will be to perform an experiment to investigate the motion of a ball rolling down an

incline plane. For an incline of 30°, the expected relationship between the distance travelled by the ball rolling down

the incline (𝑠) and the time (𝑡) taken to travel this distance is:

𝑠 = 2.45 𝑡2 . (1)

This experiment is to be conducted in groups of 2 or 3, however the experimental write-up and discussion of results

will be done independently. You will have 2 hours to complete the experiment, with the write-up to be done in the

booklet provided. This booklet must be handed up at the end of the lesson. There will also be marks assigned to

safe and effective use of equipment, positive and effective teamwork, both of which the teacher will assess during

the experimentation stage, and effective communication skills determined from the responses to the questions in

the practical booklet.

Preparation: First individually read the introduction and answer the questions in part (a). Then with your partner(s)

briefly consider how you will undertake the experiment by identifying the independent and the dependent variables

in order to verify the relationship above.

Your answers to parts (a) will be collected at the beginning of the practical session. Complete your group design on

a separate piece of paper as this will assist you in completing the investigation.

Introduction

For an object falling under the influence of gravity near the Earth’s surface, the gravitational force is effectively

constant leading to a constant acceleration we call 𝑔, the acceleration due to gravity. As we have constant

acceleration, if the object starts at rest, then the distance travelled during a time 𝑡 is given by:

𝑠 =1

2𝑔𝑡2 .

In this practical we shall consider the situation in which a ball rolls down an incline plane. This is a similar problem

to that of the falling object, however in this case the ramp provides an additional force (the normal force which is

perpendicular and away from the ramp). To understand the resulting motion, we resolve the force due to gravity

into components along the ramp and perpendicular to the ramp. In doing this we find that the normal force

completely cancels with the component of gravity perpendicular to the ramp, resulting in no net force in the

perpendicular direction. However, the component of gravity along the ramp is unbalanced and so there is a net

force in this direction.

Working through the trigonometry, we can show that the magnitude of this force is:

𝐹𝑥 = 𝑚𝑔 sin 𝜃 .

Using Newton’s second law we know that:

𝐹𝑥 = 𝑚𝑎𝑥

⇒ 𝑎𝑥 = 𝑔 sin 𝜃 .

Therefore, if the object starts at rest, the distance travelled down the incline plane during a time 𝑡 is given by:

𝑠 =1

2(𝑔 sin 𝜃)𝑡2 .

𝑚𝑔 sin 𝜃

𝑥

𝑦

𝜃

𝐹𝑁

𝐹𝑔 = 𝑚𝑔

𝑚𝑔 cos 𝜃 𝜃

Part (a): Individual Questions

In this practical, we shall verify this relationship by considering the motion of a solid ball bearing rolling down an

incline plane.

1) Give a brief explanation as to why you would expect the forces in the direction perpendicular to the ramp

to cancel. (Hint: What would happen if the forces did not cancel each other?) (KU1)

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2) i) In this practical, the angle of the ramp will be set at 𝜃 = 30°. Show that the exact equation that we wish

to verify is: (A2)

𝑠 = 2.45 𝑡2 .

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3) In deriving the expression for the distance travelled down an incline plane, we neglected the effects of

friction. Friction is a resistive force which opposes the motion of a moving object. (KU1)

i. On the diagram, draw an arrow indicating the direction of the frictional force, 𝐹𝑓𝑟.

ii. What effect would including this force have on the resulting acceleration?

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4) In this experiment, you will release the ball at a series of different points along an inclined ramp and time

how long it takes for the ball to reach the end of the ramp. To ensure that the ramp is set an angle of 30°,

you will need to calculate the height of the end of the ramp. If the length of the ramp is 1.5m, use

trigonometry to calculate the required height of the ramp. (A2)

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Part (b): Group Planning

Before the practical, you will need to get together with your partner(s) to briefly consider how you will do the

experiment. On a piece of paper record:

which variable you will change (the independent variable)

which variable you will measure (the dependent variable)

any variables you should hold fixed (constant variables)

A brief outline of steps that will later form your method.

During the practical session you will have access to a stopwatch, a metre ruler, a solid steel ball bearing, a V-shaped

aluminium track of length ≈ 1.5m (you should check this!) and a retort stand.

1.5 m

30°

Summative Practical: Motion down an Incline Plane

During this lesson, you will have 2 hours to perform the experiment and to write up your findings in this booklet.

Be aware that marks have been also been allocated to:

Effective and safe use of apparatus (I3) (4 marks)

Positive and effective collaborative work (A3) (4 marks)

Effective communication (KU3) (3 marks)

During the first hour you will be able to work within your groups to perform the experiment, however the write-up

should be done independently (i.e. in your own words). At the end of the first hour you should have written your

method, made all your measurements and have these recorded in a table in your own booklet. In the following

hour, you will work individually to graph your data, analyse your results and write your discussion. At the end of

the second hour you must hand up your booklet.

Aim and Hypothesis:

State the aim for this experiment: (I1)

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The hypothesis we wish to test for this experiment is:

The relationship between the distance travelled by a rolling ball down an incline plane at an angle

of 30° and the time taken to traverse this distance is given by,

𝑠 = 2.45 𝑡2, or equivalently 𝑡2 =1

2.45 𝑠 .

In order to verify this hypothesis, you will need to graph your results in such a way that you should observe a linear

relationship in the plotted data if the theoretical result holds true.

i. By considering one of the above expressions, identify what variables should be plotted on the horizontal

and vertical axes in order to obtain a linear graph. (I1)

Horizontal axis: __________________ Vertical axis: __________________ (1 mark)

ii. List any constant variables you identified in your planning. (I1)

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iii. If linear behaviour is observed in the data, what features do you expect to observe for the line-of-best fit

given your answer (i)? (AE1)

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marks

Method:

In the space below, provide a step-by-step outline of the method you will use to conduct this experiment. The first

step should outline how to assemble the apparatus and should include a suitably labelled diagram. Note that you

will need to make measurements for at least five different distances.

Be sure to include any steps taken to reduce the effect of random uncertainties, as well as any comments or

precautions that should be noted to ensure the experiment is done safely. (I1)

Note: To ensure the angle of incline is 30° the height of the end of the rod should be half the length of the rod

above the bench. Measure and include the length of the rod in you method.

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Results:

Data:

Construct a suitable table in which to record your results. Perform measurements for at least 5 different distances

up the track. (I4)

(6 marks)

Graph:

On the grid below, plot the data using the choice of variables you identified in question (1) of the Aim and

Hypothesis section. Be sure to provide suitable axis labels, relevant units and a suitable title. Also include the line-

of-best-fit for your data. (I4)

(6 marks)

Analysis:

i. Using the graph, determine the slope for the line-of-best-fit. (AE1)

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ii. Calculate the percentage-error ( |𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 − 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒

𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 | × 100%) for the slope from part (i).

(AE1)

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Discussion: Provide a discussion of your results. Be sure to:

relate your findings to your expectations (detailed in the Aim and Hypothesis section)

identify evidence for and possible sources of error in this practical. In discussing each error, you should

distinguish whether the error is random or systematic with some explanation as to why.

provide suggestions for how the experiment could be modified to either remove or reduce the impact of

any experimental errors you identify. (AE1,AE2)

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Conclusion: Provide a conclusion that summarises your findings, with particular reference to the aim and hypothesis for the

experiment. (AE1)

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Practical and Collaborative Skills Assessment Sheet:

I3: Manipulates apparatus and technological tools carefully and highly effectively to implement well-organised, safe, and ethical investigation procedures.

A3: Demonstrates initiative in applying constructive and focused individual and collaborative work skills.

Indicator A (4) B (3) C (2) D (1) E (0)

I3 Uses equipment safely,

Recognises hazards and takes required precautions

Ability to problem solve (issues with practical)

A3 Cooperates with all group members

Shows initiative

Uses time effectively

Logical and systematic approach to the undertaking of the experiment.