Topic 9.2
Using F = ma
Force and mass
Aims
In this experiment you will be testing the relationship
Force = mass  acceleration
which is usually written more simply as
F = ma
You will vary the accelerating force and calculate the resulting acceleration for each force.
You will then plot a graph to test the relationship F = ma. This will encourage you to
consider all the factors involved when a falling mass is used to accelerate a trolley.
Safety
 Take care to ensure that the falling masses land safely.
 The pulley at the end of the ramp should be strong enough to stop the trolley passing over
the end.
 The ramp may need to be clamped to the bench. Masses attached to the trolley may need
to be secured with tape.
Equipment, materials and method
1 For this experiment you will need a ramp with a pulley attached to one end, a trolley with
a number of 100 g masses attached, some string, some 100 g masses and a mass hanger, a
metre ruler, a stopwatch (or light gates and a data logger or a motion sensor) and some
wooden blocks.
2 Set up the equipment as shown below.
3 Compensate for friction by raising the ramp slightly so that the trolley travels along the
ramp at a constant speed when no force is pulling it.
4 Consider what you will need to measure to calculate the acceleration of the trolley. If you
use light gates and a data logger or a motion sensor, add these to your diagram.
5 Decide whether or not the distance the trolley travels needs to be constant.
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Topic 9.2
Using F = ma
6 Increase the accelerating force (= mg) by transferring masses one at a time from the
trolley to the mass hanger. For a range of accelerating forces (= mg), record your
measurements and calculate the acceleration of the trolley for each value of force.
7 Using the same accelerating force each time, record measurements for a range of masses
on the trolley. Record your measurements and calculate the acceleration of the trolley for
each value of mass.
Questions
1 Consider carefully the total mass that is being accelerated in step 6. Does this mass remain
constant? Give a reason for your answer.
2 How do you think increasing the accelerating force will affect the acceleration?
3 How do you think increasing the number of masses on the trolley when the accelerating
force is constant will affect the acceleration?
Results
Tabulate your results from steps 6 and 7 in two tables. Add headings to each column
according to the guidance provided below.
Independent
variable and unit
Dependent
variable and unit
Repeat
dependent
variable and unit
Repeat
dependent
variable and unit
Calculated
variable and unit
Discussion
1 Write an equation in terms of the acceleration a, the mass of the trolley M and the falling
mass m.
2 (a) What graph should be plotted in order to test this equation?
(b) Plot your suggested graph. What conclusions can you draw from your results and
graph?
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Topic 9.2
Using F = ma
Force and mass
Equipment and materials required
Each student or pair of students will require the following equipment:
 a trolley with several masses attached (This may be done by attaching a mass hanger to
the top of the trolley, allowing the masses to be added and removed during the
experiment.)
 about 1.5 m of string attached to the trolley
 tape (masking tape is suitable)
 a ramp with a pulley attached to one end (ramp should be a board about 1.5 m long)
 wooden blocks or similar to raise the ramp slightly to compensate for friction
 9  100 g masses and a 100 g mass hanger
 a metre ruler
 a stopwatch (or light gates and a data logger or motion sensor)
 a G-clamp
 graph paper
Safety
 The students must take care to ensure that the falling masses land safely. It may be
necessary to put some protection on the floor.
 The pulley at the end of the ramp should be strong enough to stop the trolley and prevent
it falling. If not, a block may be required.
 The ramp may need clamping to the bench.
 Masses attached to the trolley may need securing with tape.
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Topic 9.2
Using F = ma
Teachers Notes
Aims
 To test the relationship F = ma
 To make suitable measurements in order to calculate the acceleration of a trolley.
 To consider carefully the factors that are involved when a falling mass is used to
accelerate a trolley along a ramp.
Safety
 The students must take care to ensure that the falling masses land safely. It may be
necessary to put some protection on the floor.
 The pulley at the end of the ramp should be strong enough to stop the trolley and prevent it
falling. If not, a block may be required.
 The ramp may need clamping to the bench.
 The masses attached to the trolley may need securing with tape.
Teaching notes
3 It may take students about 45 minutes to set up the apparatus and obtain readings.
2 The drop must be 1.00 m so that the mass does not hit the floor before the trolley passes
the timing line.
1 2
at (u = 0 m s1)
2
Several timings should be measured, even if using sensing equipment.
4 It could be pointed out to more able students that the experiment presupposes its own
result as the mass produces a force equal to mg. This does not invalidate the experiment.
3 The acceleration can be calculated using s =
Answers to questions
The distance does not need to be constant. However, there is less likelihood of error during
the calculations if the distance (s) remains the same for each calculation.
1 The total mass being accelerated is M + m (the mass of the trolley plus the accelerating
mass).
2 The acceleration will increase if the falling mass is increased. A graph of the accelerating
force (= mg) against the acceleration will have a positive gradient.
3 A graph of m against
1
will have a positive gradient.
a
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Topic 9.2
Using F = ma
Discussion
4 mg = (M + m)a
More able students could be encouraged to include friction in their equation giving
mg − F0 = (M + m)a, where F0 is friction (which may not be constant).
5 (a) (M + m)a on the y-axis against m on the x-axis
(c) The graph should be a straight line with a gradient g and a negative intercept − F0
Practical assessment opportunities
6 ISA preparation:
practical task – practice in recording measurements, accurate measurement of timings and
a fixed distance, plotting a graph
written task Section A and B – opportunities to analyse data and errors and draw
conclusions

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