10.9 Required Practicals: Springs and Acceleration

A free GCSE Physics lesson for AQA (8463) from OBA School: required practicals: force and extension of a spring; force, mass and acceleration. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

• Describe how to measure the extension of a spring for increasing forces, and plot and use a force–extension graph
• Describe how to investigate the effect of force, and of mass, on the acceleration of a trolley
• Identify the independent, dependent and control variables, the hazards and how to control them
• Process results: calculate extensions, spring constants, speeds and accelerations, and draw lines of best fit
• Evaluate results: spot anomalies, explain sources of error and suggest improvements

Key words

• Independent variable: The variable you change on purpose (for example, the force on the spring).
• Dependent variable: The variable you measure (for example, the extension or the acceleration).
• Control variable: A variable kept the same so the test is fair.
• Resolution: The smallest change an instrument can show. A metre rule has a resolution of 1 mm.
• Parallax error: A reading error caused by looking at a scale from an angle instead of straight on.
• Zero error: A reading that is not zero when it should be, for example a rule whose zero is not level with the top of the spring.
• Anomalous result: A result that does not fit the pattern of the others.
• Light gate: A sensor that records the time for which a card on a moving object blocks a beam of light.

Required practical 1: force and extension of a spring

Aim: to find how the extension of a spring depends on the force applied, and to find its spring constant.

Method

1. Clamp the spring and a vertical metre rule to the stand. Fix a pointer to the bottom of the spring.

2. Hang the empty hanger on the spring and read the pointer position at eye level. This is the original length reading.

3. Add a slotted mass (for example 1.0 N at a time). Record the force and the new pointer reading.

4. Repeat until you have at least six readings. Then remove the masses one at a time and check the spring returns to its original length.

5. Calculate extension = reading − original reading for each force.

• Independent; In this practical force (weight hung on the spring)
• Dependent; In this practical extension of the spring
• Control; In this practical the same spring; same point on the spring used for readings; same rule

Safety: Hazards: masses falling on feet – keep feet clear and put a cushion or tray underneath; the stand toppling – clamp it to the bench or use a counterweight; the spring flying back if it snaps – wear eye protection.

Processing and evaluating the spring results

• Reading in mm; 0 40; 1.0 60; 2.0 80; 3.0 100; 4.0 120; 5.0 140; 6.0 166
• Extension in mm; 0 0; 1.0 20; 2.0 40; 3.0 60; 4.0 80; 5.0 100; 6.0 126

• Up to 5.0 N each 1.0 N adds 20 mm: extension is directly proportional to force. At 6.0 N it adds 26 mm, so the limit of proportionality has been passed.
• k = gradient of the straight part = 5.0 N ÷ 0.100 m = 50 N/m (convert mm to m first).
• Errors and improvements: read the scale at eye level to avoid parallax; use a pointer or a fixed marker on the spring; check the zero of the rule; make sure the spring has stopped moving before reading; use smaller force steps near the limit of proportionality; repeat the readings while unloading and take a mean.

Required practical 2: force, mass and acceleration

Aim: to find how the acceleration of an object depends on (a) the resultant force on it and (b) its mass.

• Independent; Changing the force accelerating force (weight on hanger); Changing the mass mass of trolley
• Dependent; Changing the force acceleration; Changing the mass acceleration
• Control; Changing the force total mass; runway slope; start position; distance between gates; Changing the mass accelerating force; runway slope; start position

Method – changing the force

1. Tilt the runway slightly until a gently pushed trolley moves at a steady speed. This compensates for friction.

2. Attach the string to the trolley, over the pulley, to a hanger. Put the slotted masses on the trolley.

3. Release the trolley from the same point. The light gates measure the speed of the card at each gate and the time between them.

4. Move one mass from the trolley to the hanger and repeat. This increases the force but keeps the total accelerating mass (trolley + hanger + masses) the same.

5. Repeat each force three times and calculate a mean acceleration.

Changing the mass: keep the hanging mass the same and add masses to the trolley instead.

Worked example: acceleration from two light gates

A 0.050 m card blocks gate 1 for 0.125 s and gate 2 for 0.0625 s. The trolley takes 0.50 s to go between the gates.
v₁ = 0.050 ÷ 0.125 = 0.40 m/s; v₂ = 0.050 ÷ 0.0625 = 0.80 m/s
a = (v₂ − v₁) ÷ t = (0.80 − 0.40) ÷ 0.50

Answer: a = 0.80 m/s²

Without light gates, release the trolley from rest and time it over a measured distance s with a stopwatch. Then a = 2s ÷ t². Human reaction time makes stopwatch times less accurate, especially for short times.

Safety: Hazards: falling masses – put a sand tray or cushion under the hanger and keep feet clear; trolley running off the end – clamp a stop block to the bench.

Processing and evaluating the trolley results

• The points lie close to a straight line through the origin, so a ∝ F (for a fixed mass). The gradient is 1/m.
• The point at 0.60 N is anomalous. Possible causes: the string snagged, the trolley was pushed or released from a different place, or a mass was not moved across. Repeat it; leave it out of the line of best fit.
• For the mass experiment, a × m is about the same for every mass, so a ∝ 1/m. A graph of a against 1/m is a straight line through the origin.
• A line that does not pass through the origin suggests friction was not fully compensated (it cuts the force axis) or a systematic error in the timing.

Exam tip: Light gates give more precise times than a stopwatch and remove human reaction time. Repeating each reading and calculating a mean reduces the effect of random errors.

Common mistakes

• Recording the length of the spring instead of the extension.
• Adding masses to the hanger from the bench when investigating force – this also changes the total mass, so it is no longer a fair test.
• Forgetting that the hanging masses are part of the mass being accelerated.
• Reading the rule from above or below the pointer (parallax error).
• Forcing the line of best fit through an anomalous point.

Revision questions

Try these, then check your answers below each one.

Question 1. In the required practical to investigate the force and extension of a spring, what is the dependent variable? (Choose from: The original length of the spring, The type of spring, The extension of the spring, The force on the spring.)

Answer: The extension of the spring

Working: You change the force (independent variable) and measure the extension (dependent variable). The same spring is a control variable.

Question 2. In a spring experiment a force of 4.0 N gives an extension of 80 mm. Calculate the spring constant.

Answer: 50 N/m

Working: e = 80 mm = 0.080 m. k = 4.0 ÷ 0.080 = 50 N/m.

Question 3. True or false? When investigating how force affects acceleration, masses are moved from the trolley to the hanger so that the total mass being accelerated stays the same.

Answer: True

Working: True. Moving a mass from trolley to hanger increases the accelerating force but keeps the total accelerating mass constant, so only one variable changes.

Related lessons

• Previous lesson: 10.8 Forces and Elasticity
• Next lesson: 11.1 Pressure and Surfaces
• In this chapter: 10.1 Force and Acceleration
• In this chapter: 10.2 Weight and Terminal Velocity
• In this chapter: 10.3 Forces and Braking

Continue in the full course

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