Lesson overview
Stretching springs: How far will a spring stretch?
Hang a steel spring from a clamped stand, load it 100 g at a time and read its pointer at eye level against a metre rule: measure every extension from the zero reading, plot a load–extension graph and use it to weigh a stone. Then find the spring constant from the gradient, in N/m, load a softer spring in smaller steps, and find its limit of proportionality, where the line stops being straight.
Suggested sequence
- Lesson 1 · Loading a spring. Forces change the size and shape of objects; load and extension, measured from the zero reading with the hanger on; how to load a spring and read it at eye level; plotting a load–extension graph and reading a load from it. Read together (10–15 min), show or explore the experiment (10 min), practise with self-checking (15–20 min).
- Lesson 2 · Spring constant and the limit of proportionality. Supplement: the spring constant k = F/x in N/m, and k as the gradient of the load–extension graph; the limit of proportionality, where the line stops being straight, on either way round of the axes. Read together (10–15 min), show or explore the experiment (10 min), practise with self-checking (15–20 min).
- End of module · final check. 2 new questions, 20–30 min, without hints or notes; pupils check their answers once they have answered them all.
- One to two weeks later · return questions. 2 questions, 15 min, lesson closed.
Learning goals
Part 1: Loading a spring
- Know that forces may produce changes in the size and shape of an object (1.5.1.1)
- Sketch, plot and interpret load–extension graphs for an elastic solid and describe the associated experimental procedures (1.5.1.2)
Part 2: Spring constant and the limit of proportionality
- Supplement: define the spring constant as force per unit extension; recall and use the equation k = F/x (1.5.1.9)
- Supplement: define and use the term ‘limit of proportionality’ for a load–extension graph and identify this point on the graph (an understanding of the elastic limit is not required) (1.5.1.10)
Misconceptions to listen for
- “The steel shelf does not change shape, because steel is too hard.” — The books push down on the shelf, and it sags a little in the middle: it bends. Every solid changes shape a little when a force acts on it.
- “The fishing rod stretches.” — The rod hardly gets longer. Its tip is pulled down and the whole rod curves: it bends.
- “The tennis ball bends.” — The racket pushes on one side of the ball and the ball gets flatter, shorter in that direction: it is squashed.
- “The rubber motor of the toy plane stretches.” — Winding the propeller turns one end of the rubber round while the other end stays still. That is a twist.
- “The load is 650 g, the hanger and the masses together.” — The hanger was already on for the zero reading, so the extension measured from it is caused only by the 600 g added.
- “The load is 600.” — A load is a force, in newtons. 600 g is a mass: change it to kilograms and multiply by g.
- “The extension is 14.3 cm, the reading on the rule.” — The spring was already at 9.5 cm before the load went on. The extension is the change: 14.3 cm − 9.5 cm.
- “Read the pointer straight after adding each mass.” — The spring bounces when a mass goes on. Wait until it is still, or the pointer is caught at the wrong place.
- “Plot the readings, not the extensions.” — Load against reading is a straight line that does not go through the origin. Plot the extension, the reading minus the zero reading.
- “Take the zero reading after the first mass goes on.” — The zero reading is where the pointer is before any mass is added. Every extension is measured from it, so it comes first.
Scope
Forces may produce changes in the size and shape of an object (1.5.1.1); sketch, plot and interpret load–extension graphs for an elastic solid and describe the associated experimental procedures (1.5.1.2); the spring constant as force per unit extension, k = F/x (1.5.1.9); the limit of proportionality of a load–extension graph, identified on the graph (1.5.1.10). 1.5.1.9 and 1.5.1.10 are Supplement. The elastic limit is not required and is not used. Resultant forces and F = ma are in Resultant force, friction and drag in Acceleration, falling and drag, moments in Moments and balance, and elastic potential energy in Energy, work and power.