Force and extension required practical

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

Variables

• Independent: Force (weight) applied to the spring
• Dependent: Extension of the spring
• Control: Using the same spring throughout; Position of the ruler and the pointer; Staying within the limit of proportionality

Equipment

• Clamp stand with two bosses and clamps
• Spring
• Metre rule held vertically
• Pointer (e.g. a splint taped to the bottom of the spring)
• Slotted masses and hanger (100 g, weight about 1 N)
• Set square
• Heavy weight or G-clamp to hold the stand steady

Method

1. Clamp the stand firmly to the bench and hang the spring from the upper clamp.
2. Clamp a metre rule vertically beside the spring with its zero level with the top of the spring.
3. Fix a pointer to the bottom of the spring and record its position on the ruler with no load: this is the original length.
4. Hang the mass hanger on the spring and record the new pointer position.
5. Add masses one at a time, recording the pointer position after each, until a total of about 5 N or 6 N.
6. Calculate the extension each time by subtracting the original length from the new length.
7. Convert each mass to weight using W = m g, with g = 9.8 N/kg and mass in kg.
8. Remove the masses and check the spring returns to its original length.

Safety

• Wear eye protection in case the spring snaps or flies off.
• Clamp the stand to the bench so it cannot tip over.
• Keep feet clear of the masses and do not overload the spring; place a tray or foam under the masses.

Results and calculations

Record force, pointer reading and extension in a table. Plot force (y-axis) against extension (x-axis); the straight part through the origin shows extension is directly proportional to force, and its gradient is the spring constant k from F = k e (with e in metres). The graph curves once the limit of proportionality is passed.

Common mistakes and improvements

• Reading the ruler at an angle causes parallax error: read at eye level and use a set square to line up the pointer with the scale.
• Using the length of the spring instead of the extension on the graph: always subtract the original length.
• Loading the spring past the limit of proportionality so it stays stretched: add small masses and stop if it no longer returns to its original length.
• The spring still bounces when the reading is taken: wait for it to settle before reading.

Exam tips

• Know Hooke's law: extension is directly proportional to force, up to the limit of proportionality.
• Practise finding k from the gradient and remember to convert extension from cm to m.
• Be able to calculate elastic potential energy using E_e = ½ k e², which is given on the equation sheet.
• Describe how to spot the limit of proportionality on a graph: the point where the straight line starts to curve.
• Explain the difference between elastic deformation (returns to original shape) and inelastic deformation (stays stretched).