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2.3.1 Stretching, bending and compressing

Changing the shape of an object

Definition

Deformation

A change in the shape or size of an object caused by the forces acting on it.

Definition

Extension

The increase in the length of an object when it is stretched, equal to its stretched length minus its original length.

  1. An object undergoes deformation when the forces acting on it change its shape or size.
  2. The three basic types of deformation are stretching, compressing and bending.
    1. Stretching pulls an object so that it becomes longer, as when you pull a spring or a rubber band.
    2. Compressing squashes an object so that it becomes shorter or thinner, as when you squeeze a sponge or sit on a cushion.
    3. Bending makes an object curve, as when a diving board sags under a diver or a ruler bows when you press its middle.
  3. When an object is stretched, the increase in its length is called its extension.
  4. The extension is found by subtracting the original length from the stretched length.
    1. A spring with an original length of 8.0 cm8.0\ \text{cm}8.0 cm that is stretched to 11.0 cm11.0\ \text{cm}11.0 cm has an extension of 3.0 cm3.0\ \text{cm}3.0 cm.
  5. When an object is compressed, the decrease in its length is called its compression.

Why one force is not enough

Definition

Resultant force

The single force that has the same effect on an object as all of the forces acting on it combined.

  1. If only one force acts on an object, the resultant force on it cannot be zero.
  2. An unbalanced resultant force makes the whole object accelerate in the direction of that force, so the object moves off instead of changing shape.
    1. If you pull one end of a spring lying loose on a smooth bench, the whole spring slides towards you and does not stretch.
  3. To change the shape of an object, more than one force must act on it, and the forces must act on different parts of the object.
  4. The forces together stop the object as a whole from moving off, while its different parts are pulled apart, pushed together or made to curve.
    1. To stretch the spring on the bench, you must hold its other end still, so that a second force pulls on it in the opposite direction.
  5. The forces that deform an object are often balanced, so the object stays still while its shape changes.

Stretching forces

Definition

Tension

The pulling force in a stretched object, such as a spring, rope or cable, that acts along its length.

  1. To stretch an object, forces must pull on it in opposite directions, away from each other.
  2. A spring hanging from a clamp stand with a mass on its lower end is stretched by two forces.
    1. The weight of the mass pulls the bottom of the spring downwards.
    2. The clamp pulls the top of the spring upwards.
  3. The pulling force that is set up inside a stretched spring, rope or cable is called tension.
  4. In a tug of war, the two teams pull the rope in opposite directions, so the rope is stretched tight and is under tension.
  5. A bungee cord is stretched between the jump platform that holds its top end and the weight of the jumper hanging from its lower end.

Compressing forces

Definition

Compressive force

A pushing force that acts towards an object from opposite sides and squashes it into a shorter or smaller shape.

  1. To compress an object, forces must push on it in opposite directions, towards each other.
  2. When you press down on a sponge resting on a table, your hand pushes down on the top of the sponge while the table pushes up on its bottom, so the sponge is squashed between them.
  3. A car's suspension springs are compressed because the car body pushes down on the top of each spring while the axle pushes up on its bottom.
  4. The legs of a chair are compressed between the weight of the person sitting on it and the upward push of the floor.
  5. The sole of a trainer is compressed between your foot and the ground every time you take a step.

Bending forces

  1. To bend an object, forces must act at different places along its length, usually with forces in one direction at the ends and a force in the opposite direction in between, or the other way round.
  2. A ruler resting on two books bends when you press down on its middle, because the books push up at each end while your finger pushes down at the centre.
  3. A shelf sags under a row of heavy books because the brackets push up near its ends while the weight of the books pushes down along its length.
  4. A diving board curves downwards because the clamp and the support hold one end while the weight of the diver pushes down on the free end.
  5. When an object bends, the material on the outside of the curve is stretched and the material on the inside of the curve is compressed.
  6. A fishing rod bends when a fish pulls on the line at the tip while the angler holds the handle firmly at the other end.

Deformation in everyday objects

  1. A trampoline works because the springs around its edge are stretched between the frame and the mat each time you land on it.
  2. A climbing rope is stretched between the anchor point above the climber and the weight of the climber below.
  3. A tennis ball is squashed against the racket strings during a shot, because the strings push on one side of the ball while the ball presses back on the strings.
  4. In every case you can name two objects in contact with the deformed object, and each of them supplies one of the forces that changes its shape.
Example

Forces on a stretched spring

  • A spring with an original length of 10.0 cm10.0\ \text{cm}10.0 cm hangs from a clamp, and a load with a weight of 2.0 N2.0\ \text{N}2.0 N is hung from its lower end.
  • The load pulls down on the bottom of the spring with a force of 2.0 N2.0\ \text{N}2.0 N.
  • The spring stays still, so the clamp must pull up on the top of the spring with an equal force of 2.0 N2.0\ \text{N}2.0 N.
  • The resultant force on the spring is zero, so the spring does not accelerate.
  • The two forces pull on opposite ends of the spring, so the spring is stretched to a new length of 14.0 cm14.0\ \text{cm}14.0 cm.
extension=stretched length−original length \text{extension}=\text{stretched length}-\text{original length} extension=stretched length−original length extension=14.0 cm−10.0 cm=4.0 cm \text{extension}=14.0\ \text{cm}-10.0\ \text{cm}=4.0\ \text{cm} extension=14.0 cm−10.0 cm=4.0 cm
Example

Forces on a compressed cushion

  • You sit on a cushion placed on a chair, and your weight of 600 N600\ \text{N}600 N pushes down on the top of the cushion.
  • The seat of the chair pushes up on the bottom of the cushion with a force of 600 N600\ \text{N}600 N.
  • The two forces push towards each other on opposite faces of the cushion, so the cushion is compressed and becomes thinner.
  • If the chair seat were taken away, only your push would act on the cushion, so the cushion would fall instead of being squashed.
Practical

Exploring stretching with a spring and a liquorice bungee

  • Aim: to explore how a steel spring and a strip of liquorice stretch as hanging masses are added, and to identify the forces that cause the stretching.
  • Apparatus: a clamp stand with two bosses and clamps, a G-clamp to fix the stand to the bench, a steel spring, a long strip of liquorice, a 100 g100\ \text{g}100 g mass hanger with 100 g100\ \text{g}100 g slotted masses, a metre rule, a set square, a pin or a strip of tape to act as a pointer, and eye protection.
  • Method, the spring:
    • Fix the clamp stand to the bench with the G-clamp so that it cannot tip over as masses are added.
    • Hang the spring from the upper clamp and hold the metre rule vertically beside it in the lower clamp.
    • Fix the pointer to the bottom of the spring so that it lies horizontally across the scale of the metre rule.
    • Read the position of the pointer with your eye level with it, using the set square to line it up against the scale, and record this as the original position.
    • Hang the mass hanger on the spring, wait for the spring to stop bouncing, and read the new position of the pointer.
    • Add one 100 g100\ \text{g}100 g slotted mass at a time, which adds a weight of 1 N1\ \text{N}1 N each time, and record the pointer position after each addition.
    • Subtract the original position from each new position to find the extension for each load.
  • Method, the liquorice bungee:
    • Tie one end of the liquorice strip firmly around the upper clamp and tie a loop in its lower end to hold the mass hanger.
    • Measure the length of the liquorice from the bottom of the clamp to the top of the loop with the metre rule.
    • Hang the mass hanger in the loop and add masses one at a time, measuring the length of the liquorice after each addition.
    • Keep adding masses until the liquorice snaps, and record the load at which this happens.
  • Results: each added mass makes both the spring and the liquorice longer, and the liquorice thins noticeably and stretches much further than the spring before it snaps.
  • Conclusion: the spring and the liquorice stretch only because two forces act on opposite ends of them, the downward pull of the hanging masses at the bottom and the upward pull of the clamp at the top.
  • Watch out: read the scale at eye level to avoid parallax error, use the same point on the pointer for every reading, and wait until the spring is completely still before reading it.
  • Safety: wear eye protection in case the spring or liquorice snaps and flicks upwards, keep your feet clear of the area beneath the masses, and never eat anything used in the laboratory.
Common Mistake
  • Do not write that a single force stretches, bends or compresses an object, because one force acting alone makes the whole object accelerate instead.
  • Do not leave out the force from a support, because a clamp, a hook, a table or the floor pushes or pulls on the object just as the load does.
  • Do not confuse extension with stretched length, because extension is only the increase in length.
Exam technique

Explaining stretching, bending and compressing

  • Name both forces in your answer, saying what exerts each force and which way it acts.
  • State that the forces act on different parts of the object, such as opposite ends of a spring or opposite faces of a sponge.
  • Link the forces to the result, for example "so the spring is pulled apart and its length increases", because the final mark is usually for the effect on the object.
  • For a real object such as a trampoline or a car seat, identify the two objects touching it, because each of them supplies one of the forces.
Self review
  • Explain why a single force acting on an object cannot stretch it.
  • Name the two forces that stretch a spring hanging from a clamp stand with a mass attached.
  • Describe the forces that compress a sponge pressed onto a table.
  • State what happens to the material on the inside and on the outside of a bent ruler.
  • Calculate the extension of a spring that stretches from 12.0 cm12.0\ \text{cm}12.0 cm to 15.5 cm15.5\ \text{cm}15.5 cm.
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2.3.1 Stretching, bending and compressing Revision Guide

  1. GCSE
  2. /Physics
  3. /2.3.1 Stretching, bending and compressing

Revision notes for OCR GCSE Physics 2.3.1 Stretching, bending and compressing: explanations and worked examples.

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