levo

Solids Under Stress

Work done in deforming a solid

  • 3 things to know
  • Component 2

Overview

Recall questions on the area under a force–extension graph, the equation ½Fx and its equivalent ½kx², why the factor of a half appears, the energy stored elastically, and what the area of a loading and unloading loop represents.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

How is the work done in deforming a solid found from a force–extension graph?

Key term

State the expression for the work done in stretching a solid that obeys Hooke's law.

Key term

Why is the work done in stretching a Hookean spring ½Fx rather than Fx?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How is the work done in deforming a solid found from a force–extension graph?

    Model answer

    The work done is the area between the force–extension curve and the extension axis.

  2. 2

    State the expression for the work done in stretching a solid that obeys Hooke's law.

    Model answer

    The work done is ½Fx, where F is the final force in newtons and x is the final extension in metres.

  3. 3

    Why is the work done in stretching a Hookean spring ½Fx rather than Fx?

    Model answer

    The force rises steadily from zero to F as the extension grows, so the average force acting over the extension is only ½F.

  4. 4

    Give the expression for the work done in stretching a spring in terms of its spring constant.

    Model answer

    Substituting F = kx into ½Fx gives a work done of ½kx².

  5. 5

    What is meant by elastic strain energy?

    Model answer

    Elastic strain energy is the energy stored in a deformed solid that is recovered when the deforming force is removed.

  6. 6

    A spring of spring constant 50 N m⁻¹ is stretched by 4.0 cm. Calculate the elastic strain energy stored.

    Model answer

    The energy is ½kx² = 0.5 × 50 × (0.040)² = 0.040 J. The force at that extension is 2.0 N, and ½Fx = 0.5 × 2.0 × 0.040 gives the same 0.040 J.

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.

1Closed book
2Open book
3Closed book

The 3-step method, run for you

Answer cold, learn it, then prove it stuck. Levo tracks the jump between your first attempt and your last.

Basic Physics
Kinematics
Dynamics
Energy Concepts

Cram a whole paper in one sitting

Sort every topic into what you know and what you do not, then drill only the weak ones.

The wires .
attractrepeltwist

Blank Blitz makes facts automatic

Rapid timed gap-fills on the terms and numbers you need to recall without thinking.

AThe equation is pV = NkT.
BThe pressure, p, is in Pa.
CThe volume V is in m³.

Build It gets the exam shape right

Assemble a full-mark answer from its marking points, in the order an examiner wants them.

The joule is a unit of energy.
TrueFalse

Test It catches misconceptions

Spot the fault in a statement. The traps are the mistakes students actually make.

721941163128510

Brain Breaks between sessions

Short focus games to reset attention, so the next set lands better than the last.

Every question in Solids Under Stress, on a schedule.

Attempt a question from memory, write the correct version, then attempt it again. Levo records the jump between your first attempt and your last, and brings each question back on the day you are due to forget it.

Or £46 a year, about £3.83 a month. Cancel anytime.