Physics of solids

NUST NET (Engineering) · Physics · Solids and electronics. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

When a force stretches a solid, stress is the force on each square metre of cross-section and strain is the fractional change in length. Up to the proportional limit stress is proportional to strain. Their ratio is Young's modulus, a property of the material and not of the size or shape of the sample.

Solids are classed by how their atoms are arranged. Crystalline solids have a regular repeating pattern and a sharp melting point, amorphous solids such as glass have no long-range order, and polymeric solids are made of long chain molecules.

Magnetic materials are diamagnetic, paramagnetic or ferromagnetic. Ferromagnets contain domains that line up in a field; this is lost above the Curie temperature.

Rules to remember

Common mistake

Treating area as proportional to diameter. Area depends on diameter squared, so a wire of twice the diameter has four times the area and a quarter of the extension for the same force and length.

Worked example

A wire 2.0 m long with cross-sectional area 1.0 × 10−6 m2 is stretched by a force of 100 N. Its Young's modulus is 2.0 × 1011 Pa. What is its extension?

  1. Stress = F/A = 100/(1.0 × 10−6) = 1.0 × 108 Pa.
  2. Strain = stress/Y = (1.0 × 108)/(2.0 × 1011) = 5.0 × 10−4.
  3. Extension = strain × length = 5.0 × 10−4 × 2.0 = 1.0 × 10−3 m.

Answer: 1.0 × 10−3 m (1.0 mm)

Practice questions

Try each one, then open the answer.

1. A wire is stretched within its elastic limit so that the stress in it is 3.0 × 108 Pa and the strain is 2.0 × 10−3. The elastic energy stored per unit volume of the wire is

  1. A
    6.0 × 105 J m−3
  2. B
    3.0 × 105 J m−3
  3. C
    1.5 × 1011 J m−3
  4. D
    3.0 × 10−5 J m−3
Show answer

Answer: B. Energy per unit volume = ½ × stress × strain = ½ × 3.0 × 108 × 2.0 × 10−3 = 3.0 × 105 J m−3. Leaving out the ½ gives 6.0 × 105; 1.5 × 1011 is stress ÷ strain, the Young's modulus in Pa, not an energy.

2. Wires A and B are made of the same material. B is twice as long as A and has twice its diameter. When the same force stretches each, the ratio of the extension of B to that of A is

  1. A
    1 : 2
  2. B
    2 : 1
  3. C
    1 : 1
  4. D
    1 : 4
Show answer

Answer: A. Extension ΔL = FL/(AY) ∝ L/d2. For B this is 2/22 = ½ of A's extension. Using the diameter instead of the area (2/2) gives 1 : 1.

3. The core of a transformer is made of a soft magnetic material such as soft iron because such a material has

  1. A
    a hysteresis loop of small area, so little energy is lost in each cycle
  2. B
    a hysteresis loop of large area, so it keeps its magnetism
  3. C
    a very high electrical resistance
  4. D
    no magnetic domains
Show answer

Answer: A. Soft iron is easily magnetised and demagnetised; its narrow hysteresis loop means little energy is wasted as heat in each cycle. Materials with wide loops, such as steel, suit permanent magnets.

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