2.2 materials materials

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2.2 Materials Materials Breithaupt pages 162 to 171

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2.2 Materials Materials. Breithaupt pages 162 to 171. AQA AS Specification. Elasticity and springs. Elastic limit and Yield point. Elasticity and springs. Elastic limit and Yield point. Hooke’s Law. - PowerPoint PPT Presentation

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Page 1: 2.2 Materials Materials

2.2 Materials Materials

Breithaupt pages 162 to 171

Page 2: 2.2 Materials Materials

AQA AS SpecificationLessons Topics

1 to 4 Bulk properties of solidsDensityρ = m / VHooke’s law, elastic limit, experimental investigations.F = k ΔLTensile strain and tensile stress.Elastic strain energy, breaking stress.Derivation of energy stored = ½ FΔLDescription of plastic behaviour, fracture and brittleness; interpretation of simple stress-strain curves.

5 & 6 The Young modulusThe Young modulus = tensile stress = FL

tensile strain AΔLOne simple method of measurement.Use of stress-strain graphs to find the Young modulus.

Page 3: 2.2 Materials Materials

Elastic limit and Yield point

Elasticity and springs

Page 4: 2.2 Materials Materials

Elastic limit and Yield point

Elasticity and springs

Page 5: 2.2 Materials Materials
Page 6: 2.2 Materials Materials
Page 7: 2.2 Materials Materials

Hooke’s Law

Page 8: 2.2 Materials Materials

Experiment to investigate Hooke’s Law

Obtain data to plot graphs on the same axes for the following spring combinations:

Page 9: 2.2 Materials Materials

Hooke’s lawThe force (F ) needed to stretch a spring is directly proportional to the extension (ΔL ) of a spring from its natural length.

F α ΔL

Adding a constant of proportionality: F = k ΔL or F = -K ΔL

k is called the spring constant

The spring constant is the force required to produce an extension of one metre.

unit = Nm-1

Page 10: 2.2 Materials Materials

Elastic limitUp to a certain extension if the force is removed the spring will return to its original length. The spring is said to be behaving elastically.

If this critical extension is exceeded, known as the elastic limit, the spring will be permanently stretched.

Plastic behaviour then occurs and Hooke’s law is no longer obeyed by the spring.

Page 11: 2.2 Materials Materials

QuestionA spring of natural length 15cm is extended by 3cm by a force of 6N. Calculate (a) the spring constant and (b) the length of the spring if a force of 18N is applied.

(a) F = k ΔL → k = F / ΔL = 6N / 0.03m spring constant, k = 200 Nm-1

(b) F = k ΔL

→ ΔL = F / k

= 18N / 200 Nm-1

ΔL = 0.09 m

= 9 cm

And so the spring’s length

= 24 cm

Page 12: 2.2 Materials Materials

Tensile stress (σ) A stretching force is also called a tensile force.

Tensile stress = tensile force cross-section area

σ = F / A

unit – Pa (pascal) or Nm-2

Note: 1 Pa = 1 Nm-2

Page 13: 2.2 Materials Materials

Breaking stress

This is the stress required to cause a material to break.

Page 14: 2.2 Materials Materials

Tensile strain (ε)

Tensile strain = extension

original length

ε = ΔL / L

unit – none (it’s a ratio like pi)

Page 15: 2.2 Materials Materials

QuestionA wire of natural length 2.5 m and diameter 0.5 mm is extended by 5 cm by a force of 40 N. Calculate: (a) the tensile strain ε = ΔL / L(b) the tensile stress σ = F / A(c) the force required to break the wire if its breaking stress is 1.5 x 109 Pa. σ = F / A

(a) ε = ΔL / L= 0.05m / 2.5mtensile strain, ε = 0.02

Page 16: 2.2 Materials Materials

Question(b) σ = F / A

A = Area = π r2 = π x (0.25 x 10-3 )2 m2 = 1.96 x 10-7 m2

σ = 40N / 1.96 x 10-7 m2

stress, σ = 2.04 x 108 Pa

(c) σ = F / A

→ F = σ A = 1.5 x 109 Pa x 1.96 x 10-7 m2

Breaking Force, F = 294 N

Page 17: 2.2 Materials Materials

Key points

1. Springs in series are ‘slacker’

Page 18: 2.2 Materials Materials

Key points

1. Springs in series are ‘slacker’

Page 19: 2.2 Materials Materials

Key points

1. Springs in series are ‘slacker’

Page 20: 2.2 Materials Materials

Key points

2. Springs in parallel are ‘stiffer’

Page 21: 2.2 Materials Materials

Key points

2. Springs in parallel are ‘stiffer’

Page 22: 2.2 Materials Materials

Key points

2. Springs in parallel are ‘stiffer’

Page 23: 2.2 Materials Materials

Key points

2. Springs in parallel are ‘stiffer’

Page 24: 2.2 Materials Materials

Electromechanical analogies

Page 25: 2.2 Materials Materials
Page 26: 2.2 Materials Materials

Notes on Hooke’s law and Springs from Breithaupt pages 164 to 166

1. Define Hooke’s law. Quote the equation for Hooke’s law.2. What is meant by (a) the spring constant and (b) the elastic

limit.

3. A spring of natural length 40 cm is extended to 50 cm by a force of 2N. Calculate (a) the spring constant in Nm-1 (b) the expected length of the spring if it were to be extended by a force of 5N.

4. Show that the overall spring constant, k for (a) springs in series is given by k = k1 + k2; (b) springs in parallel is given by 1 / k = 1 / k1 + 1 / k2 where k1 and k2 are the spring constants of the individual springs.

5. Try Summary Questions 1, 2 & 3 on page 166

Page 27: 2.2 Materials Materials

Internet Links• Stretching Springs - PhET - A realistic mass and spring

laboratory. Hang masses from springs and adjust the spring stiffness and damping. You can even slow time. Transport the lab to different planets. A chart shows the kinetic, potential, and thermal energy for each spring.