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.
Breithaupt pages 162 to 171
Obtain data to plot graphs on the same axes for
the following spring combinations:
The 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
kis called the spring constant
The spring constant is the force required to produce an extension of one metre.
unit = Nm-1
Up 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.
(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
A 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
A stretching force is also called a tensile force.
Tensile stress = tensile force
σ = F / A
unit – Pa (pascal) or Nm-2
Note: 1 Pa = 1 Nm-2
This is the stress required to cause a material to break.
Tensile strain = extension
ε = ΔL / L
unit – none (it’s a ratio like pi)
A 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 / 2.5m
tensile strain, ε = 0.02
(c)σ = F / A
→ F = σ A
= 1.5 x 109 Pa x 1.96 x 10-7 m2
Breaking Force, F = 294 N
(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 108Pa