(a) State Hook's law. [2] (b) The walls of the tyres on a car are made of a rubber
compound. The variation with stress of the strain of a
specimen of this rubber compound is shown in Fig. 1.2.
As the car moves, the walls of the tyres end and straighten
continuously. Use Fig. 1.2 to explain why the walls of the
tyres become warm
[3]
hin
Fig. 1.2.

Hooke's law gives the relationship between the force applied and observed compression and expansion

(a) Hooke's law states that force applied is proportional to the deformation of an object

(b) The tube becomes warm from the excess of the energy absorbed but not given off back as the straightening of the tyre

The reason for the above explanation are as follows;

(a) Hooke's law states that for little deformations, the change in the dimension, Δx, of an extended or compressed object is directly proportional to the applied force, F

Mathematically, we get;

F = k × ΔL

Given that the material cross sectional area = A, and the original length of the material = L, we get;

F/A = Stress = σ, ΔL/L = strain = ε

Therefore, Hooke's law can be expressed as a form of Young's Modulus for a given length to area ratio of a material

(b) The given graph of stress to strain curve, is attached, from which area under the curve gives the energy absorbed by the the material during deformation

Therefore during bending, the stress is increasing as shown in the top of the two curve, and the energy absorbed is given by the area under the curve

As the tyre straightens, the path of the stress change curve is given by the lower curve

The area under the top (bending) curve is larger than the area under the lower (straightening) curve, therefore, the energy absorbed during bending is larger than the energy given off during straightening

Energy absorbed < Energy released

The balance energy is transformed into other forms of energy, including  heat energy, which is observed by the raising in temperature, warming, of the tyre

Energy absorbed = Energy released + Heat energy

Learn more about Hooke's law here;

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