Answer :
Hookes law state that provided that the elastic limit is not exceeded, the extension is directly proportional to the force
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
[tex]k = \mathbf{\dfrac{F}{\Delta L}}[/tex]
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
[tex]\mathbf{Young's \ Modulus, \ E} = \mathbf{\dfrac{\sigma}{\varepsilon}} = \dfrac{\left(\dfrac{F}{A} \right) }{\left(\dfrac{\Delta L}{L} \right) } = \mathbf{\dfrac{F}{\Delta L } \times \dfrac{L}{A}}[/tex]
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
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