 Solution

ID: past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2018/paper-1/section-c/c12/b/solution

The torque rises linearly with elastic twist, so the stored elastic energy is the work integral

U = \int_{0}^{ϕ} \frac{G J _{p}}{L} ϕ^{'} d ϕ^{'} = \frac{1}{2} Cϕ .

Using the transmitted torque and end twist,

U ≃ \frac{1}{2} (133.3) (1.243 \times 1 0^{- 3}) J = 8.29 \times 1 0^{- 2} J .

This is energy associated with deformation, distinct from the much larger kinetic energy of the whole spinning shaft.

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