Physics 9702 · AS & A Level · Stress and strain

Stress and strain — practice question

Fig. 2.1 depicts a square metal sheet with non-uniform density and a thin wooden rod attached at its centre. One corner of the sheet is marked X. The rod has negligible mass. The metal sheet has mass $2.8\,\text{kg}$. The rod is held so that it is horizontal while the metal sheet hangs vertically.
(a)[2]

Define, in words, the torque of a couple.

(b)[1]

If the rod is supported so that it may turn freely in its support, the sheet hangs in equilibrium with point X vertically above the rod, as shown in Fig. 2.2. On Fig. 2.2, draw a line to show the possible positions of the centre of gravity of the metal sheet.

(c(i))[1]

When a torque of $3.3\,\text{N m}$ acts on the rod, the sheet is held in equilibrium with two of its edges horizontal, as shown in Fig. 2.3. Point X is at the top-left corner. Explain whether the torque applied to the rod to hold the sheet in equilibrium is clockwise or anticlockwise.

(c(ii))[1]

Show that the centre of gravity of the sheet has a horizontal displacement of $0.12\,\text{m}$ from the rod.

(d)[3]

The square metal sheet has an average density of $3000\,\text{kg m}^{-3}$ and a uniform thickness of $4.0\,\text{mm}$. Show that the side length of the sheet is $0.48\,\text{m}$.

(e)[2]

Use the answer in (b) and the information in (c) and (d) to work out the position of the centre of gravity of the sheet. Show this position on Fig. 2.3 as a point labelled Y.

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