(a) You are provided with a set of masses, a metre rule, a thread, two retort stands and clamps, a stop watch, a knife edge and split corks.
Carry out the following instructions using the diagram above as a guide.
(i) Determine the centre of gravity, C, of the metre rule using the knife edge.
(ii) Read and record the mass, M, of the metre rule written on the reverse side of it.
(iii) Suspend the metre rule by means of two parallel threads of equal length, h= 70 cm with one at the 10 cm mark and the other at 90 cm mark of the metre rule.
(iv) Attach a mass m = 30g firmly to the metre rule at C. Ensure that the graduated face of the metre rule is facing upwards and that d= 80 cm throughout the experiment. (v) Set the metre rule into small angular oscillations about the vertical axis through its centre of gravity by displacing its ends in opposite directions.
(VI) Determine the time,i, for 20 oscillations and evaluate the period T, T\(^2\) and T\(^{-2}\).
(vii) Repeat the procedure for four other values of m =40 g, 50 g, 60 g and 70 g n each case, determine I and evaluate T\(^2\) and T\(^{-2}\).
(viii) Plot a graph of T on the vertical axis and m on the horizontal axis.
(ix) Determine the slope, s, of the graph.
(x) Evaluate Q= 0.68 / s.
(xi) State two precautions taken to ensure accurate results.
(b) (i) Give two examples of simple harmonic motion other than the motion of a simple pendulum.
(ii) Explain the term centre of gravity of a body.
Nature of the experiment. The metre rule hangs horizontally from two equal parallel threads (a bifilar suspension) and is set into small angular (torsional) oscillations about the vertical axis through its centre of gravity. The period T is found for several attached masses m.
Procedure summary. For each mass m (30, 40, 50, 60, 70 g attached at C), the time t for 20 complete oscillations is measured, and the period and its powers are evaluated:
\[ T = \frac{t}{20}, \qquad T^{2}, \qquad T^{-2} \]
Sample table (headings).
| m (g) | t for 20 osc. (s) | T (s) | \(T^{2}\) | \(T^{-2}\) |
|---|
| 30 | - | - | - | - |
| 40 | - | - | - | - |
| 50 | - | - | - | - |
| 60 | - | - | - | - |
| 70 | - | - | - | - |
Graph and evaluation. Plot T (vertical) against m (horizontal). Determine the slope s from \(s = \dfrac{\Delta T}{\Delta m}\), then evaluate
\[ Q = \frac{0.68}{s} \]
Two precautions.
- The oscillations were kept small (small angular displacement) and purely rotational, and timing was taken over 20 swings to reduce reaction-time error.
- The two threads were of equal length and vertical, the mass firmly attached at C, and the eye kept steady to avoid parallax/miscounting; timing started and stopped at an end position of the swing.
(b)(i) Two examples of simple harmonic motion (other than the simple pendulum): the vertical oscillation of a mass on a spiral spring; the vibration of a tuning-fork prong; the up-and-down motion of a loaded test-tube (or hydrometer) floating in a liquid; the oscillation of liquid in a U-tube.
(b)(ii) Centre of gravity. The centre of gravity of a body is the single point through which the whole weight of the body appears to act, irrespective of the position of the body.
Nature of the experiment. The metre rule hangs horizontally from two equal parallel threads (a bifilar suspension) and is set into small angular (torsional) oscillations about the vertical axis through its centre of gravity. The period T is found for several attached masses m.
Procedure summary. For each mass m (30, 40, 50, 60, 70 g attached at C), the time t for 20 complete oscillations is measured, and the period and its powers are evaluated:
\[ T = \frac{t}{20}, \qquad T^{2}, \qquad T^{-2} \]
Sample table (headings).
| m (g) | t for 20 osc. (s) | T (s) | \(T^{2}\) | \(T^{-2}\) |
|---|
| 30 | - | - | - | - |
| 40 | - | - | - | - |
| 50 | - | - | - | - |
| 60 | - | - | - | - |
| 70 | - | - | - | - |
Graph and evaluation. Plot T (vertical) against m (horizontal). Determine the slope s from \(s = \dfrac{\Delta T}{\Delta m}\), then evaluate
\[ Q = \frac{0.68}{s} \]
Two precautions.
- The oscillations were kept small (small angular displacement) and purely rotational, and timing was taken over 20 swings to reduce reaction-time error.
- The two threads were of equal length and vertical, the mass firmly attached at C, and the eye kept steady to avoid parallax/miscounting; timing started and stopped at an end position of the swing.
(b)(i) Two examples of simple harmonic motion (other than the simple pendulum): the vertical oscillation of a mass on a spiral spring; the vibration of a tuning-fork prong; the up-and-down motion of a loaded test-tube (or hydrometer) floating in a liquid; the oscillation of liquid in a U-tube.
(b)(ii) Centre of gravity. The centre of gravity of a body is the single point through which the whole weight of the body appears to act, irrespective of the position of the body.
