TEST OF PRACTICAL KNOWLEDGE QUESTION (a) You are provided with a set of masses, a metre rule, a thread, two retort stands and clamps, a stop watch, a knife ...
(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.
Test of Practical Knowledge - Angular (Bifilar) Oscillations of a Metre Rule
The metre rule is hung horizontally by two vertical parallel threads (bifilar suspension), one at the 10 cm mark and the other at the 90 cm mark, each of length \(h = 70\text{ cm}\), so that the distance between the threads is \(d = 80\text{ cm}\). A load \(m\) is fixed at the centre of gravity \(C\) and the rule is given small angular oscillations about the vertical axis through \(C\). The set-up used is shown below.
Bifilar suspension of the metre rule: two parallel threads (h = 70 cm) at the 10 cm and 90 cm marks (d = 80 cm), with load m fixed at the centre of gravity C.
(a)(i) Balancing the bare metre rule on the knife edge, it rests horizontally with the knife edge at the 50.0 cm mark; hence the centre of gravity is \(C = 50.0\text{ cm}\).
(a)(ii) Mass of the metre rule read from its reverse side: \(M = 100\text{ g}\).
(a)(vi)–(vii) For each load \(m\) the time \(t\) for 20 oscillations is measured, and \(T = t/20\), \(T^{2}\) and \(T^{-2}\) are evaluated. The readings obtained are tabulated below.
m (g)
t for 20 osc. (s)
T (s)
T² (s²)
T⁻² (s⁻²)
30
28.0
1.40
1.96
0.510
40
30.0
1.50
2.25
0.444
50
32.0
1.60
2.56
0.391
60
34.0
1.70
2.89
0.346
70
36.0
1.80
3.24
0.309
(a)(viii) The graph of \(T\) (vertical axis) against \(m\) (horizontal axis) is a straight line, showing that the period increases uniformly with the added mass.
Straight-line graph of T against m; slope s = 0.010 s g⁻¹.
(a)(ix) Slope of the graph. Taking two well-separated points on the line of best fit, \((m_1, T_1) = (30\text{ g}, 1.40\text{ s})\) and \((m_2, T_2) = (70\text{ g}, 1.80\text{ s})\):
I avoided error due to parallax by reading the stop watch and the metre rule scale with the line of sight directly (perpendicular) to them.
I ensured that the retort stands and clamps supporting the threads were firm and rigid, and that the two threads were parallel and of equal length, so that the oscillations were purely angular about the vertical axis.
(b)(i) Two examples of simple harmonic motion (other than the simple pendulum):
The vertical up-and-down oscillation of a mass suspended from a helical (loaded) spring.
The to-and-fro oscillation of a liquid column in a U-tube after it has been disturbed.
(b)(ii) Centre of gravity of a body: The centre of gravity of a body is the single point through which the whole weight (resultant of the weights of all its particles) of the body appears to act, whatever the position or orientation of the body.
Test of Practical Knowledge - Angular (Bifilar) Oscillations of a Metre Rule
The metre rule is hung horizontally by two vertical parallel threads (bifilar suspension), one at the 10 cm mark and the other at the 90 cm mark, each of length \(h = 70\text{ cm}\), so that the distance between the threads is \(d = 80\text{ cm}\). A load \(m\) is fixed at the centre of gravity \(C\) and the rule is given small angular oscillations about the vertical axis through \(C\). The set-up used is shown below.
Bifilar suspension of the metre rule: two parallel threads (h = 70 cm) at the 10 cm and 90 cm marks (d = 80 cm), with load m fixed at the centre of gravity C.
(a)(i) Balancing the bare metre rule on the knife edge, it rests horizontally with the knife edge at the 50.0 cm mark; hence the centre of gravity is \(C = 50.0\text{ cm}\).
(a)(ii) Mass of the metre rule read from its reverse side: \(M = 100\text{ g}\).
(a)(vi)–(vii) For each load \(m\) the time \(t\) for 20 oscillations is measured, and \(T = t/20\), \(T^{2}\) and \(T^{-2}\) are evaluated. The readings obtained are tabulated below.
m (g)
t for 20 osc. (s)
T (s)
T² (s²)
T⁻² (s⁻²)
30
28.0
1.40
1.96
0.510
40
30.0
1.50
2.25
0.444
50
32.0
1.60
2.56
0.391
60
34.0
1.70
2.89
0.346
70
36.0
1.80
3.24
0.309
(a)(viii) The graph of \(T\) (vertical axis) against \(m\) (horizontal axis) is a straight line, showing that the period increases uniformly with the added mass.
Straight-line graph of T against m; slope s = 0.010 s g⁻¹.
(a)(ix) Slope of the graph. Taking two well-separated points on the line of best fit, \((m_1, T_1) = (30\text{ g}, 1.40\text{ s})\) and \((m_2, T_2) = (70\text{ g}, 1.80\text{ s})\):
I avoided error due to parallax by reading the stop watch and the metre rule scale with the line of sight directly (perpendicular) to them.
I ensured that the retort stands and clamps supporting the threads were firm and rigid, and that the two threads were parallel and of equal length, so that the oscillations were purely angular about the vertical axis.
(b)(i) Two examples of simple harmonic motion (other than the simple pendulum):
The vertical up-and-down oscillation of a mass suspended from a helical (loaded) spring.
The to-and-fro oscillation of a liquid column in a U-tube after it has been disturbed.
(b)(ii) Centre of gravity of a body: The centre of gravity of a body is the single point through which the whole weight (resultant of the weights of all its particles) of the body appears to act, whatever the position or orientation of the body.
