You are provided with a metre rule, a knife edge, two pieces of thread and two masses m\(_{1}\) and m\(_{2}\) Record the values of m\(_{1}\) and m\(_{2}\). ...
Question 1 Report
You are provided with a metre rule, a knife edge, two pieces of thread and two masses m\(_{1}\) and m\(_{2}\)
- Record the values of m\(_{1}\) and m\(_{2}\).
- Balance the metre rule horizontally on the knife edge and record the balance point G.
- With the knife edge at the 60 cm mark of the metre rule, suspend m\(_{1}\) at the 20 cm mark and m\(_{2}\) at a suitable mark such that the rule balances horizontally as illustrated in the diagram above.
- Record the positions Y of m\(_{1}\) and Q of m\(_{2}\).
- Evaluate 1= P - Y and d = Q - P
- Repeat the procedure for four other positions of m, at 18, 16, 14 and 12 cm marks.
- In each case, evaluate and record l and d.
- Tabulate your readings.
- Plot a graph of l on the vertical axis against d on the horizontal axis.
- Determine the slope of the graph.
- State two precautions taken to ensure accurate results.
(b}i. With the aid of a diagram, indicate the forces acting on the metre rule in the experimental set-up above.
ii. Define moment of a force about a point and state its S.1. unit.
Answer Details
(a) Metre rule and knife-edge experiment
Recorded fixed values:
\(m_1 = 20.0\ \text{g}\), \(\quad m_2 = 50.0\ \text{g}\), \(\quad\) balance point (centre of gravity) \(G = 50.0\ \text{cm}\).
The knife edge (pivot) is kept fixed at the \(P = 60.0\ \text{cm}\) mark. Mass \(m_1\) is suspended at the mark \(Y\) (left of the pivot) and mass \(m_2\) at the mark \(Q\) (right of the pivot) so that the rule balances horizontally. For each setting, \(l = P - Y\) and \(d = Q - P\).
Table of readings
| S/N | \(Y\) (cm) | \(Q\) (cm) | \(l = P - Y\) (cm) | \(d = Q - P\) (cm) |
|---|---|---|---|---|
| 1 | 20.0 | 96.0 | 40.0 | 36.0 |
| 2 | 18.0 | 96.8 | 42.0 | 36.8 |
| 3 | 16.0 | 97.6 | 44.0 | 37.6 |
| 4 | 14.0 | 98.4 | 46.0 | 38.4 |
| 5 | 12.0 | 99.2 | 48.0 | 39.2 |
Graph of \(l\) against \(d\)
The points lie on a straight line. Taking two widely separated points on the line of best fit, \((d_1, l_1) = (36.0,\ 40.0)\) and \((d_2, l_2) = (39.2,\ 48.0)\):
\[ \text{slope } s = \frac{l_2 - l_1}{d_2 - d_1} = \frac{48.0 - 40.0}{39.2 - 36.0} = \frac{8.0}{3.2} = 2.5 \]
The slope is \(2.5\) (no unit). It equals the ratio \(\dfrac{m_2}{m_1} = \dfrac{50.0}{20.0} = 2.5\), confirming the principle of moments \(m_1 g\, l + W g\,(P-G) = m_2 g\, d\), which rearranges to \(l = \dfrac{m_2}{m_1}\,d - \dfrac{W(P-G)}{m_1}\).
Two precautions
- The eye was placed vertically above the metre-rule mark when taking each reading to avoid error due to parallax.
- The rule was checked to be exactly horizontal, and the suspended masses were not allowed to touch the table before each reading was recorded.
(b)(i) Forces acting on the metre rule
Four forces act on the rule: the upward normal reaction \(R\) at the knife edge (60 cm mark); the downward weight \(m_1 g\) at \(Y\); the downward weight of the rule \(W\) at its centre of gravity \(G\) (50 cm mark); and the downward weight \(m_2 g\) at \(Q\). For equilibrium, \(R = m_1 g + W + m_2 g\), and the total anticlockwise moment about the pivot equals the total clockwise moment.
(b)(ii) Moment of a force
The moment of a force about a point is the product of the force and the perpendicular distance from that point to the line of action of the force; it is the turning effect of the force about the point.
\[ \text{moment} = F \times d \]
Its S.I. unit is the newton metre (N m).
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