You are provided with a uniform metre rule, a knife-edge, some masses and other necessary materials.
i. Determine and record the centre of gravity of the metre rule.
ii. Fix the 100g mass marked N at a point Y, the 80cm mark of the rule using a sellotape.
iii. Suspend another 50g mass marked M at X, a distance A = 1Ocm from the 0cm mark of the rule.
iv. Balance the arrangement horizontally on the knife edge as illustrated in the diagram above.
v. Measure and record the distance B of a knife-edge from the 0cm mark of the rule.
vi. Repeat the procedure for four other values of A =15cm, 20cm, 25cm and 30cm.
vii. Tabulate your readings.
viii. Plot a graph with B on the vertical axis and A on the horizontal axis.
ix. Determine the slope, s, of the graph.
x. Also determine the intercept, c, on the vertical axis.
xi. Evaluate:
\(\propto\)) = k\(_{1}\) = (\(\frac{1 – 2s}{s}\))100
(\(\beta\)) = k\(_{2}\) = \(\frac{2c}{s}\) = 160
xii. State two precautions taken to obtain accurate results.
(b)i. Define the moment of a force about a point.
ii. State two conditions under which a rigid body at rest remains in equilibrium when acted upon by non-parallel coplanar forces.
Explanation
| S/N | A/cm | B/cm |
| 1.0 | 10.0 | 54.00 |
| 2.0 | 15.0 | 55.00 |
| 3.0 | 20.0 | 56.00 |
| 4.0 | 25.0 | 57.00 |
| 5.0 | 30.0 | 57.00 |
| 6.0 | 35.0 | 58.00 |
Slope (s) = \(\frac{\bigtriangleup {B}}{\bigtriangleup {A}}\) = \(\frac{B_{2} - B_{1}}{A_{2} - A_{1}}\)
= \(\frac{59 - 53}{30 - 0} = \frac{6}{30}\) = \(\frac{1}{6}\)
= 0.2
Intercept C on the vertical axis
C = 53
Evaluate (a) k\(_{1}\) = [\(\frac{1 - 2S}{S}\)]100
= (\(\frac{1 - 2 \times 0.2}{0.2}\)) 100
= (\(\frac{1 - 0.4}{0.2}\))100
k\(_{1}\) = \(\frac{0.6}{0.2}\) 100
= 300
k\(_{2}\) = \(\frac{2C}{S}\) - 160
= \(\frac{2 \times 52}{0.2}\) - 160
= \(\frac{106}{0.2}= \frac{1060}{2}\) = 530 - 160
= 370
Precautions;
- Avoided draught
- Ensured mass did not touch/rest on the table.
- Avoided error due to parallax on the metre rule.
- Noted zero error on metre rule.
- Repeated readings (shown on the table).
(b)i. The moment of a force about a point is defined as the product of the force and the perpendicular distance from the point to the line of action of the force.
ii. Conditions of rigid bodies in equilibrium;
1. The resultant of the forces in a given direction must be zero/the algebraic sum of resolved components in a given direction must be zero/the vector sum of all the points must = 0
2. The algebraic sum of the moments about any point is zero.
3. The forces must be concurrent or meet at a point.