Using the diagram above as a guide, carry out the following instructions.
- Place the meter rule provided on the knife edge and adjust the position until it balances horizontally.
- Read and record the balance point, G. Keep the knife edge at this point throughout the experiment.
- Suspend a mass Q= 50.0g at a point P 30cm from the 0cm end of the rule.
- On the other side of G, suspend the mass M =30g. Adjust its position until the rule settles down horizontally as shown in the diagram above.
- Read and record the position R of M.
- Record the distance, d, between G and R. Also read and record the distance, a, between P and G.
- Repeat the procedure for four other values of M = 40, 50, 60, and 70 with Q kept in the same position. Evaluate d\(^{-1}\) in each case. Tabulate your readings.
- Plot a graph of M on the vertical axis against d\(^{-1}\) on the horizontal axis.
- Determine the slope,s, of the graph.
- Evaluate k = \(\frac{s}{Q}\)
- State two precautions taken to ensure accurate results.
(b)i. Explain the moment of a force about a point
ii. State the conditions necessary for a body to be in equilibrium when acted upon by a number of parallel end forces
Explanation
1. 49.50cm
5. 82cm from 0
6. a = 19.50cm
d = 32.50cm
7. Table of values/observation
| S/N | M(g) | d(/cm) | d\(^{-1}\) | d\(^{-1}\)(cm\(^{-1}\))x10\(^{-2}\) |
| 1 | 30.0 | 32.50 | 0.0308 | 3.08 |
| 2 | 40.0 | 24.38 | 0.0410 | 4.10 |
| 3 | 50.0 | 19.50 | 0.0513 | 5.13 |
| 4 | 60.0 | 16.25 | 0.0615 | 6.15 |
| 5 | 70.0 | 13.93 | 0.0718 | 7.18 |
8.
9. Slope = \(\frac{\bigtriangleup {m(g)}}{\bigtriangleup {d}^{-1}(cm^{-1})}\)
= \(\frac{60-10.8}{(6.16-1.04) \times 10^{-2}}\)
slope (s) = \(\frac{49.2}{5.12 \times 10^{-2}}\)
K = \(\frac{S}{Q} = \frac{960.94}{50}\) =19.2g
Precautions taken to ensure results are as follows:
- Avoid the error of parallax in reading the meter-rule
- Avoid draught-free wind.
- Repeated readings must be shown on the table of values/observations.
(b)i. The moment of a force about a point is the product of the force and the perpendicular distance from the point to the line of action of the force.
ii. For a body to be in equilibrium under the action of parallel forces,
- The forces must all act in the same plane
- The sum of the forces in one direction must be equal to the sum of the forces in the opposite direction ie Total upward force is equal to the total downward force.
- The algebraic sum of the moments about any point is equal to zero. i.e. The sum of the clockwise moment about a point is equal to the sum of the anti-clockwise moment about the same point.