In the diagram, a thread AC, fixed at pulley A passes over pulley C on a force board and carries an unknown mass m\(_{o}\). Retain this mass m\(_{o}\) throughout the experiment. Draw a line along the direction of AC on the paper held behind the thread. Locate the mid-point B of AC and mark its position on this line. Draw BP at right angles to AC. By means of a loop of thread, suspend a mass M 50 g from AC and adjust the position of the loop so that the line of action of the weight of M lies along with BP. Ensure that M and m\(_{o}\), hang off the force board. Measure BO = y and AO. Evaluate y / AO. Repeat the experiment for M = 70,90,110 and 130g respectively. In each case, determine the corresponding values of y, AO, and y / AO. Tabulate your readings. Plot a graph of Y/AO on the vertical axis and M on the horizontal axis. Determine the slopes s of the graph. State two precautions taken to ensure accurate results. Attach your traces to your answer script.
(b)i. Distinguish between the resultant and the equilibrant of forces.
ii. State two conditions necessary for the equilibrium of three non-parallel coplanar forces.
Explanation
Table of values/observation
| S/N | M(g) | y(cm) | Ao(cm) | \(\frac{y}{AO}\) |
| 1 | 50.00 | 2.30 | 8.00 | 0.288 |
| 2 | 70.00 | 2.45 | 8.20 | 0.378 |
| 3 | 90.00 | 3.65 | 8.40 | 0.417 |
| 4 | 110.00 | 4.10 | 8.60 | 0.465 |
| 5 | 130.00 | 5.00 | 9.10 | 0.549 |
Slope (s) = \(\frac{\bigtriangleup {(\frac{y}{AO})}}{\bigtriangleup {m(g)}} = \frac{0.55-0.15}{130-6} = \frac{0.4}{124}\)
0.003226g\(^{-1}\)
Precautions:
- Force board must be firmly fixed.
- Avoid parallax errors when reading the metre rule.
(b)i. The resultant and the equilibrant of forces have the same magnitude but opposite directions.
ii. The conditions for the equilibrium of three non-parallel co-planar forces are:
- The lines of action of the forces must meet at a point.
- All the three forces must be concurrent (i.e, meet at a point).
- The algebraic sum of their moment about a point must be zero.
- The algebraic sum of the forces at a point must be equal to zero.