You are provided with a grooved inclined plane, a solid sphere, a stopwatch, and other necessary apparatus.
- Place the pile of paper towels at the tail end of the inclined plane to stop the sphere from rolling off the table.
- Release the sphere from a point at distance D= 140cm from the tail end of the inclined plane.
- Determine the average time t taken by the sphere to cover this distance.
- Evaluate W = D/t.
- Calculate V= 2W.
- Repeat the procedure for four other values of D= 120cm 100cm, 80 cm and 60cm respectively.
- Tabulate your readings.
- Plot a graph with V on the vertical axis and t on the horizontal axis
- Determine the slope, s, of the graph.
- What is the significance of s?
- State two precautions taken to obtain accurate results.
(b)i. Write the equation for the velocity ratio of an inclined plane, giving the meaning of the symbols used.
ii. An object of mass 5kg is placed on a place inclined at an angle of 30° to the horizontal. Calculate the force on the object perpendicular to the plane when the object is at rest. (g =10ms\(^{-2}\)).
Explanation
| \(\frac{t_{1}}{s}\) | \(\frac{t_{2}}{s}\) | mean \(\frac{t}{s}\) | w=\(\frac{D}{t}\) | v=dw | |
| 140.0 | 4.50 | 5.00 | 4.750 | 29.474 | 58.948 |
| 120.0 | 4.20 | 4.40 | 4.300 | 27.907 | 55.814 |
| 100.0 | 4.00 | 3.80 | 3.980 | 25.641 | 51.282 |
| 80.0 | 3.80 | 3.50 | 3.650 | 21.918 | 43.836 |
| 60.00 | 3.20 | 3.40 | 3.300 | 18.182 | 36.364 |
Slope = \(\frac{70-32}{5.6-2.3} = \frac{38}{3.3}\)
= 11.51
X = Slope 's" signifies acceleration due to gravity.
Precaution; i
- ensured that l avoided parallax error when taking readings on the metre rule.
- ensured that i took care of zero when recording the period of oscillation.
- ensured that I took repeated readings in order to avoid random errors.
(b)i. Velocity ratio (VR) of an inclined plane
VR = \(\frac{1}{sin \theta}\), where \(\theta\) is the inclination to the horizontal.
ii. Mass of an object = 5kg
Angle of inclination = 30°
Acceleration due to gravity 10m/s\(^{2}\)
F = mgsin \(\theta\)
F = 5 x 10 x sin 30°
= 5 x 10 x 0.5
= 25N
