TEST OF PRACTICAL KNOWLEDGE QUESTION
You are provided with a wooden block to which a hook is fixed, a set of masses, spring balance, and other necessary materials. Using the diagram above as a guide, carry out the following instructions.
- Record the mass m\(_{0}\), indicated on the wooden block.
- Place the block on the table.
- Attach the spring balance to the hook.
- Pull the spring balance horizontally with a gradual increase in force until the block just starts to move Record the spring balance reading F.
- Repeat the procedure by placing in turn mass m=200, 400, 600, and 800g on top of the block. In each case, read and record the corresponding value of F.
- Evaluate M = m\(_{0}\) + m and R = \(\frac{m}{100}\) in each case
- Tabulate your readings.
- Plot a graph with F on the vertical axis and R on the horizontal axis
- Determine the slope, s, of the graph.
- State two precautions taken to ensure accurate results.
(b)i. Define coefficient of static friction.
ii. A block of wood of mass 0.5 kg is pulled horizontally on a table by a force of 2.5 N. Calculate the coefficient of static friction between the two surfaces.(g = 10ms\(^{-2}\))
(a) The friction experiment
The block just begins to move when the pulling force F equals the limiting (static) friction. Limiting friction is proportional to the normal reaction, and here the normal reaction equals the total weight Mg, where \(M = m_0 + m\). A specimen table (readings depend on your own apparatus) has this form:
| m (g) | M = m0 + m (g) | R = m/100 | F (N) |
|---|
| 0 | m0 | 0.0 | F0 |
| 200 | m0 + 200 | 2.0 | F1 |
| 400 | m0 + 400 | 4.0 | F2 |
| 600 | m0 + 600 | 6.0 | F3 |
| 800 | m0 + 800 | 8.0 | F4 |
Graph: plot F (vertical) against R (horizontal). A straight line of positive gradient is obtained.
Slope: \[ s = \frac{F_2 - F_1}{R_2 - R_1} \] read from two widely separated points on the best-fit line (unit: N per unit R).
Two precautions:
- Pull the spring balance strictly horizontally so the full weight acts as the normal reaction.
- Read F at the exact instant the block just begins to move, with the eye positioned to avoid parallax.
(b)(i) The coefficient of static friction is the ratio of the limiting (maximum) frictional force between two surfaces to the normal reaction between them, just before relative motion begins: \[ \mu_s = \frac{F}{R} \]
(b)(ii) Normal reaction \(R = mg = 0.5 \times 10 = 5\ \text{N}\). At the point of moving, friction equals the applied force, \(F = 2.5\ \text{N}\).
\[ \mu_s = \frac{F}{R} = \frac{2.5}{5} = 0.5 \]
The coefficient of static friction is 0.5.
(a) The friction experiment
The block just begins to move when the pulling force F equals the limiting (static) friction. Limiting friction is proportional to the normal reaction, and here the normal reaction equals the total weight Mg, where \(M = m_0 + m\). A specimen table (readings depend on your own apparatus) has this form:
| m (g) | M = m0 + m (g) | R = m/100 | F (N) |
|---|
| 0 | m0 | 0.0 | F0 |
| 200 | m0 + 200 | 2.0 | F1 |
| 400 | m0 + 400 | 4.0 | F2 |
| 600 | m0 + 600 | 6.0 | F3 |
| 800 | m0 + 800 | 8.0 | F4 |
Graph: plot F (vertical) against R (horizontal). A straight line of positive gradient is obtained.
Slope: \[ s = \frac{F_2 - F_1}{R_2 - R_1} \] read from two widely separated points on the best-fit line (unit: N per unit R).
Two precautions:
- Pull the spring balance strictly horizontally so the full weight acts as the normal reaction.
- Read F at the exact instant the block just begins to move, with the eye positioned to avoid parallax.
(b)(i) The coefficient of static friction is the ratio of the limiting (maximum) frictional force between two surfaces to the normal reaction between them, just before relative motion begins: \[ \mu_s = \frac{F}{R} \]
(b)(ii) Normal reaction \(R = mg = 0.5 \times 10 = 5\ \text{N}\). At the point of moving, friction equals the applied force, \(F = 2.5\ \text{N}\).
\[ \mu_s = \frac{F}{R} = \frac{2.5}{5} = 0.5 \]
The coefficient of static friction is 0.5.