WAEC SSCE - Physics - 2010 (Practical)
Swali 1 Ripoti
You are provided with a glass block, plane mirror, and optical pins.
- Place the glass block on a drawing sheet and trace its outline ABCD as shown in the diagram above.
- Remove the block, measure, and record the width W of the block.
- Draw a normal ON to DC at a point about one-quarter the length of DC.
- Draw a line making an angle \(i = 10^\circ\) with the normal.
- Replace the block on its outline and mount the plane mirror vertically behind the block such that it makes good contact with the face AB.
- Stick two pins \(P_{1}\) and \(P_{2}\) on the line MO.
- Looking through the face CD, stick two other pins \(P_{3}\) and \(P_{4}\) such that they appear to be in a straight line with the images of pins \(P_{1}\) and \(P_{2}\) seen through the block.
- Join \(P_{3}\) and \(P_{4}\) with a straight line and extend it to touch the face CD at O.
- Draw a perpendicular line from the midpoint of OO to meet AB at QD.
- Draw lines OQ, O'Q, and normal O'N' produced.
- Measure and record \(\theta\), e and d.
- Evaluate \(m = \sin e\) and \(n = \cos\left(\frac{\theta}{2}\right)\)
- Repeat the procedure for \(i = 20^\circ\), \(30^\circ\), \(40^\circ\) and \(50^\circ\).
- Tabulate your readings.
- Plot a graph with m on the vertical axis and n on the horizontal axis.
- Determine the slope, s, of the graph and evaluate \(q = 2Ws\).
- State two precautions taken to ensure accurate results. (Attach your traces to your answer booklet.)
(b)i. Explain the term refractive index and give a mathematical expression for it in terms of wavelength.
ii. State the conditions necessary for total internal reflection to occur for a given pair of media.
Refraction through a glass block with a plane mirror on face AB
The block is traced as ABCD, the width is measured as \(W = 5.0\ \text{cm}\). For each angle of incidence the emergent ray is fixed by no-parallax pins \(P_3\) and \(P_4\), and the angles \(\theta\) and \(e\) together with the lateral displacement \(d\) are measured directly from the traces. The full set of readings and the derived quantities \(m = \sin e\) and \(n = \cos\!\left(\dfrac{\theta}{2}\right)\) are tabulated below.
Table of readings
| \(i/^{\circ}\) | \(\theta/^{\circ}\) | \(e/^{\circ}\) | \(d/\text{cm}\) | \(m = \sin e\) | \(n = \cos\left(\frac{\theta}{2}\right)\) |
|---|---|---|---|---|---|
| 10 | 10.4 | 10.0 | 3.00 | 0.174 | 0.996 |
| 20 | 19.0 | 20.4 | 3.90 | 0.349 | 0.986 |
| 30 | 20.0 | 30.0 | 6.00 | 0.500 | 0.985 |
| 40 | 30.0 | 40.0 | 7.00 | 0.643 | 0.966 |
| 50 | 30.0 | 50.0 | 7.50 | 0.766 | 0.966 |
Sample evaluations: for \(i = 30^{\circ}\), \(m = \sin 30.0^{\circ} = 0.500\) and \(n = \cos\!\left(\tfrac{20.0^{\circ}}{2}\right) = \cos 10.0^{\circ} = 0.985\). For \(i = 50^{\circ}\), \(m = \sin 50.0^{\circ} = 0.766\) and \(n = \cos 15.0^{\circ} = 0.966\).
Graph of \(m\) against \(n\)
Slope of the graph
Two points on the line of best fit are \((n_1, m_1) = (0.996,\ 0.174)\) and \((n_2, m_2) = (0.966,\ 0.766)\).
\[ s = \frac{m_2 - m_1}{n_2 - n_1} = \frac{0.766 - 0.174}{0.966 - 0.996} = \frac{0.592}{-0.030} = -19.7 \]The slope is \(s = -19.7\) (magnitude \(19.7\)).
Evaluation of \(q = 2Ws\)
With \(W = 5.0\ \text{cm}\) and \(s = -19.7\):
\[ q = 2Ws = 2 \times 5.0\ \text{cm} \times (-19.7) = -197\ \text{cm} \]Hence \(|q| = 197\ \text{cm}\).
Two precautions
- The optical pins were fixed vertically, well separated, and the outline of the block was traced neatly with a sharp pencil so that the rays could be drawn accurately.
- Parallax error was avoided when reading the protractor and metre rule, and zero error on the metre rule was checked before measuring the width \(W\).
(b)(i) Refractive index
The refractive index is the ratio of the velocity of light in air (vacuum) to the velocity of light in a material medium as light waves pass from air into the medium. In terms of wavelength, since the frequency is unchanged on refraction,
\[ n = \frac{\lambda_{1}}{\lambda_{2}} \]where \(\lambda_{1}\) is the wavelength in air, \(\lambda_{2}\) is the wavelength in the material, and \(n\) is the refractive index of the material.
(b)(ii) Conditions for total internal reflection
- The light must be travelling from a denser medium to a less dense medium.
- The angle of incidence in the denser medium must be greater than the critical angle.
Maelezo ya Majibu
Refraction through a glass block with a plane mirror on face AB
The block is traced as ABCD, the width is measured as \(W = 5.0\ \text{cm}\). For each angle of incidence the emergent ray is fixed by no-parallax pins \(P_3\) and \(P_4\), and the angles \(\theta\) and \(e\) together with the lateral displacement \(d\) are measured directly from the traces. The full set of readings and the derived quantities \(m = \sin e\) and \(n = \cos\!\left(\dfrac{\theta}{2}\right)\) are tabulated below.
Table of readings
| \(i/^{\circ}\) | \(\theta/^{\circ}\) | \(e/^{\circ}\) | \(d/\text{cm}\) | \(m = \sin e\) | \(n = \cos\left(\frac{\theta}{2}\right)\) |
|---|---|---|---|---|---|
| 10 | 10.4 | 10.0 | 3.00 | 0.174 | 0.996 |
| 20 | 19.0 | 20.4 | 3.90 | 0.349 | 0.986 |
| 30 | 20.0 | 30.0 | 6.00 | 0.500 | 0.985 |
| 40 | 30.0 | 40.0 | 7.00 | 0.643 | 0.966 |
| 50 | 30.0 | 50.0 | 7.50 | 0.766 | 0.966 |
Sample evaluations: for \(i = 30^{\circ}\), \(m = \sin 30.0^{\circ} = 0.500\) and \(n = \cos\!\left(\tfrac{20.0^{\circ}}{2}\right) = \cos 10.0^{\circ} = 0.985\). For \(i = 50^{\circ}\), \(m = \sin 50.0^{\circ} = 0.766\) and \(n = \cos 15.0^{\circ} = 0.966\).
Graph of \(m\) against \(n\)
Slope of the graph
Two points on the line of best fit are \((n_1, m_1) = (0.996,\ 0.174)\) and \((n_2, m_2) = (0.966,\ 0.766)\).
\[ s = \frac{m_2 - m_1}{n_2 - n_1} = \frac{0.766 - 0.174}{0.966 - 0.996} = \frac{0.592}{-0.030} = -19.7 \]The slope is \(s = -19.7\) (magnitude \(19.7\)).
Evaluation of \(q = 2Ws\)
With \(W = 5.0\ \text{cm}\) and \(s = -19.7\):
\[ q = 2Ws = 2 \times 5.0\ \text{cm} \times (-19.7) = -197\ \text{cm} \]Hence \(|q| = 197\ \text{cm}\).
Two precautions
- The optical pins were fixed vertically, well separated, and the outline of the block was traced neatly with a sharp pencil so that the rays could be drawn accurately.
- Parallax error was avoided when reading the protractor and metre rule, and zero error on the metre rule was checked before measuring the width \(W\).
(b)(i) Refractive index
The refractive index is the ratio of the velocity of light in air (vacuum) to the velocity of light in a material medium as light waves pass from air into the medium. In terms of wavelength, since the frequency is unchanged on refraction,
\[ n = \frac{\lambda_{1}}{\lambda_{2}} \]where \(\lambda_{1}\) is the wavelength in air, \(\lambda_{2}\) is the wavelength in the material, and \(n\) is the refractive index of the material.
(b)(ii) Conditions for total internal reflection
- The light must be travelling from a denser medium to a less dense medium.
- The angle of incidence in the denser medium must be greater than the critical angle.
Swali 2 Ripoti
You are provided with a voltmeter V, a chemical cell/ battery E; two standard resistors R, and R a potentiometer a key K a jockey, and other necessary materials.
- Set up a circuit as shown in the diagram above.
- Close the key K.
- Make contact with the potentiometer wire AB using the jockey at a point C such that AC = x = 20cm
- Read and record the voltmeter reading
- Evaluate x\(^{-1}\) and v\(^{-1}\)
- Repeat the procedure for other values of x= 30, 40, 50, 60 and 80cm.
- Tabulate your readings.
- Plot a graph with V\(^{-1}\) on the vertical axis and x\(^{-1}\) on the horizontal axis, starting both axes from the origin (0, 0).
- Determine the:
(a) slope, s, of the graph;
(b) intercept, c, on the vertical axis. - State two precautions taken to ensure accurate results.
(b)i. State the two devices in which ohm's law does not apply.
ii. A current of 1 A is supplied to two resistors of resistance 2\(\Omega\) and 3\(\Omega\) connected in parallel. Calculate the current in each resistor.
Circuit
The circuit is connected as shown, with the cell E and key K driving the potentiometer wire AB, and the voltmeter V connected across the length AC = x.
Table of readings
With the key K closed, the jockey is placed on the wire at C so that AC = x, and the voltmeter reading V is taken for each length. The reciprocals \(x^{-1}\) and \(V^{-1}\) are then evaluated.
| \(x\,/\,\text{cm}\) | \(V\,/\,\text{V}\) | \(x^{-1}\,/\,\text{cm}^{-1}\) | \(V^{-1}\,/\,\text{V}^{-1}\) |
|---|---|---|---|
| 20 | 0.15 | 0.050 | 6.667 |
| 30 | 0.20 | 0.033 | 5.000 |
| 40 | 0.30 | 0.025 | 3.333 |
| 50 | 0.40 | 0.020 | 2.500 |
| 60 | 0.50 | 0.017 | 2.000 |
| 80 | 0.60 | 0.013 | 1.667 |
Graph of \(V^{-1}\) against \(x^{-1}\)
The graph of \(V^{-1}\) (vertical axis) against \(x^{-1}\) (horizontal axis) is a straight line passing through the origin.
(a) Slope of the graph
Taking two widely separated points on the line of best fit, \((0.050,\;6.667)\) and \((0.013,\;1.667)\):
\[ s = \frac{V_2^{-1}-V_1^{-1}}{x_2^{-1}-x_1^{-1}} = \frac{6.667-1.667}{0.050-0.013} = \frac{5.000}{0.037} = 135.1\ \text{cm}\,\text{V}^{-1} \](b) Intercept on the vertical axis
The line of best fit passes through the origin, so the intercept on the vertical axis is
\[ c = 0 \]Two precautions
- Tight, clean connections at all terminals were ensured before taking readings.
- The key K was opened between successive readings so that the wire did not heat up.
(b)(i) Two devices in which Ohm's law does not apply
- A semiconductor diode (rectifier).
- A thermionic (vacuum) diode/valve.
(b)(ii) Current in each parallel resistor
A total current of \(1\ \text{A}\) is supplied to \(2\ \Omega\) and \(3\ \Omega\) in parallel. The current divides in the inverse ratio of the resistances:
\[ I_{2\Omega} = 1 \times \frac{3}{2+3} = \frac{3}{5} = 0.6\ \text{A} \] \[ I_{3\Omega} = 1 \times \frac{2}{2+3} = \frac{2}{5} = 0.4\ \text{A} \]Therefore \(0.6\ \text{A}\) flows through the \(2\ \Omega\) resistor and \(0.4\ \text{A}\) through the \(3\ \Omega\) resistor.
Maelezo ya Majibu
Circuit
The circuit is connected as shown, with the cell E and key K driving the potentiometer wire AB, and the voltmeter V connected across the length AC = x.
Table of readings
With the key K closed, the jockey is placed on the wire at C so that AC = x, and the voltmeter reading V is taken for each length. The reciprocals \(x^{-1}\) and \(V^{-1}\) are then evaluated.
| \(x\,/\,\text{cm}\) | \(V\,/\,\text{V}\) | \(x^{-1}\,/\,\text{cm}^{-1}\) | \(V^{-1}\,/\,\text{V}^{-1}\) |
|---|---|---|---|
| 20 | 0.15 | 0.050 | 6.667 |
| 30 | 0.20 | 0.033 | 5.000 |
| 40 | 0.30 | 0.025 | 3.333 |
| 50 | 0.40 | 0.020 | 2.500 |
| 60 | 0.50 | 0.017 | 2.000 |
| 80 | 0.60 | 0.013 | 1.667 |
Graph of \(V^{-1}\) against \(x^{-1}\)
The graph of \(V^{-1}\) (vertical axis) against \(x^{-1}\) (horizontal axis) is a straight line passing through the origin.
(a) Slope of the graph
Taking two widely separated points on the line of best fit, \((0.050,\;6.667)\) and \((0.013,\;1.667)\):
\[ s = \frac{V_2^{-1}-V_1^{-1}}{x_2^{-1}-x_1^{-1}} = \frac{6.667-1.667}{0.050-0.013} = \frac{5.000}{0.037} = 135.1\ \text{cm}\,\text{V}^{-1} \](b) Intercept on the vertical axis
The line of best fit passes through the origin, so the intercept on the vertical axis is
\[ c = 0 \]Two precautions
- Tight, clean connections at all terminals were ensured before taking readings.
- The key K was opened between successive readings so that the wire did not heat up.
(b)(i) Two devices in which Ohm's law does not apply
- A semiconductor diode (rectifier).
- A thermionic (vacuum) diode/valve.
(b)(ii) Current in each parallel resistor
A total current of \(1\ \text{A}\) is supplied to \(2\ \Omega\) and \(3\ \Omega\) in parallel. The current divides in the inverse ratio of the resistances:
\[ I_{2\Omega} = 1 \times \frac{3}{2+3} = \frac{3}{5} = 0.6\ \text{A} \] \[ I_{3\Omega} = 1 \times \frac{2}{2+3} = \frac{2}{5} = 0.4\ \text{A} \]Therefore \(0.6\ \text{A}\) flows through the \(2\ \Omega\) resistor and \(0.4\ \text{A}\) through the \(3\ \Omega\) resistor.
Swali 3 Ripoti
You are provided with three retort stands, a pendulum bob, a drawing board, a stopwatch, and other necessary apparatus. Using the diagram above as a guide, carry out the following instructions.
- Fix the drawing paper on the drawing board and hold the board with two clamps such that it is vertical.
- Suspend the pendulum bob such that it hangs freely in front of the drawing paper.
- Draw a line RP representing the rest position of the pendulum string and mark the position P of the centre of the pendulum bob at rest.
- Displace the pendulum bob to one side in a plane parallel to the drawing board.
- Mark the new position P\(^{1}\) of the centre of the bob.
- Measure and record the perpendicular distance, d of P\(^{1}\) from the line RP
- Evaluate and record d\(^{2}\).
- Measure and record the vertical height h of P\(^{1}\) above P.
- Evaluate G =\(\frac{d^{2}}{h}\)
- Repeat the procedure for four other positions of P\(^{1}\).
- Tabulate your readings.
- Remove the drawing board so that the pendulum bo can swing freely.
- Set the pendulum bob oscillating through a small bob amplitude and determine the time, t for 20 oscillations.
- Determine and record the period, T.
- Plot a graph with G on the vertical axis and h on the horizontal axis, starting both axes from the origin (0,0).
- Determine the intercept I on the horizontal axis.
- Evaluate A = \(\frac{1}{19.7T^{2}}\)
- State two precautions taken to obtain accuratee results. (Attach your drawing paper to your answer booklet.)
(b)i. Distinguish between the period and frequency of oscillation of a simple pendulum.
ii. Differentiate between oscillatory and rotational motions.
Test of Practical Knowledge: Simple Pendulum
The drawing paper is fixed to the vertical board. The line RP is drawn as the rest position of the string, with P marked at the centre of the bob at rest. When the bob is displaced to a new position P¹, the perpendicular distance d of P¹ from the line RP and the vertical height h of P¹ above P are measured as shown below.
For each of the five positions the readings are taken and \(d^{2}\) and \(G=\dfrac{d^{2}}{h}\) are evaluated.
Table of readings (RP = 20 cm)
| S/N | d / cm | d² / cm² | h / cm | G = d²/h / cm |
|---|---|---|---|---|
| P₁ | 3.30 | 10.89 | 3.00 | 3.63 |
| P₂ | 5.50 | 30.25 | 2.80 | 10.80 |
| P₃ | 7.60 | 57.76 | 2.60 | 22.22 |
| P₄ | 9.60 | 92.16 | 2.40 | 38.40 |
| P₅ | 10.50 | 110.25 | 2.20 | 50.11 |
Sample evaluations: \(G_{1}=\dfrac{10.89}{3.00}=3.63\,\text{cm}\), and \(G_{5}=\dfrac{110.25}{2.20}=50.11\,\text{cm}\).
Oscillations
With the board removed, the bob is set oscillating through a small amplitude. Time for 20 oscillations, \(t = 21.76\,\text{s}\), \(n = 20\).
\[T=\frac{t}{n}=\frac{21.76}{20}=1.088\,\text{s}\]Graph of G against h
G is plotted on the vertical axis against h on the horizontal axis, both axes starting from the origin.
The best-fit line cuts the horizontal (h) axis where \(G=0\). Reading from the graph, the intercept on the horizontal axis is
\[I \approx 3.0\,\text{cm}\]Evaluation of A
\[A=\frac{1}{19.7\,T^{2}}=\frac{1}{19.7\times(1.088)^{2}}=\frac{1}{19.7\times1.1837}=\frac{1}{23.32}\]\[A \approx 0.0429\,\text{s}^{-2}\]Precautions (any two)
- Parallax error was avoided by viewing the metre rule and stopwatch scales squarely (line of sight perpendicular to the scale).
- Conical (elliptical) oscillation was avoided by releasing the bob so that it swung in a single vertical plane through a small amplitude.
(b)(i) Period vs Frequency
| Period (T) | Frequency (f) |
|---|---|
| The time taken to complete one complete oscillation (one to-and-fro cycle). Its SI unit is the second (s). | The number of complete oscillations made in one second. Its SI unit is the hertz (Hz). |
They are reciprocals: \(f=\dfrac{1}{T}\).
(b)(ii) Oscillatory vs Rotational motion
| Oscillatory motion | Rotational motion |
|---|---|
| A body moves to and fro (back and forth) about a fixed mean position along a path, repeating the motion at regular intervals. Examples: a swinging pendulum, a vibrating string, a loaded test tube bobbing in water, a vibrating tuning fork. | A body turns (spins) about a fixed axis passing through or near the body, every particle moving in a circle about that axis. Examples: the blades of a fan in motion, the Earth spinning about its axis, a spinning wheel. |
Maelezo ya Majibu
Test of Practical Knowledge: Simple Pendulum
The drawing paper is fixed to the vertical board. The line RP is drawn as the rest position of the string, with P marked at the centre of the bob at rest. When the bob is displaced to a new position P¹, the perpendicular distance d of P¹ from the line RP and the vertical height h of P¹ above P are measured as shown below.
For each of the five positions the readings are taken and \(d^{2}\) and \(G=\dfrac{d^{2}}{h}\) are evaluated.
Table of readings (RP = 20 cm)
| S/N | d / cm | d² / cm² | h / cm | G = d²/h / cm |
|---|---|---|---|---|
| P₁ | 3.30 | 10.89 | 3.00 | 3.63 |
| P₂ | 5.50 | 30.25 | 2.80 | 10.80 |
| P₃ | 7.60 | 57.76 | 2.60 | 22.22 |
| P₄ | 9.60 | 92.16 | 2.40 | 38.40 |
| P₅ | 10.50 | 110.25 | 2.20 | 50.11 |
Sample evaluations: \(G_{1}=\dfrac{10.89}{3.00}=3.63\,\text{cm}\), and \(G_{5}=\dfrac{110.25}{2.20}=50.11\,\text{cm}\).
Oscillations
With the board removed, the bob is set oscillating through a small amplitude. Time for 20 oscillations, \(t = 21.76\,\text{s}\), \(n = 20\).
\[T=\frac{t}{n}=\frac{21.76}{20}=1.088\,\text{s}\]Graph of G against h
G is plotted on the vertical axis against h on the horizontal axis, both axes starting from the origin.
The best-fit line cuts the horizontal (h) axis where \(G=0\). Reading from the graph, the intercept on the horizontal axis is
\[I \approx 3.0\,\text{cm}\]Evaluation of A
\[A=\frac{1}{19.7\,T^{2}}=\frac{1}{19.7\times(1.088)^{2}}=\frac{1}{19.7\times1.1837}=\frac{1}{23.32}\]\[A \approx 0.0429\,\text{s}^{-2}\]Precautions (any two)
- Parallax error was avoided by viewing the metre rule and stopwatch scales squarely (line of sight perpendicular to the scale).
- Conical (elliptical) oscillation was avoided by releasing the bob so that it swung in a single vertical plane through a small amplitude.
(b)(i) Period vs Frequency
| Period (T) | Frequency (f) |
|---|---|
| The time taken to complete one complete oscillation (one to-and-fro cycle). Its SI unit is the second (s). | The number of complete oscillations made in one second. Its SI unit is the hertz (Hz). |
They are reciprocals: \(f=\dfrac{1}{T}\).
(b)(ii) Oscillatory vs Rotational motion
| Oscillatory motion | Rotational motion |
|---|---|
| A body moves to and fro (back and forth) about a fixed mean position along a path, repeating the motion at regular intervals. Examples: a swinging pendulum, a vibrating string, a loaded test tube bobbing in water, a vibrating tuning fork. | A body turns (spins) about a fixed axis passing through or near the body, every particle moving in a circle about that axis. Examples: the blades of a fan in motion, the Earth spinning about its axis, a spinning wheel. |
