WAEC SSCE - Physics - 1997 (Essay)
Question 1 Report
(a) Sketch the form of the magnetic flux pattern due to a current flowing
(i) in a long solenoid
(ii) through two long straight parallel wires when the directions of the current are opposite. (Neglect the earth's magnetic field).
(b) Draw a labelled diagram of an electric bell and explain how it works
(c) An electric bell takes a current of 0.2A groin a battery of two dry cells connected in series. Each cell has an e.m.f. of 1.5V and an internal resistance of 1.0\(\Omega\).
(i) Calculate the effective resistance of the bell
(ii) What current would the bells take in the cells were arranged in parallel?
(a) Magnetic flux patterns
(i) Long solenoid
The magnetic field is strong and nearly uniform inside the solenoid. Its pattern is like that of a bar magnet: field lines emerge from the north pole and return to the south pole outside the solenoid.
(ii) Two long parallel wires carrying currents in opposite directions
The magnetic fields are circular about each wire. In the region between the wires, the fields are in the same direction and reinforce; outside the wires, they oppose.
(b) Electric bell
When the switch is closed, current flows through the coils and magnetises the soft-iron cores of the electromagnet. The electromagnet attracts the soft-iron armature, causing the hammer to strike the gong.
As the armature moves towards the electromagnet, it moves away from the contact screw and breaks the circuit. The electromagnet then loses its magnetism. The spring pulls the armature back, restoring contact with the screw and completing the circuit again. This rapid make-and-break action continues while the switch is pressed, making the hammer strike the gong repeatedly.
(c) Calculations
For two cells in series:
\[E=2(1.5)=3.0\text{ V},\qquad r=2(1.0)=2.0\ \Omega\]
(i) If \(R\) is the effective resistance of the bell,
\[I=\frac{E}{R+r}\]
\[0.2=\frac{3.0}{R+2.0}\]
\[R+2.0=\frac{3.0}{0.2}=15\]
\[\boxed{R=13\ \Omega}\]
(ii) With the cells in parallel,
\[E=1.5\text{ V},\qquad r=\frac{1.0}{2}=0.5\ \Omega\]
\[I=\frac{E}{R+r}=\frac{1.5}{13+0.5}=\frac{1.5}{13.5}=0.111\ldots\text{ A}\]
\[\boxed{I\approx 0.11\text{ A}}\]
Answer Details
(a) Magnetic flux patterns
(i) Long solenoid
The magnetic field is strong and nearly uniform inside the solenoid. Its pattern is like that of a bar magnet: field lines emerge from the north pole and return to the south pole outside the solenoid.
(ii) Two long parallel wires carrying currents in opposite directions
The magnetic fields are circular about each wire. In the region between the wires, the fields are in the same direction and reinforce; outside the wires, they oppose.
(b) Electric bell
When the switch is closed, current flows through the coils and magnetises the soft-iron cores of the electromagnet. The electromagnet attracts the soft-iron armature, causing the hammer to strike the gong.
As the armature moves towards the electromagnet, it moves away from the contact screw and breaks the circuit. The electromagnet then loses its magnetism. The spring pulls the armature back, restoring contact with the screw and completing the circuit again. This rapid make-and-break action continues while the switch is pressed, making the hammer strike the gong repeatedly.
(c) Calculations
For two cells in series:
\[E=2(1.5)=3.0\text{ V},\qquad r=2(1.0)=2.0\ \Omega\]
(i) If \(R\) is the effective resistance of the bell,
\[I=\frac{E}{R+r}\]
\[0.2=\frac{3.0}{R+2.0}\]
\[R+2.0=\frac{3.0}{0.2}=15\]
\[\boxed{R=13\ \Omega}\]
(ii) With the cells in parallel,
\[E=1.5\text{ V},\qquad r=\frac{1.0}{2}=0.5\ \Omega\]
\[I=\frac{E}{R+r}=\frac{1.5}{13+0.5}=\frac{1.5}{13.5}=0.111\ldots\text{ A}\]
\[\boxed{I\approx 0.11\text{ A}}\]
Question 2 Report
(a) Explain the term resonance and give two examples
(b)(i) Describe, with the aid of a labelled diagram, an experiment to show how the frequency of the note emitted by a vibrating string depends on the length of the string.
(ii) State two precautions necessary to obtain an accurate result.
(c) A sonometer wire is plucked and it vibrates emitting a fundamental note. State the effect on the frequency of the note if the
(i) tension in the wire were made nine times as large with no change in the length of the wire;
(ii) length of the wire were doubled with no change in the tension.
(a) Resonance
Resonance is the phenomenon in which a body is forced to vibrate at its natural frequency by a periodic force of the same frequency, producing vibrations of maximum amplitude.
Examples are:
- tuning a radio receiver to a particular station;
- a diver's board vibrating strongly when it is periodically forced at its natural frequency.
(b)(i) Experiment to investigate the effect of length on the frequency of a vibrating string
A sonometer wire is stretched over two bridges, A and B, on a hollow wooden box. The wire passes over a smooth pulley and is kept taut by a constant load, W. Bridge B is movable, so that the vibrating length, L, between the bridges can be altered. A light paper rider is placed at the middle of the vibrating length.
A tuning fork of known frequency is struck gently with a rubber bung and its stem is placed on the sonometer box. The movable bridge is adjusted until resonance occurs. Resonance is indicated when the paper rider is thrown off the wire or when the sound becomes loud. The resonating length, L, is measured.
The procedure is repeated with tuning forks of different known frequencies while the load, and hence the tension, is kept constant. The readings may be recorded as follows:
| Frequency, f (Hz) | Resonating length, L (m) | 1/L (m−1) |
|---|---|---|
| 100 | 1.600 | 0.625 |
| 128 | 1.250 | 0.800 |
| 160 | 1.000 | 1.000 |
| 200 | 0.800 | 1.250 |
| 256 | 0.625 | 1.600 |
A graph of frequency, f, against reciprocal length, 1/L, is plotted.
The straight line through the origin shows that, for constant tension and the same wire,
\[f \propto \frac{1}{L}.\]
(b)(ii) Precautions
- Keep the tension constant throughout by using the same load and a smooth pulley.
- Strike each tuning fork gently on a rubber bung and measure the distance between the inner edges of the bridges without parallax.
(c) For the fundamental mode of a stretched string,
\[f=\frac{1}{2L}\sqrt{\frac{T}{\mu}},\]
where \(T\) is the tension and \(\mu\) is the mass per unit length of the wire.
(i) If \(T\) becomes \(9T\),
\[f'\propto\sqrt{9T}=3\sqrt{T}.\]
Therefore, the fundamental frequency is tripled.
(ii) If the length becomes \(2L\),
\[f'=\frac{1}{2L}f.\]
Therefore, the fundamental frequency is halved.
Answer Details
(a) Resonance
Resonance is the phenomenon in which a body is forced to vibrate at its natural frequency by a periodic force of the same frequency, producing vibrations of maximum amplitude.
Examples are:
- tuning a radio receiver to a particular station;
- a diver's board vibrating strongly when it is periodically forced at its natural frequency.
(b)(i) Experiment to investigate the effect of length on the frequency of a vibrating string
A sonometer wire is stretched over two bridges, A and B, on a hollow wooden box. The wire passes over a smooth pulley and is kept taut by a constant load, W. Bridge B is movable, so that the vibrating length, L, between the bridges can be altered. A light paper rider is placed at the middle of the vibrating length.
A tuning fork of known frequency is struck gently with a rubber bung and its stem is placed on the sonometer box. The movable bridge is adjusted until resonance occurs. Resonance is indicated when the paper rider is thrown off the wire or when the sound becomes loud. The resonating length, L, is measured.
The procedure is repeated with tuning forks of different known frequencies while the load, and hence the tension, is kept constant. The readings may be recorded as follows:
| Frequency, f (Hz) | Resonating length, L (m) | 1/L (m−1) |
|---|---|---|
| 100 | 1.600 | 0.625 |
| 128 | 1.250 | 0.800 |
| 160 | 1.000 | 1.000 |
| 200 | 0.800 | 1.250 |
| 256 | 0.625 | 1.600 |
A graph of frequency, f, against reciprocal length, 1/L, is plotted.
The straight line through the origin shows that, for constant tension and the same wire,
\[f \propto \frac{1}{L}.\]
(b)(ii) Precautions
- Keep the tension constant throughout by using the same load and a smooth pulley.
- Strike each tuning fork gently on a rubber bung and measure the distance between the inner edges of the bridges without parallax.
(c) For the fundamental mode of a stretched string,
\[f=\frac{1}{2L}\sqrt{\frac{T}{\mu}},\]
where \(T\) is the tension and \(\mu\) is the mass per unit length of the wire.
(i) If \(T\) becomes \(9T\),
\[f'\propto\sqrt{9T}=3\sqrt{T}.\]
Therefore, the fundamental frequency is tripled.
(ii) If the length becomes \(2L\),
\[f'=\frac{1}{2L}f.\]
Therefore, the fundamental frequency is halved.
Question 3 Report
(a) Explain the term work
(b) Draw a diagram of a pulley system with a velocity ratio of 5.
(c) A man pulls up a box of mass 70kg using an inclined plane of effective length 5m onto a platform 2.5m high at uniform speed. If the frictional force between the box and the plane is 100N, draw the diagram of all the forces acting on the box when in motion and calculate the
(i) minimum effort applied in pulling up the box
(ii) velocity ratio of the plane
(iii) mechanical advantage of the plane
(iv) efficiency of the plane
(v) energy lost in the system
(vi) work output of the man
(vii) total power developed by the man given that the time taken to raise the box onto the platform is 50s. (g = 10ms\(^{-2}\)).
(a) Work
Work is done when a force moves a body through a distance in the direction of the force. Thus,
\[W=Fs\]
where \(F\) is the force and \(s\) is the displacement in its direction. Work is a scalar quantity and its SI unit is the joule (J).
(b) Pulley system of velocity ratio 5
There are five rope sections supporting the movable block. Hence,
\[V.R.=5\]
(c) Inclined plane
The weight of the box is
\[W=mg=70\times10=700\ \text{N}.\]
The plane makes an angle \(\theta\) with the horizontal such that
\[\sin\theta=\frac{h}{L}=\frac{2.5}{5}=0.5,\qquad \theta=30^\circ.\]
The force diagram for the box moving up the plane is shown below.
(i) Minimum effort applied
Since the box moves at uniform speed, the effort balances the component of weight down the plane and the frictional force:
\[E=mg\sin\theta+F=700(0.5)+100=450\ \text{N}.\]
(ii) Velocity ratio of the plane
\[V.R.=\frac{\text{distance moved by effort}}{\text{distance moved by load}}=\frac{L}{h}=\frac{5}{2.5}=2.\]
(iii) Mechanical advantage of the plane
\[M.A.=\frac{\text{Load}}{\text{Effort}}=\frac{700}{450}=1.56.\]
(iv) Efficiency of the plane
\[\eta=\frac{M.A.}{V.R.}\times100\%=\frac{1.56}{2}\times100\%=77.8\%\approx78\%.\]
(v) Energy lost in the system
Energy is lost in overcoming friction:
\[E_{\text{lost}}=F\times L=100\times5=500\ \text{J}.\]
(vi) Work output
\[W_{\text{output}}=mgh=70\times10\times2.5=1750\ \text{J}.\]
(vii) Total power developed by the man
The work input is
\[W_{\text{input}}=E\times L=450\times5=2250\ \text{J}.\]
Therefore,
\[P=\frac{W_{\text{input}}}{t}=\frac{2250}{50}=45\ \text{W}.\]
Answer Details
(a) Work
Work is done when a force moves a body through a distance in the direction of the force. Thus,
\[W=Fs\]
where \(F\) is the force and \(s\) is the displacement in its direction. Work is a scalar quantity and its SI unit is the joule (J).
(b) Pulley system of velocity ratio 5
There are five rope sections supporting the movable block. Hence,
\[V.R.=5\]
(c) Inclined plane
The weight of the box is
\[W=mg=70\times10=700\ \text{N}.\]
The plane makes an angle \(\theta\) with the horizontal such that
\[\sin\theta=\frac{h}{L}=\frac{2.5}{5}=0.5,\qquad \theta=30^\circ.\]
The force diagram for the box moving up the plane is shown below.
(i) Minimum effort applied
Since the box moves at uniform speed, the effort balances the component of weight down the plane and the frictional force:
\[E=mg\sin\theta+F=700(0.5)+100=450\ \text{N}.\]
(ii) Velocity ratio of the plane
\[V.R.=\frac{\text{distance moved by effort}}{\text{distance moved by load}}=\frac{L}{h}=\frac{5}{2.5}=2.\]
(iii) Mechanical advantage of the plane
\[M.A.=\frac{\text{Load}}{\text{Effort}}=\frac{700}{450}=1.56.\]
(iv) Efficiency of the plane
\[\eta=\frac{M.A.}{V.R.}\times100\%=\frac{1.56}{2}\times100\%=77.8\%\approx78\%.\]
(v) Energy lost in the system
Energy is lost in overcoming friction:
\[E_{\text{lost}}=F\times L=100\times5=500\ \text{J}.\]
(vi) Work output
\[W_{\text{output}}=mgh=70\times10\times2.5=1750\ \text{J}.\]
(vii) Total power developed by the man
The work input is
\[W_{\text{input}}=E\times L=450\times5=2250\ \text{J}.\]
Therefore,
\[P=\frac{W_{\text{input}}}{t}=\frac{2250}{50}=45\ \text{W}.\]
Question 4 Report
(a) Briefly explain what would happen to a stable element if it is bombarded by \(\alpha\)-particles
(b) Explain how the bombardment of Uranium with neutrons could lead to nuclear fission chain reaction and hence nuclear explosion.
(c) State three characteristics of nuclear activity
(d) State three applications of atomic energy
(e) State two postulates of Bohr's model of the atom and two limitations of such a model
(a) A stable element bombarded by alpha-particles
The alpha-particle (a helium nucleus) may penetrate the nucleus of the stable atom and be captured, forming a new, heavier and usually unstable (radioactive) nucleus, often with the emission of another particle such as a proton or a neutron. This is artificial transmutation: the target element is changed into a different element (a new nuclide), which may then be radioactive. (For example, alpha bombardment of nitrogen produces oxygen and a proton.)
(b) Nuclear fission chain reaction
When a slow (thermal) neutron strikes a nucleus of uranium-235, the nucleus captures it, becomes highly unstable and splits (fissions) into two lighter nuclei, releasing a large amount of energy. Crucially, each fission also releases two or three fresh neutrons. If enough fissile material is present (a critical mass), these new neutrons go on to split further uranium nuclei, each releasing yet more neutrons, so the number of fissions multiplies rapidly. This self-sustaining, ever-growing sequence is a chain reaction. If it is uncontrolled, an enormous amount of energy is released in a very short time, producing a nuclear explosion. (In a reactor the reaction is controlled by absorbing surplus neutrons.)
(c) Three characteristics of nuclear activity
- It is spontaneous and random, and unaffected by temperature, pressure or chemical combination.
- It releases very large amounts of energy compared with chemical reactions.
- It involves changes within the nucleus, producing new elements and emitting radiation (\(\alpha\), \(\beta\), \(\gamma\)).
(d) Three applications of atomic (nuclear) energy
- Generation of electricity in nuclear power stations.
- Use of radioisotopes in medicine (diagnosis, treatment of cancer, sterilization).
- Use as tracers in agriculture/industry, in carbon dating, and in propulsion (nuclear submarines).
(e) Bohr's model
Two postulates:
- An electron moves round the nucleus only in certain allowed circular orbits (stationary states) in which it does not radiate energy; each orbit has a fixed energy.
- Energy is emitted or absorbed only when an electron jumps from one allowed orbit to another, the photon energy being \(hf = E_2 - E_1\).
Two limitations:
- It successfully explains only the hydrogen (one-electron) atom and fails for atoms with more than one electron.
- It cannot account for the fine structure (splitting) of spectral lines or their relative intensities, and it violates later quantum ideas (the uncertainty principle).
Answer Details
(a) A stable element bombarded by alpha-particles
The alpha-particle (a helium nucleus) may penetrate the nucleus of the stable atom and be captured, forming a new, heavier and usually unstable (radioactive) nucleus, often with the emission of another particle such as a proton or a neutron. This is artificial transmutation: the target element is changed into a different element (a new nuclide), which may then be radioactive. (For example, alpha bombardment of nitrogen produces oxygen and a proton.)
(b) Nuclear fission chain reaction
When a slow (thermal) neutron strikes a nucleus of uranium-235, the nucleus captures it, becomes highly unstable and splits (fissions) into two lighter nuclei, releasing a large amount of energy. Crucially, each fission also releases two or three fresh neutrons. If enough fissile material is present (a critical mass), these new neutrons go on to split further uranium nuclei, each releasing yet more neutrons, so the number of fissions multiplies rapidly. This self-sustaining, ever-growing sequence is a chain reaction. If it is uncontrolled, an enormous amount of energy is released in a very short time, producing a nuclear explosion. (In a reactor the reaction is controlled by absorbing surplus neutrons.)
(c) Three characteristics of nuclear activity
- It is spontaneous and random, and unaffected by temperature, pressure or chemical combination.
- It releases very large amounts of energy compared with chemical reactions.
- It involves changes within the nucleus, producing new elements and emitting radiation (\(\alpha\), \(\beta\), \(\gamma\)).
(d) Three applications of atomic (nuclear) energy
- Generation of electricity in nuclear power stations.
- Use of radioisotopes in medicine (diagnosis, treatment of cancer, sterilization).
- Use as tracers in agriculture/industry, in carbon dating, and in propulsion (nuclear submarines).
(e) Bohr's model
Two postulates:
- An electron moves round the nucleus only in certain allowed circular orbits (stationary states) in which it does not radiate energy; each orbit has a fixed energy.
- Energy is emitted or absorbed only when an electron jumps from one allowed orbit to another, the photon energy being \(hf = E_2 - E_1\).
Two limitations:
- It successfully explains only the hydrogen (one-electron) atom and fails for atoms with more than one electron.
- It cannot account for the fine structure (splitting) of spectral lines or their relative intensities, and it violates later quantum ideas (the uncertainty principle).
