Measure and record the emf, V\(_{o}\) of the cell provided.
Connect a circuit as shown in the diagram above.
With the key, K closed vary the rheostat, Rh to obtain a current 1 = 0.20A. Read and record the corresponding value of the potential difference, V on the voltmeter.
Evaluate 1\(^{-1}\) and V\(^{-1}\).
Repeat the procedure for four other values of l = 0.25, 0.30, 0.35 and 0.40 A. Tabulate your readings.
Plot a graph V\(^{-1}\) on the vertical axis against 1\(^{-1}\) on the horizontal axis.
Determine the slope, s, of the graph
Evaluate s\(^{-1}\).
State two precautions taken to ensure accurate results.
(b)i. Explain Ohmic conductor:
ii. Explain resistivity of the material of a wire.
(a) Measurement and tabulation
The emf of the cell was measured with the voltmeter when the circuit was open:
\[
V_o = 3.0\ \text{V}
\]
The circuit was connected as shown, with the ammeter in series and the voltmeter connected across the resistor/load. The key was closed briefly and the rheostat adjusted to obtain the stated current values. The corresponding voltmeter readings were recorded.
The emf of the cell was measured with the voltmeter when the circuit was open:
\[
V_o = 3.0\ \text{V}
\]
The circuit was connected as shown, with the ammeter in series and the voltmeter connected across the resistor/load. The key was closed briefly and the rheostat adjusted to obtain the stated current values. The corresponding voltmeter readings were recorded.
Determine and record the approximate focal length f\(_{o}\) of the concave mirror provided.
Arrange the ray box, the mirror, and the screen as shown in the diagram above.
Adjust the ray box to a distance b = 20.0cm from the mirror.
Adjust the position of the screen until a sharp image of the cross wire of the ray box is formed on it.
Measure and record the distance, a, of the screen from the mirror. Evaluate \(\frac{a}{a}\) =1.
Repeat the procedure for four other values of b = 25.0, 30.0, 35.0, and 40.0cm. Tabulate your readings.
Plot a graph of l on the vertical axis against a on the horizontal axis.
Determine the slope,.s, of the graph. Evaluate S\(^{-1}\).
State two precautions taken to ensure accurate results.
(b)i. An object is placed at a distance of 10cm in front of a concave mirror of focal length of 15cm. Determine the characteristics of the image formed.
ii. Briefly describe how you obtained f\(_{o}\) in (a)i) above.
The diagram shows the apparatus: a ray box carrying an illuminated cross-wire object, a concave mirror facing it, and a small screen between them. The distance from the ray box (object) to the mirror is b and the distance from the screen (image) to the mirror is a.
(a) The practical
For each object distance \(b\) (20.0, 25.0, 30.0, 35.0, 40.0 cm) the screen is moved until the cross-wire image is sharp, and \(a\) is read off. The mirror equation is
\[\frac{1}{a}+\frac{1}{b}=\frac{1}{f_o}\]
Writing \(l=\dfrac{1}{a}\) and rearranging,
\[l=\frac{1}{a}=\frac{1}{f_o}-\frac{1}{b}.\]
A graph of \(l=\dfrac{1}{a}\) (vertical) against \(\dfrac{1}{b}\) (horizontal) is a straight line of slope \(S=-1\) whose intercept on the vertical axis equals \(\dfrac{1}{f_o}\). Hence the focal length is obtained from that intercept, \(f_o=\dfrac{1}{\text{intercept}}\), and \(S^{-1}=-1\).
Sample table (illustrative)
b/cm
a/cm
l = 1/a (cm-1)
20.0
~30.0
0.033
25.0
~26.0
0.038
30.0
~24.0
0.042
35.0
~22.5
0.044
40.0
~21.5
0.047
Two precautions:
The image on the screen was made as sharp as possible before each reading to avoid parallax and focusing error.
The distances \(a\) and \(b\) were measured horizontally from the pole of the mirror, with the ray box, screen and mirror kept on the same straight line (aligned axis).
(b)(i) Object 10 cm in front of a concave mirror, f = 15 cm
Here \(u=10\text{ cm}\), \(f=15\text{ cm}\) (object inside the focal point).
The negative \(v\) means the image is behind the mirror. Characteristics of the image: it is virtual, erect (upright), magnified (three times the object size), and formed 30 cm behind the mirror.
(b)(ii) How \(f_o\) was obtained in (a): A graph of \(l=\tfrac{1}{a}\) against \(\tfrac{1}{b}\) was plotted; the intercept on the vertical axis is \(\tfrac{1}{f_o}\), so \(f_o\) is the reciprocal of that intercept.
The diagram shows the apparatus: a ray box carrying an illuminated cross-wire object, a concave mirror facing it, and a small screen between them. The distance from the ray box (object) to the mirror is b and the distance from the screen (image) to the mirror is a.
(a) The practical
For each object distance \(b\) (20.0, 25.0, 30.0, 35.0, 40.0 cm) the screen is moved until the cross-wire image is sharp, and \(a\) is read off. The mirror equation is
\[\frac{1}{a}+\frac{1}{b}=\frac{1}{f_o}\]
Writing \(l=\dfrac{1}{a}\) and rearranging,
\[l=\frac{1}{a}=\frac{1}{f_o}-\frac{1}{b}.\]
A graph of \(l=\dfrac{1}{a}\) (vertical) against \(\dfrac{1}{b}\) (horizontal) is a straight line of slope \(S=-1\) whose intercept on the vertical axis equals \(\dfrac{1}{f_o}\). Hence the focal length is obtained from that intercept, \(f_o=\dfrac{1}{\text{intercept}}\), and \(S^{-1}=-1\).
Sample table (illustrative)
b/cm
a/cm
l = 1/a (cm-1)
20.0
~30.0
0.033
25.0
~26.0
0.038
30.0
~24.0
0.042
35.0
~22.5
0.044
40.0
~21.5
0.047
Two precautions:
The image on the screen was made as sharp as possible before each reading to avoid parallax and focusing error.
The distances \(a\) and \(b\) were measured horizontally from the pole of the mirror, with the ray box, screen and mirror kept on the same straight line (aligned axis).
(b)(i) Object 10 cm in front of a concave mirror, f = 15 cm
Here \(u=10\text{ cm}\), \(f=15\text{ cm}\) (object inside the focal point).
The negative \(v\) means the image is behind the mirror. Characteristics of the image: it is virtual, erect (upright), magnified (three times the object size), and formed 30 cm behind the mirror.
(b)(ii) How \(f_o\) was obtained in (a): A graph of \(l=\tfrac{1}{a}\) against \(\tfrac{1}{b}\) was plotted; the intercept on the vertical axis is \(\tfrac{1}{f_o}\), so \(f_o\) is the reciprocal of that intercept.
Using the diagram above as a guide, carry out the following instructions.
Place the meter rule provided on the knife edge and adjust the position until it balances horizontally.
Read and record the balance point, G. Keep the knife edge at this point throughout the experiment.
Suspend a mass Q= 50.0g at a point P 30cm from the 0cm end of the rule.
On the other side of G, suspend the mass M =30g. Adjust its position until the rule settles down horizontally as shown in the diagram above.
Read and record the position R of M.
Record the distance, d, between G and R. Also read and record the distance, a, between P and G.
Repeat the procedure for four other values of M = 40, 50, 60, and 70 with Q kept in the same position. Evaluate d\(^{-1}\) in each case. Tabulate your readings.
Plot a graph of M on the vertical axis against d\(^{-1}\) on the horizontal axis.
Determine the slope,s, of the graph.
Evaluate k = \(\frac{s}{Q}\)
State two precautions taken to ensure accurate results.
(b)i. Explain the moment of a force about a point
ii. State the conditions necessary for a body to be in equilibrium when acted upon by a number of parallel end forces
Principle of the experiment
When the metre rule rests horizontally on the knife edge at the balance point \(G\), it is in equilibrium under the two suspended weights. Taking moments about \(G\), the anticlockwise moment of \(Q\) equals the clockwise moment of \(M\):
\[ Q \times a = M \times d \]
where \(a\) is the fixed distance \(PG\) and \(d\) is the distance \(GR\). Rearranging for \(M\):
\[ M = (Q\,a)\,d^{-1} \]
So a graph of \(M\) (vertical axis) against \(d^{-1}\) (horizontal axis) is a straight line through the origin whose slope is \(s = Q\,a\).
Metre rule balanced on the knife edge at G, with Q at P and M at R; a = PG, d = GR.
Recorded readings
Balance point: \(G = 49.50\ \text{cm}\). Mass \(Q = 50.0\ \text{g}\) suspended at \(P = 30.0\ \text{cm}\), so the fixed distance
\[ a = PG = 49.50 - 30.00 = 19.50\ \text{cm}. \]
For each mass \(M\) the position \(R\) is read, and \(d = R - G\), then \(d^{-1}\) is evaluated.
S/N
M (g)
R (cm)
d = R − G (cm)
d−1 (cm−1)
d−1 ×10−2 (cm−1)
a (cm)
1
30.0
82.00
32.50
0.0308
3.08
19.50
2
40.0
73.88
24.38
0.0410
4.10
19.50
3
50.0
69.00
19.50
0.0513
5.13
19.50
4
60.0
65.75
16.25
0.0615
6.15
19.50
5
70.0
63.43
13.93
0.0718
7.18
19.50
Graph of M against d−1
Straight line through the origin; slope s = Qa = 975 g cm.
Slope of the graph
Taking two widely separated points on the line of best fit, \((d^{-1}_1,\,M_1) = (0.0308\ \text{cm}^{-1},\ 30.0\ \text{g})\) and \((d^{-1}_2,\,M_2) = (0.0718\ \text{cm}^{-1},\ 70.0\ \text{g})\):
\[ k = \frac{s}{Q} = \frac{975}{50.0} = 19.5\ \text{g}. \]
This equals the fixed distance \(a = PG = 19.50\ \text{cm}\), as expected since \(s = Q\,a\) and therefore \(k = s/Q = a\).
Two precautions
The scale readings were taken with the eye placed vertically above the mark to avoid the error of parallax.
The rule was allowed to come completely to rest in the horizontal position before each reading, and the knife edge was kept fixed at \(G\) throughout the experiment.
(b)(i) Moment of a force about a point
The moment of a force about a point is the product of the force and the perpendicular distance from that point (the pivot) to the line of action of the force. Its SI unit is the newton metre (N m).
(b)(ii) Conditions for equilibrium under parallel forces
The algebraic sum of the forces is zero, i.e. the total upward force equals the total downward force.
The algebraic sum of the moments of the forces about any point is zero, i.e. the total clockwise moment equals the total anticlockwise moment about that point.
When the metre rule rests horizontally on the knife edge at the balance point \(G\), it is in equilibrium under the two suspended weights. Taking moments about \(G\), the anticlockwise moment of \(Q\) equals the clockwise moment of \(M\):
\[ Q \times a = M \times d \]
where \(a\) is the fixed distance \(PG\) and \(d\) is the distance \(GR\). Rearranging for \(M\):
\[ M = (Q\,a)\,d^{-1} \]
So a graph of \(M\) (vertical axis) against \(d^{-1}\) (horizontal axis) is a straight line through the origin whose slope is \(s = Q\,a\).
Metre rule balanced on the knife edge at G, with Q at P and M at R; a = PG, d = GR.
Recorded readings
Balance point: \(G = 49.50\ \text{cm}\). Mass \(Q = 50.0\ \text{g}\) suspended at \(P = 30.0\ \text{cm}\), so the fixed distance
\[ a = PG = 49.50 - 30.00 = 19.50\ \text{cm}. \]
For each mass \(M\) the position \(R\) is read, and \(d = R - G\), then \(d^{-1}\) is evaluated.
S/N
M (g)
R (cm)
d = R − G (cm)
d−1 (cm−1)
d−1 ×10−2 (cm−1)
a (cm)
1
30.0
82.00
32.50
0.0308
3.08
19.50
2
40.0
73.88
24.38
0.0410
4.10
19.50
3
50.0
69.00
19.50
0.0513
5.13
19.50
4
60.0
65.75
16.25
0.0615
6.15
19.50
5
70.0
63.43
13.93
0.0718
7.18
19.50
Graph of M against d−1
Straight line through the origin; slope s = Qa = 975 g cm.
Slope of the graph
Taking two widely separated points on the line of best fit, \((d^{-1}_1,\,M_1) = (0.0308\ \text{cm}^{-1},\ 30.0\ \text{g})\) and \((d^{-1}_2,\,M_2) = (0.0718\ \text{cm}^{-1},\ 70.0\ \text{g})\):
\[ k = \frac{s}{Q} = \frac{975}{50.0} = 19.5\ \text{g}. \]
This equals the fixed distance \(a = PG = 19.50\ \text{cm}\), as expected since \(s = Q\,a\) and therefore \(k = s/Q = a\).
Two precautions
The scale readings were taken with the eye placed vertically above the mark to avoid the error of parallax.
The rule was allowed to come completely to rest in the horizontal position before each reading, and the knife edge was kept fixed at \(G\) throughout the experiment.
(b)(i) Moment of a force about a point
The moment of a force about a point is the product of the force and the perpendicular distance from that point (the pivot) to the line of action of the force. Its SI unit is the newton metre (N m).
(b)(ii) Conditions for equilibrium under parallel forces
The algebraic sum of the forces is zero, i.e. the total upward force equals the total downward force.
The algebraic sum of the moments of the forces about any point is zero, i.e. the total clockwise moment equals the total anticlockwise moment about that point.
