Question: 1:
The Voltage V across an inductor L, in LR electrical circuit drops exponentially over time t(s)
The relationship is V=Ee-1/τ . Where the emf, E and τ are constants. Use the table of values for t and v and logarithms to plot an appropriate straight line graph
|
t
|
0.00
|
0.010
|
0.020
|
0.025
|
0.030
|
0.040
|
0.050
|
|
v
|
5.0
|
2.350
|
1.400
|
1.050
|
0.750
|
0.550
|
0.350
|
Question:2
The amount of solute that will dissolve in a given volume of water depends on the temperature of the water. For a particular substance it is believed that the amount that will dissolve in 10 litres of water is governed by relationship:
m = Aekθ Where θ is the water temperature and A and k are constants. An experiment was performed to test this hypothesis and the following data was recorded.
|
temperature
|
10
|
20
|
30
|
40
|
50
|
60
|
70
|
|
Mass
|
4.72
|
5.32
|
6.02
|
7.83
|
8.77
|
9.87
|
10.14
|
Plot a linear graph which confirms that the relationship is exponential
Find the values of A and K.
Question: 3
The following data are for cold worked carbon steel tested in a tensile test:
Original diameter: 12.78 mm
Final diameter: 8.43 mm
Original gauge length: 49.8 mm
Final gauge length: 61.51 mm
|
Load (kN)
|
5.5
|
11.7
|
17.0
|
27.4
|
40.5
|
53.1
|
60.5
|
64.7
|
66.9
|
|
Extension
|
0.010
|
0.020
|
0.030
|
0.040
|
0.050
|
0.076
|
0.102
|
0.127
|
0.152
|
| Load (kN) |
68.7 |
70.5 |
71.5 |
72.1 |
72.8 |
| Extension |
0.203 |
0.254 |
0.305 |
0.356 |
0.508 |
The maximum load was 75.1 Kn. Plot the stress-strain graph and determine
a. Realistic estimation of the modulus of elasticity.
b. Relationship between stress and strain.
Question: 4
The electric current charging a capacitor is related to time by the following law.
I = 10 (1-e-t/2)
Calculate the charge Q (area under the graph) between the limits t=0 and t=6 seconds. Use calculus trapezoidal rule.