P3 QUESTION-3 Linearise the following equations, also indicate (with the aid of a sketch) what would be plotted on the y
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P3 QUESTION-3 Linearise the following equations, also indicate (with the aid of a sketch) what would be plotted on the y- and x-axis and what would be obtained from the slope and intercept. Variables are indicated in brackets. W (i) Y= axb (Y, X) (ii) C=aT + BT? (CT) [6]
QUESTION-2 Suppose that you have determined the volume of a metal sphere by immersing it in a measuring cylinder, and you find the result to be 50.0 +0.5 cmº. Calculate the radius of the sphere and its associated absolute error in cm using a maximum error analysis. The volume of a sphere is VS 3 = far. -3 The mass of the sphere is found to be 250 £ 1 g. Find the density in kg.m and its associated relative error. [6]
QUESTION-4 A spring is clamped at one end and allowed to oscillate vertically up and down. At the bottom end of the spring is a scalepan to which weights may be added. The period of oscillation (7) depends on the spring constant (k) and the mass of the system, where we distinguish between the mass of the scalepan itself (u, which is a constant) and the mass added to the scalepan (m), which is a variable. The relationship is (m+11) T=271 k Linearize this equation. Complete the columns in the table below and then plot a graph to obtain u and k using the linearized equation. Put the best and a worst straight line through the data, and determine the slopes and intercepts. From these results estimate u and k and their absolute errors. Mass in scalepan Time for 20
esware Mass in scalepan Time for 20 oscillations (s) (kg) 0.10 0.15 0.20 0.25 0.30 0.35 6.51 7.72 8.88 9.85 10.64 11.41 [14]
P3 QUESTION-3 Linearise the following equations, also indicate (with the aid of a sketch) what would be plotted on the y- and x-axis and what would be obtained from the slope and intercept. Variables are indicated in brackets. W (i) Y= axb (Y, X) (ii) C=aT + BT? (CT) [6]
QUESTION-2 Suppose that you have determined the volume of a metal sphere by immersing it in a measuring cylinder, and you find the result to be 50.0 +0.5 cmº. Calculate the radius of the sphere and its associated absolute error in cm using a maximum error analysis. The volume of a sphere is VS 3 = far. -3 The mass of the sphere is found to be 250 £ 1 g. Find the density in kg.m and its associated relative error. [6]
QUESTION-4 A spring is clamped at one end and allowed to oscillate vertically up and down. At the bottom end of the spring is a scalepan to which weights may be added. The period of oscillation (7) depends on the spring constant (k) and the mass of the system, where we distinguish between the mass of the scalepan itself (u, which is a constant) and the mass added to the scalepan (m), which is a variable. The relationship is (m+11) T=271 k Linearize this equation. Complete the columns in the table below and then plot a graph to obtain u and k using the linearized equation. Put the best and a worst straight line through the data, and determine the slopes and intercepts. From these results estimate u and k and their absolute errors. Mass in scalepan Time for 20
esware Mass in scalepan Time for 20 oscillations (s) (kg) 0.10 0.15 0.20 0.25 0.30 0.35 6.51 7.72 8.88 9.85 10.64 11.41 [14]