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Mechanical Measurements

A student wants to calculate the volume of a metal tube 3.47±0.05m long. She measures the diameter of the tube in a number of places along its length. Her results (in m) are shown below:

D = 0.48, 0.47, 0.49, 0.48, 0.50, 0.45

a) The percentage uncertainty in the length (I)

b) The mean value of D (in m)

c) The range in measurements of D

d) The absolute uncertainty in D (in m)

e) The percentage uncertainty in D(2 marks)

V=\frac{\pi D^{2} l}{4}

f) The volume of the metal tube using the formula below. State your answer to 2decimal places.(2 marks)

g) The percentage uncertainty in V

h) The absolute uncertainty in V

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Mechanical Measurements

Determine the reading in mm on these micrometer scales. State your answer with an appropriate uncertainty.

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Mechanical Measurements

Determine the reading in mm on these Vernier scales. State your answer with an appropriate uncertainty.

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Mechanical Measurements

A student wants to calculate the volume of a metal tube 3.47±0.05m long.She measures the diameter of the tube in a number of places along itslength. Her results (in m) are shown below:

D = 0.48, 0.47, 0.49, 0.48, 0.50, 0.45

a) The percentage uncertainty in the length (1)

b) The mean value of D (in m)

The range in measurements of D

) The absolute uncertainty in D (in m)

The percentage uncertainty in D

O The volume of the metal tube using the formula below. State your answer to 2 decimal places.

) The percentage uncertainty in V

-) The absolute uncertainty in V

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Mechanical Measurements

Determine the reading in mm on these micrometer scales. State youranswer with an appropriate uncertainty.

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Mechanical Measurements

Determine the reading in mm on these Vernier scales. State your answer with an appropriate uncertainty.

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Mechanical Measurements

A. Consider a plane OA at an angle y with the horizon as shown below. If a projectile is fired up the inclined surface from the point O with an initial velocity v making an angle of with the horizon. The projectile follows a parabolic path and strikes the inclined surface at A.

\text { 1. Derive an expression for the time of flight of the projectile in terms of } v_{n} \gamma \text { and } \theta \text {. }

\text { 2. Derive an expression for the range } \mathrm{R} \text { along the inclined surface in terms of } v, \gamma \text { and } \theta \text {. }

3. Derive an expression for the maximum range Rmax änd the corresponding angle ofprojection.

4. Derive an expression for maximum hight (Hmax) as shown in the figure.

5. Support your answers in (3) and (4) by numerical values.

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Mechanical Measurements

A mass-spring-damping system is shown in Figure Q4.

Equation (Q4) below describes the input (f(t)) and output (x(t)) function obtained from Newton's law:

f(t)=m \frac{d^{2} x}{d t^{2}}+d \frac{d x}{d t}+k \cdot x(t)

where k = 1kN/m, d = 20N s/m, m= kg

(a) With the given input/output and Equation (Q4), calculate the transfer function.Denote this transfer function as G(s).

(b) Calculate the poles of this system and assess its stability.

(c) Calculate the impulse response of this system. Show details of your calculation.

(d) Calculate the step response for the sampling points given in Table Q4. Show details of calculation.

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Mechanical Measurements

For the approximate magnitude Bode plot shown in Figure Q5 below, find:

(a) Corresponding transfer function H(s).

(b) Corresponding approximate Phase Bode plot.

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Mechanical Measurements

Measurements were taken as a ball falls a distance D in a time T are:

D = 1.215+ 0.004 m

T = 0.495, 0.498, 0.530, 0.496, 0.501 s

) The mean value of T.

The acceleration due to gravity g, using the formula:

g=\frac{2 D}{T^{2}}

Percentage uncertainty in D.

Range in measurements of T

The percentage uncertainty in the average value of T.

) The absolute uncertainty in the average value of T.

The percentage uncertainty in g.

) The absolute uncertainty in g.

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