Reference no: EM132323472
Assignment
Question 1
Locomotives travelling through tunnels affect the pressure of the air immediately in front of them. An approximate formula for the air pressure P (in atm) at a distance x (in m) from the front of the locomotive is
P=Ae^(-Bx)+1
where A and B are constants.
(A) If P=3 when x=0, determine the value of A.
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The value of A is... Replace this text with your answer.
(B) If P=1.03 when x=10, determine the value of B.
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The value of B is... Replace this text with your answer.
(C) Hence determine the air pressure at a distance of 5 min front of the locomotive.
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The air pressure at a distance of 5 min front of the locomotive is... Replace this text with your answer.
(D) Produce a fully labelled graph of P on the vertical axis against x on the horizontal axis (remember to include units and use a sensible range of x) and use it to infer the air pressure in the tunnel when no locomotive is present.
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The air pressure in the tunnel when no locomotive is present is... Replace this text with your answer.
Question 2
The efficiency η (in %) of a DC motor is related to the toque τ (in N mm) being generated by the motor. For one particular machine this relationship takes the form
η= (20800τ-4680τ^2)/(200τ+22)
for τ≥0.
(A) Find dη/dτ.
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dη/dτ= Replace this text with your answer.
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(B) Use your result from part a) to determine the torque at which motor efficiency is a maximum and the value of that maximum efficiency.
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Torque (τ) for max. efficiency is... Replace this text with your answer.
Max. efficiency (η) is... Replace this text with your answer.
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Question 3
The vertical speed v (in m s^(-1)) of a lift through its lift shaft varies over time t (in s) in accordance with the equation
v= 4/5 (1-cos?(4π/9 t) )
for 0≤t≤ 9/2.
(A) Find the angular frequency and period of the function cos?(4π/9 t).
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Angular frequency, ω= Replace this text with your answer.
Period, T= Replace this text with your answer.
(B) Determine the values of tfor which v=1.
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The values of tfor which v=1are... Replace this text with your answer.
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Question 4
A particular shaft cap design may be thought of as the solid of revolution created by rotating the curve
y= 9/10 √(1-16x^2 )
around the x-axis where 0≤x≤ 1/4.
Determine ¯xi.e. the horizontal centre of mass for this solid.
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x ¯= Replace this text with your answer.
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