Determine the torque at which motor efficiency is a max

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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.

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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.

Evidence of checking

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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.

Evidence of checking

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Comment on evidence

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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.

Evidence of checking

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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.

Evidence of checking

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Reference no: EM132323472

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