Questions from a mechanics exam

Soldato
Joined
29 Jun 2006
Posts
3,372
Location
Sheffield
A small aeroplane has a propeller whose tip P describes a radius of 0.7m. At the end of the runway, the pilot idles the endine in preparation for clearance to take off. The engine has an idle speed of 800rpm.

(a) What is the engine idle speed of 800rpm in rad/s? [1]
(b) What is the velocity of the propeller tip P? [2]
(c) What is the acceleration of the propeller tip P? [2]

The pilot then accelerates the propeller at a rate of 150rad/s^2 to prepare for take off.

(d) What is the acceleration of the propeller tip P IMMEDITELY after the engine starts to accelerate from the idle speed of 800rpm? [5]
(e) What is the speed of the propeller 0.75 seconds after the pilot starts to accelerate the engine, expressed in rad/s? [2]
(f) What is the sped of the propeller 0.75 seconds after the pilot starts to accelerate the engine, expressed in rpm? [1]

I am pretty sure I got all those right. But could someone please do them to confirm?

O.........B
---------
|.w....../
|......../
|......./
|....../
|...../
|..../
|.../
|../
|./
|/ <- theta
A

O and A are NOT connected btw! Just need to make that clear cause the diagram is pretty poor.

That is a diagram of a crank OB attached to a fixed point O, and another crank, AB, linked to the point B on OB. The end A moves through a guide slot on a 20 degree incline.

AB = 500mm
OB = 250mm
w = angular velocity = 0.8rad/s

At the instant shown in the diagram, the crank OB is passing the horizontal position and has a clockwise angular velocity of w = 0.8rad/s. The guide roller at A is constrained to move in the slot.

(a) What is the velocity of B? [2]
(b) Show that the angle theta, that the link makes with the vertical is 30 degrees. [1]
(c) Draw a VELOCITY DIAGRAM for the link AB [6]
(d) What is the velocity of the guide roller A? [2]
(e) What is the angular velocity of the link AB? [3]

This question I'm not sure I got anything right, aside from parts a and b.

Part a was just v = rw = 0.8x250mm
Part b was just arcsin(250/500) = arcsin(1/2) = 30 degrees.
 
Caporegime
Joined
20 Jan 2005
Posts
45,621
Location
Co Durham
EDIT: I am rusty! :o

a) is 83.77 Rads
b) is 58.64 m/s
and (c) is unanswerable as you do not know the air resistance of the propeller.;)
 
Last edited:
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