Engineering Mechanics

(^584) „„„„„ A Textbook of Engineering Mechanics

3. An aeroplane is travelling with a velocity of 450 km.p.h. in a curve of radius 1000 m.
   Find the angle at which it must incline with the horizontal. Take g = 9·8 m/s^2.
   (Ans. 32.1°)


4. A metre gauge railway track is to be taken along a circular path of radius 400 m. Find the
   minimum superelevation required for a train travelling at 36 km.p.h. (Ans. 25·5 mm)


5. A loaded truck is transmitting 10 kN pressure on each wheel. The centre of gravity of the
   loaded truck is 1·2 m above the road level and the centre to centre distance of wheels is
   2 m. Find the pressure exerted by the inner and outer wheels, when the truck is going
   round a curve of 440 m radius at 48 km.p.h. (Ans. 9·95 kN ; 10·05 kN)


6. A racing motor car is negotiating a curve of radius 50 m. The distance between the centre
   to centre of the wheels is 1·5 m and height of the c.g. of the car is 90 cm above the ground
   level. Find the maximum speed of the motor car to avoid overturning.
   (Ans. 72·75 km. p.h.)


7. A motor cyclist riding at 20 km.p.h. has to turn a corner. Find the least radius of the
   curve, he should follow for safe travelling, if the coefficient of friction between the tyres
   and the road is 0·2. (Ans. 15·8 m)

QUESTIONS

1. What is centripetal force? Explain clearly when it comes into play?


2. Derive an expression for the centrifugal force of a body moving along a circular path.


3. What do you understand by the term ‘superelevation’? Discuss the necessity of providing
   a superelevation on railways.


4. Explain, why a cyclist has to lean inwards while negotiating a curve.


5. Obtain an expression for the reactions of a vehicle, moving on a level circular path.
   6. Derive an equation for the maximum velocity of a vehicle moving on a level circular path.
   (a) to avoid its overturning path :
   (b) to avoid its skidding away.

OBJECTIVE TYPE QUESTIONS

1. Which of the following statements is correct?
   (a) When a body moves along a circular path with a uniform velocity, there will be a
   tangential acceleration.
   (b) When a body moves along a circular path with a uniform acceleration, there will be a
   tangential acceleration.
   (c) When a body moves along a circular path with a uniform velocity, there will be no
   tangential acceleration.
   (d) When a body moves along a circular path with a uniform acceleration, there will be no
   tangential acceleration.


2. The slope on the road surface generally provided on the curves is known as
   (a) angle of friction (b) angle of repose
   (c) angle of banking (d) none of the above