Q.

Q1.

A. What is an inertial reference?

B. Determine the resultant of the three forces F1 = 2.0i + 3.3j – 2.6k; F2 = - i + 5.2j – 2.9k; and F3 = 8.3i – 6.6j + 5.8k, which are concurrent at the point (2, 2, -5.). The forces are in Newton’s and the distances are in meters.

Q2.

A. A light plain is coming in for a landing at a speed of 100 km/hr. The wheels have zero rotation just before touching the runway. If 1/10 the weight of the plane is maintained by the upward force of the runway for the first second, what is the approximate length of the skid mark left by the wheel on the runway? The wheels each weigh 100 N and have a radius of gyration of 180mm and a diameter of 450 mm. The plane weighs with load 8,000 N. The coefficient of friction between the tire and runway is .3.

B. Write a short note on :

(i) Varignon's theorem (ii) the Coulomb's laws of dry friction.

Q3.

A. A car is traveling at a speed of 55 mi/hr along a banked highway having a radius of curvature of 500 ft. At what angle should the road be banked in order that a zero friction force is needed for the car to go around this curve?

C. A belt embraces an angle of 200? over the surface of a pulley of 500 mm diameter. If the tight side tension of the belt is 2.5 kN. Find out the slack side tension of the belt. The coefficient of friction between the belt and the pulley can be taken as 0.3.

Q4.

A. State the theorems of Pappus and Guldinus to find out the surface area and the volume of a body

B. A mountain climber of weight W hangs freely suspended by one rope that is fastened at one end to his waist, wrapped one half turn about a rock with ïx = .2 and held at the other end in his hand. What minimum force in terms of W must he pull the rope into himself with to gain altitude?

Q5.

A. What is meant by the associative law of addicting?

B. The motion of a particle in defined by the relation x = t3 – 15 t2 – 20, where 'x' is expressed in metres and’t’ in seconds. Determine the acceleration of the particle at t = 3 seconds.

Q6.

A. A space station is in a circular parking orbit around the earth at a distance of 5,000 mi from the center. A projectile is fired ahead in a direction tangential to the trajectory of the space station with a speed of 5,000 mi/hr relative to the space station. What is the maximum distance from earth reached by the projectile?

B. A magnetic field is developed such that the body force on the rectangular parallelepiped of metal is given as

F=(.01x+1/8)k oz/lbm

If the mass density of the metal is 450 lbm/ft3, what is the simplest resultant body force from such a field? Note at the earth’s surface the number of pounds mass equals the number of pounds force of weight.