Classical Mechanics Answers

The elevator in an office building, starting from rest at the first floor, is accelerated 0.75 m/sec2 for 5 secs. It continues at constant velocity for 12 secs more and is then stopped in 3 secs with constant deceleration. If the floors are 3.75m apart, at what floor did the elevator stop?

Explain Hamilton's equation of motion in terms of Poisson's brackets.

What is meant by cyclic co-ordinate? Show that generalized momentum corresponding to a cyclic co-ordinate of conservative system is conserved.

A plane which is flying horizontally at a constant speed Vo and at a height h above the sea must drop a bundle of supplies to a castaway on a small raft. Write down newtons second law for the bundle as it falls from the plane, assuming you can neglect air resistance.

A point equilibrium is reached by three forces as in the diagram below. Force F1 has components 15N due south and 13N due west. What are the components of force F2?

A cube of mass 10 kg is at rest on a horizontal surface when it is subjected to a horizontal force P that varies with time t as P = 20t. If the static and kinetic coefficients of friction are both 0.4, calculate the velocity of the cube after 5 s.

A 10Mg truck rolling at a constant speed of 30 kph along a horizontal rail comes to an incline of slope sin 0.1. Calculate how far it will coil up the slope before coming to a halt, (a) ignoring all resistive forces, and (b) assuming the rolling vesistance is 5% of the normal reaction of the truck

A 5kg weight whose motion is constrained by vertically guides is dropped from rest 0.5m onto vertically aligned spring whose stiffness is 10kNm-¹. how fast is the weight travelling when the spring has been compressed by 50mm?

A balloon is rising vertically upward with a uniform

velocity 'u' as shown in Fig. 11.E22. At a certain

instant, a ball No. 1 is dropped from it, which takes a

4 sec to reach the ground. The moment this ball

strikes the ground, another ball is dropped from the

balloon and this 2nd ball takes 5 sec to reach the

ground. Find the velocity of the balloon 'u' and height

from which both the balls must have been dropped.

Objects with masses of 200kg and 500kg are separated by 0.4m

Find

a)the net gravitational force exerted by these objects on a 50kg object placed midway between them

b) at what position can the 50kg object be placed so as to experience a net force of zero