Mechanics | Relativity Answers

The efficiency of a Carnot engine is 30%. Its efficiency is to be raised to 60%. By how much must the temperature of the source be increased if the sink is at 27°C?

Establish the equation of motion of a weakly damped forced oscillator explaining the significance of each term. Differentiate between transient and steady state of the oscillator.

The position vector of two particles of mass 4 kg and 2 kg are , respectively, r1 = 3t i^ + t j^ +2t2 k^ and r2 = 3 i^ +(t2-1)j^ +4t k^ where t is in seconds and the position in metres. Determine the position vector of the centre of mass of the system , the velocity of the cm and the net force acting on the system

What should be the radius of a space station spinning with an angular speed of 2 rpm such that an astronaut inside the station experiences artificial gravity with g = 10 m /s2

A pendulum bob of mass 50 g is suspended on a string from the ceiling of an
elevator which is moving downwards with an acceleration 1.5 ms-2. Draw the free
body diagram using the non-inertial frame of reference and determine the tension in
the string. (Take g = 10 ms-2) (5

9. A satellite going around Earth in an elliptic orbit has a speed of 10 km s-1 at the perigee
which is at a distance of 227 km from the surface of the earth. Calculate the apogee
distance and its speed at that point. (10

8. A proton undergoes a head on elastic collision with a particle of unknown mass which
is initially at rest and rebounds with 16/25 of its initial kinetic energy. Calculate the
ratio of the unknown mass with respect to the mass of the proton.

The position vector of two particles of mass 4.0 kg and 2.0 kg are, respectively, kjirˆ2ˆˆ321ttt++=r and ()kjirˆ4ˆ1ˆ322tt+-+=r where t is in seconds and the position in metres. Determine the position vector of the centre of mass of the system, the velocity of the cm and the net force acting on the system.

A sonometer wire having cross-sectional area 0.85 ´ 10-6 m2 is stretched between two rigid supports 1.2 m apart. A tension of 20 N is applied at its free end. If the temperature is reduced by 12°C, calculate the final tension in the wire. Take coefficient of linear expansion (a) and isothermal Young’s modulus (g) to be 1.5 ´ 10-5 K-1 and 2.0 ´ 1011 Nm-2, respectively.

A bullet of mass 20 g, travelling at a speed of 350 m/s, strikes a steel plates at an angle of 30 degree with the plane of plate. it ricochets off at the same angle at a speed of 320 m/s. What is the magnitude of the impulse that the steel plate gives to the projectile ?If the collision with the plate take place over a time delta t=1/1000 s, what is the average force exerted by the plate on the bullet?