Classical Mechanics Answers

Two wooden cubes of side-length 'a' are placed one on another on a horizontal plane. 'M' and 'm' represent the masses of upper cube and lower cube respectively(M>m). The coefficient of dynamic friction between each surface is μ. The bottom wedge is given 'u' initial velocity and it is sufficient for that cube to slip away from the tower. Find the final horizontal displacement of the upper cube.

Two balls A and B of masses 10g and 20g moves on x axis towards each other with equal speed. They collide and stick together. What percentage of kinetic energy is lost?

540 g of ice at 0°C is mixed with 540 g of water at 80°C, what is the final temperature of the mixture?

What is displacement of an object in Simple Harmonic Motion when kinetic and potential energy are equal? please explain

In a car with 4 cylinder, four stroke petrol engine having 120.6 mm bore and 132 mm stroke, the net dynamometer load is 195 N at a diameter of 1000 mm when the speed is 2500 rpm. At this speed and throttle opening the engine requires 5.2 kW to motor it with ignition switched off

i) Calculate the mechanical efficiency and the indicated mean effective pressure,

i) During the 5 minutes run at this speed and power, the engine used 1 kg of petrol of heating value 45310 kJ/kg and 40 kg of cooling water with a temperature rise of 55.5 K Specific heat of the water is taken as 4/18 kJ/kgK. Draw the heat balance chart of the test in kJ/min

A 200g block connected to a light spring for which the force constant is 5 N/m is free to oscillate on a frictionless, horizontal surface. The block is displaced 5 cm from equilibrium and released from rest as

1.1. Find the period of motion of the block. (6)

1.2. Determine the maximum speed of the block. (4)

1.3. Determine the maximum acceleration of the block. (4)

1.4. Express the position, velocity, and acceleration as a function of time in SI units.

A particle of mass is in a concentrated potential field V (𝑟). Determine the equation of motion using the Lagrangian! Is there a constant of motion? Explain!

There is a tower built by placing N coins one on another. M, R and T represent mass, radius and thickness of a coin respectively. The coefficient of dynamic friction between two coins is μ. An external force hit the bottom coin so that it is extracted from the tower with 'u' velocity. The upper part of the tower remains steady because 'u' was very fast. What is the horizontal displacement of the coin tower afterall?

1.            A bullet moving at the rate of 300 m/s is fired into a thick target and penetrates up to 500 mm. If it is fired into a 250 mm thick target, find the velocity of emergence. Take the resistance to be uniform in both the cases.

A typical automobile under hard braking loses speed at a rate of about 7.0 m/s2 ; the typical reaction time to engage the brakes is 0.50 s. A local school board sets the speed limit in a school zone such that all cars should be able to stop in 4.0 m. (a) What maximum speed does this imply for an automobile in this zone? (b) What fraction of the 4.0 m is due to the reaction time?