# Chapter 1: Introduction and Basic Concepts (Solution)

**Problem 1.1: **A man circling the earth in a spaceship weighed 300 N at a location where the local gravitational acceleration was 3.35 m/s^{2}. Calculate the mass of the man and his weight on the earth, where the gravitational acceleration is 9.81 m/s^{2}.

**Problem 1.2:** If a man weighs 600 N at a place where the local acceleration due to gravity is 9.81 m/s^{2}, what would be his weight on the moon, where the acceleration due to gravity is 1.67 m/s^{2}?

**Problem 1.3: **A special manometer fluid has a specific gravity of 3.65 and is used to measure a pressure of 1.25 bar at a location where the barometric pressure is 760 mm Hg. What height will the manometer fluid register?

**Problem 1.4: **A mercury manometer used for pressure measurement indicates 500 mm. The density of mercury is 13.56×10^{3} kg/m3 and acceleration due to gravity is 9.81 m/s^{2}. Express the pressure indicated in bar.

**Problem 1.5: **What is the pressure exerted on a skin diver who has descended to 20 m below the surface of the sea, if the atmospheric pressure is 1 bar at the sea level and the specific gravity of the seawater is 1.03?

**Problem 1.6: **A mercury manometer used to measure pressure inside a vessel indicates 400 mm. One end of the manometer is exposed to the atmosphere. The atmospheric pressure is 1.01325 bar. The density of mercury is 13.56×103 kg/m^{3} and g = 9.81 m/s^{2}. What is the absolute pressure in the vessel in N/m^{2}?

**Problem 1.7: **The potential energy of a body of mass 20 kg is 3.5 kJ. What is the height of the body from the ground? If a body of mass 20 kg is moving at a velocity of 50 m/s, what is its kinetic energy?

**Problem 1.8: **A car having a mass of 1200 kg is running at a speed of 60 km/h. What is the kinetic energy of the car in kJ? What is the work to be done to bring the car to a stop?

**Problem 1.9: **A body of mass 50 kg is lifted through a distance of 15 m. What is the work done? If it took 2 min to lift the mass, calculate the power.

**Problem 1.10: **A man whose weight is 700 N takes 2.5 min for climbing up a staircase. What is the power developed in him, if the staircase is made up of 20 stairs each 0.18 m in height?

**Problem 1.11: **The steam supplied to an engine liberates 5000 J of heat. If the engine efficiency is only 40 percent, to what height a body of mass 10 kg can be lifted using the work output from the engine?

**Problem 1.12: **Nitrogen gas is confined in a cylinder and the pressure of the gas is maintained by a weight placed on the piston. The mass of the piston and the weight together is 100 kg. The acceleration due to gravity is 9.81 m/s^{2} and the atmospheric pressure is 1.01325 bar. Assume a frictionless piston. Determine: (a) The force exerted by the atmosphere, the piston, and the weight on the gas if the piston is 200 mm in diameter. (b) The pressure of the gas. (c) If the gas is allowed to expand pushing up the piston and the weight by 500 mm, what is the work done by the gas in kJ? (d) What is the change in the potential energy of the piston and the weight after the expansion in part (c)?

**Problem 1.13: **A spherical balloon of diameter 0.5 m contains gas at 1 bar and 300 K. The gas is heated and the balloon is allowed to expand. The pressure inside the balloon is directly proportional to the square of the diameter. What would be the work done by the gas when the pressure inside reaches 5 bar?

**Problem 1.14: **A body of mass 20 kg is dropped from a height of 15 m. What is the potential energy of the body at the time of its release? Assume that the potential energy gets converted into kinetic energy when the body strikes the ground. At what velocity does it strike the ground?

**Problem 1.15: **A balloon that was originally empty is being filled with hydrogen from a cylinder at a constant temperature of 300 K. The atmospheric pressure is 1.01325 bar. What is the work done by the balloon–cylinder system when the balloon attains a spherical shape 6 m in diameter?

**Problem 1.16: **Five kilograms of CO_{2} gas is contained in a piston-cylinder assembly at a pressure of 7.5 bar and a temperature of 300 K. The piston has a mass of 6000 kg and a surface area of 1 m^{2}. The friction of the piston on the walls is significant and cannot be ignored. The atmospheric pressure is 1.01325 bar. The latch holding the piston in position is suddenly removed and the gas is allowed to expand. The expansion is arrested when the volume is double the original volume. Determine the work done in the surroundings.