Q1. (a) Define work. (b) What are the conditions for doing work?

Q2. In which of the following work is done. Explain? (a) A man pushing a wall. (b) A girl climbing a staircase. (c) A boy swimming in a tank. (d) A man standing at a place and holding a suitcase in hand. (e) A lady cooking food. (f) A porter carrying a load on his head walking along a level road. (g) A porter carrying a load and climbing upstairs.

Q3. State the sign of work done by a force in the following. (a) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket. (b) Work done by gravitational force in the above case.

Q4. State the sign of work done by a force in the following. (a) work done by friction on a body sliding down an inclined plane. (b) work done by a gravitational force on a freely falling body.

Q5. State the sign of work done by a force in the following. (a) work done by an applied force on a body moving on a rough horizontal plane with uniform velocity. (b) work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

Q6. State the conditions under which a force does no work.

Q7. A man climbs a slope and another walks the same distance on a level road. Who does more work and why?

Q8. (a) State the CGS and SI units of work. (b) How is joule related to erg?

Q9. State the expression for work done by a force when the object experiencing the force is displaced opposite to the force.

Q10. Give an example where the displacement of a particle is in the direction perpendicular to a force acting on this particle.

Q11. The displacement of a particle makes an angle \(\theta\) with the force acting on it. For what value of \(\theta\), is the work done maximum? For which value of \(\theta\) is the work done minimum?

Q12. (a) What is energy? State and define SI unit of energy. (b) Define potential energy. Give two examples of potential energy. (c) Define kinetic energy. Give four examples of kinetic energy.

Q13. What kind of energy is possessed by a body in the following cases? (a) A cocked-up spring and an air gun. (b) A shooting arrow. (c) A stone lying on the top of a house. (d) Water stored in the dam. (e) An electron spinning around the nucleus. (f) A fish moving in water.

Q14. Give two examples of elastic potential energy.

Q15. State the law of conservation of energy.

Q16. Define: Work, Power and Energy. State their SI units.

Q17. State the relation between the kinetic energy and momentum of a body.

Q18. State the expression for the kinetic energy of a particle of mass \(m\) moving at a speed \(v\).

Q19. Does the kinetic energy of an object depend on its direction of motion?

Q20. By what factor does the kinetic energy of a particle increase if the speed is increased by a factor of 3?

Q21. What is the relation between the work done by external forces on a body and its energy?

Q22. What is mechanical energy?

Q23. Can matter be converted into energy?

Q24. Write the energy conversions in the following cases. (a) Total energy of a system is always conserved, no matter what internal and external forces on the body are present. (b) The work done by earth's gravitational force in keeping the moon in its orbit for its one revolution is zero. (c) Work done by a person on a book held in his hand while walking with uniform speed on a horizontal road.

Q25. Define kilowatt hour and convert it into joule.

Q26. Define electron volt and express it in joule.

Q27. Define power and write its unit. (a) State the absolute unit of power in SI system. (b) What is horsepower? What is its magnitude in SI unit?

Q28. Which physical quantity remains constant (i) In an elastic collision (ii) In an inelastic collision?

Q1. In which of the following cases is the work done positive, zero or negative? (a) Work done by a porter on a suitcase in lifting it from the platform on to his head. (b) Work done by the force of gravity on a suitcase as the suitcase falls down from the porter's head. (c) Work done by a person on a book held in his hand while walking with uniform speed on a horizontal road.

Q2. Why does a person standing for a long time get tired when he does not appear to do any work?

Q3. What do you understand by potential energy? Explain with two examples.

Q4. How can you justify that a body kept at a greater height has larger energy?

Q5. What is potential energy? Derive an expression for the gravitational potential energy.

Q6. A lorry and a car moving with the same momentum are brought to rest by the application of brakes, which provide equal retarding forces. Which of them will come to rest in shorter time? Which will come to rest in less distance?

Q7. Distinguish between conservative and non-conservative forces with one example each.

Q8. The work done by a force \(F_1\) is larger than the work done by another force \(F_2\). Is it necessary that power delivered by \(F_1\) is also larger than the power delivered by \(F_2\)?

Q9. Derive an expression for the height attained by a freely falling body after \(n\) number of rebounds from the floor.

Q10. Explain the law of conservation of energy.

Q11. What is the total displacement of a freely falling body, after successive rebounds from the same place of ground, before it comes to stop? Assume that 'e' is the coefficient of restitution between the body and the ground.

Q1. Develop the notions of work and kinetic energy and show that it leads to work-energy theorem.

Q2. State the law conservation of energy. Prove mathematically the law of conservation of energy in case of a freely falling body.

Q3. What are collisions? Explain the possible types of collisions. Show that in the case of one dimensional elastic collision, the relative velocity of approach of two colliding bodies before collision is equal to the relative velocity of separation after collision.

Q4. Show that two equal masses undergo oblique elastic collision will move at right angles after collision, if the second body initially at rest.

Q5. If the forces doing work are conservative, show that total mechanical energy of the system is conserved.

Q6. Obtain the expression for potential energy of a spring.

Q7. State and prove work-energy theorem for variable force.

Q8. Define the coefficient of restitution and obtain the expression for it. A body freely falling from a certain height 'h', after striking a smooth floor rebounds to a height h/2. What is the coefficient of restitution between the floor and the body?

Q9. An object is tied to a string and rotated in a vertical circle. Obtain expressions for speeds of the object at the highest and lowest points when the string becomes slack only at the highest point.

Q1. A force \(F\) acting on a particle varies with the position \(x\) as shown in the graph. Find the work done by the force in displacing the particle from \(x=-a\) to \(x=+2a\).

Q2. From a height of \(20\,\mathrm{m}\) above a horizontal floor, a ball is thrown down with initial velocity \(20\,\mathrm{m\,s^{-1}}\). After striking the floor, the ball bounces to the same height from which it was thrown. Find the coefficient of restitution for the collision between the ball and the floor? (\(g=10\,\mathrm{m\,s^{-2}}\))

Q3. A ball falls from a height of \(10\,\mathrm{m}\) on to a hard horizontal floor and repeatedly bounces. If the coefficient of restitution is \(\frac{1}{\sqrt{2}}\), What is the total distance travelled by the ball before it ceases to rebound?

Q4. A test tube of mass 10 grams closed with a cork of mass 1 gram contains some ether. When the test tube is heated the cork flies out under the pressure of the ether gas. The test tube is suspended horizontally by a weight less rigid bar of length 5 cm. What is the minimum velocity with which the cork should fly out of the tube, so that test tube describing a full vertical circle about the point O. Neglect the mass of ether.

Q5. A machine gun fires 360 bullets per minute and each bullet travels with a velocity of \(600\,\mathrm{m\,s^{-1}}\). If the mass of each bullet is \(5\,\mathrm{g}\), find the power of the machine gun.

Q6. Find the useful power used in pumping \(3425\,\mathrm{m^3}\) of water per hour from a well \(8\,\mathrm{m}\) deep to the surface, supposing 40% of the horse power during pumping is wasted. What is the horse power of the engine?

Q7. A pump is required to lift \(600\,\mathrm{kg}\) of water per minute from a well \(25\,\mathrm{m}\) deep and to eject it with a speed of \(50\,\mathrm{m\,s^{-1}}\). Calculate the power required to perform the above task.

Q8. A block of mass \(5\,\mathrm{kg}\) initially at rest at the origin is acted on by a force along the X-positive direction represented by \(F=(20+5x)\,\mathrm{N}\). Calculate the work done by the force during the displacement of the block from \(x=0\) to \(x=4\,\mathrm{m}\).

Q9. A block of mass \(2.5\,\mathrm{kg}\) is sliding down a smooth inclined plane as shown. The spring arranged near the bottom of the inclined plane has a force constant \(600\,\mathrm{N\,m^{-1}}\). Find the maximum compression in the spring just after the block strikes the spring.

Q10. A force \(F=\frac{K}{x^2}\;(x\ne0)\) acts on a particle along the X-axis. Find the work done by the force in displacing the particle from \(x=+a\) to \(x=+2a\). Take \(K\) as a positive constant.

Q1. It is well known that a raindrop falls under the influence of the downward gravitational force and the opposing resistive force. The latter is known to be proportional to the speed of the drop but is otherwise undetermined. Consider a drop of mass \(1.00\,\mathrm{g}\) falling from a height \(1.00\,\mathrm{km}\). It hits the ground with a speed of \(50.0\,\mathrm{m\,s^{-1}}\). (a) What is the work done by the gravitational force? (b) What is the work done by the unknown resistive force?

Q2. A cyclist comes to a skidding stop in \(10\,\mathrm{m}\). During this process, the force on the cycle due to the road is \(200\,\mathrm{N}\) and is directly opposed to the motion. (a) How much work does the road do on the cycle? (b) How much work does the cycle do on the road?

Q3. In a ballistics demonstration a police officer fires a bullet of mass \(50.0\,\mathrm{g}\) with speed \(200\,\mathrm{m\,s^{-1}}\) on soft plywood of thickness \(2.00\,\mathrm{cm}\). The bullet emerges with only \(10\%\) of its initial kinetic energy. What is the emergent speed of the bullet?

Q4. A woman pushes a trunk on a railway platform which has a rough surface. She applies a force of \(100\,\mathrm{N}\) over a distance of \(10\,\mathrm{m}\). Thereafter, she gets progressively tired and her applied force reduces linearly with distance to \(50\,\mathrm{N}\). The total distance through which the trunk has been moved is \(20\,\mathrm{m}\). Plot the force applied by the woman and the frictional force, which is \(50\,\mathrm{N}\) versus displacement. Calculate the work done by the two forces over \(20\,\mathrm{m}\).

Q7. To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass \(1000\,\mathrm{kg}\) moving at a speed \(18.0\,\mathrm{km\,h^{-1}}\) on a smooth road and colliding with a horizontally mounted spring of spring constant \(6.25\times10^3\,\mathrm{N\,m^{-1}}\). What is the maximum compression of the spring?

Q8. Consider Example 5.7 taking the coefficient of friction, \(\mu\), to be \(0.5\) and calculate the maximum compression of the spring.

Q9. An elevator can carry a maximum load of \(1800\,\mathrm{kg}\) (elevator + passengers) and is moving up with a constant speed of \(2\,\mathrm{m\,s^{-1}}\). The frictional force opposing the motion is \(4000\,\mathrm{N}\). Determine the minimum power delivered by the motor to the elevator in watts as well as in horse power.

Q10. Slowing down of neutrons: In a nuclear reactor a neutron of high speed (typically \(10^7\,\mathrm{m\,s^{-1}}\)) must be slowed to \(10^3\,\mathrm{m\,s^{-1}}\) so that it can have a high probability of interacting with isotope \(^{235}\mathrm{U}\) and causing it to fission. Show that a neutron can lose most of its kinetic energy in an elastic collision with a light nucleus like deuterium or carbon.

Q11. Consider the collision depicted in Fig. 5.9 to be between two billiard balls with equal masses \(m_1=m_2\). The first ball is called the cue while the second ball is called the target. The billiard player wants to 'sink' the target ball in a corner pocket, which is at an angle \(\theta_2=37^\circ\). Assume that the collision is elastic and that friction and rotational motion are not important. Obtain \(\theta_1\).