The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
(e) work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed $V$. If the collision is elastic, which of the following (Fig. 6.14) is a possible result after collision ?

Underline the correct alternative :
(d) In an inelastic collision of two bodies, the quantities which do not change after the collision are the...

The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
(d) work done by an applied force on a body moving on a rough horizontal plane with uniform velocity,

Answer carefully, with reasons :
(b) Is the total linear momentum conserved during the short time of an elastic collision of two balls ?

The blades of a windmill sweep out a circle of area $A$. (b) What is the kinetic energy of the air ?

The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
(a) work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.

A family uses 8 kW of power. (b) Compare this area to that of the roof of a typical house.

The blades of a windmill sweep out a circle of area $A$. (c) Assume that the windmill converts 25% of the wind’s energy into electrical energy, and that $A = 30 \text{ m}^2$, $v = 36 \text{ km/h}$ and the density of air is $1.2 \text{ kg m}^{-3}$. What is the electrical power produced ?

Answer carefully, with reasons :
(c) What are the answers to (a) and (b) for an inelastic collision ?

A body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1. Compute the
(a) work done by the applied force in 10 s,

The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
(b) work done by gravitational force in the above case,

A molecule in a gas container hits a horizontal wall with speed $200 \text{ m s}^{-1}$ and angle $30^{\circ}$ with the normal, and rebounds with the same speed. Is momentum conserved in the collision ? Is the collision elastic or inelastic ?

State if each of the following statements is true or false. Give reasons for your answer.
(d) In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

Given in Fig. 6.11 are examples of some potential energy functions in one dimension. The total energy of the particle is indicated by a cross on the ordinate axis. In each case, specify the regions, if any, in which the particle cannot be found for the given energy. Also, indicate the minimum total energy the particle must have in each case. Think of simple physical contexts for which these potential energy shapes are relevant.

                                     

Answer carefully, with reasons :
(a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ?

A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of $0.05 \text{ kg s}^{-1}$. What is the speed of the trolley after the entire sand bag is empty ?

A pump on the ground floor of a building can pump up water to fill a tank of volume $30 \text{ m}^3$ in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump ?

An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy 10 keV, and the second with 100 keV. Which is faster, the electron or the proton ? Obtain the ratio of their speeds. (electron mass = $9.11 \times 10^{-31}$ kg, proton mass = $1.67 \times 10^{-27}$ kg, 1 eV = $1.60 \times 10^{-19}$ J).

A body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1. Compute the
(d) change in kinetic energy of the body in 10 s,
and interpret your results.