Consider the situation of the previous problem. Take the table and the ball is then an intenal force. As the ball slows down the momentum of the system decreases. Which external force is responsible for this change in the momentum?

Newton's.. . law of motion shows the relation between external force acting on the object and change in its momentum.

The rate of change of total momentum of a many -particle system is proportional to the external force/sum of the internal forces on the system .

A ball of mass m collides horizontally with a stationary wedge on a rough horizontal surface, in the two orientations as shown. Neglect friction between ball and wedge. Two student comment on system of ball and wedge in thses situations Saurav : Momentum of system in x- direction will change by significant amout in both cases. Rahul : There are no impulsive external forces ijn y- directions in both cases hence the total momentum of system in y-directions can be treated as conserved in both cases .

Statement I: No external force acts on a system of two spheres which undergo a perfectly elastic head-on collision. The minimum kinetic energy of this system is zero if the net momentum of the system is zero. Statement II: If any two bodies undergo a perfectly elastic head-on collision, at the instant of maximum deformation. the complete kinetic energy of the system is converted to' deformation potential energy of the system.

Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : (a) Show p=p_(i).+m_(i)V where p_(i) is the momentum of the ith particle (of mass m_(i) ) and p_(i).=m_(i)v_(i). . Note v_(i). is the velocity of the i^(th) particle relative to the centre of mass Also, prove using the definition of the centre of mass Sigmap_(i).=0 (b) Show K=K.+(1)/(2)MV^(2) where K is the total kinetic energy of the system of particles, K. is the total kinetic energy of the system when the particle velocities are taken with respect to the centre of mass and (1)/(2)MV^(2) is the kinetic energy of the translation of the system as a whole (i.e. of the centre of mass motion of the system). The result has been used in Sec. 7.14). (c ) Show vecL=vecL.+vecRxxvec(MV) where vecL.=Sigmavec(r_(i)).xxvec(p_(i)). is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember vec(r._(i))=vec(r_(i))-vecR , rest of the notation is the velcities taken relative to the centre of mass. Remember vec(r._(i))=vec(r_(i))-vecR rest of the notation is the standard notation used in the chapter. Note vecL , and vec(MR)xxvecV can be said to be angular momenta, respectively, about and of the centre of mass of the system of particles. (d) Show vec(dL.)/(dt)=sumvec(r_(i).)xxvec(dp.)/(dt) Further, show that vec(dL.)/(dt)=tau._(ext) where tau._(ext) is the sum of all external torques acting on the system about the centre of mass. (Hint : Use the definition of centre of mass and Newton.s Thrid Law. Assume the internal forces between any two particles act along the line joining the particles.)

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. Which of the following may be concluded from the information in the passage?

To demonstrate the process of thermoelectric production with a model. Apparatus and materials: Pressure cooker, pipe, tennis ball, metal sheet, dynamo, bulb. Procedure : rarr Take a table-tennis ball and make three slits into it. rarr Put semicircular fins cut out of a metal sheet into these slits. rarr Pivot the tennis ball on an axle through its centre with a straight metal wire fixed to a rigid support. Ensure that the tennis ball rotates freely about the axle. rarr Now connect a cycle dynamo to this. rarr Connect a bulb in series. rarr Direct a jet of water or steam produced in a pressure cooker at the fins. Note down your observation. Observation : The bulb gets lighted. Which energy conversion do you think is taking place in this model ?