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## A Numerical for Practice

Akshay posted a numerical:
1. A disk of mass m=50g slides with zero initial velocity down an incline plane set at an angle 30 degrees to the horizontal. Having traversed the distance of 50 cm along the horizontal plane, the disc stops. Find the work performed by friction forces over the whole distance. Assume friction coefficient is 0.15 for both horizontal and incline planes.

## Derive an expression for the minimum horizontal velocity to be given to a ball hanging vertically from a point so that it is able to just complete a vertical circular path.

While pushing, we are giving the ball some kinetic energy which will be converted to potential energy as it moves upward. If the whole kinetic energy is converted to potential energy at the top most point, it will fall straight down, resulting in only a semicircle. For the ball to continue the path, it should have a centrifugal force equal to weight of the body when it is at the topmost point.

let V be the initially applied velocity and v be the velocity at the topmost point

mv²/r = mg

v²/r = g

v² = rg

v = √(rg)

Potential Energy at the topmost point , Ep = 2mgr

Ep is the difference in kinetic energy between initial point(Ei) and at topmost point(Et).

Ei – Et =  Ep

½mV² – ½mv² = 2mgr

½m(V²-v²) = 2mgr

V²-v² = 4gr

V² = 4gr + v²

V² = 4gr + rg

V² = 5rg

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## Projectile motion – A problem from real life situation

Three identical stones are thrown with the same initial speed from the top of a cliff into the river below. atone 1 is launched at an angle of 20 degrees above the horizontal; stone 2 at an angle 20 degrees below the horizontal; and stone 3 directly along the horizontal. just before entering the river, which stone has the greatest speed?

## Friction – a numerical

a force of 20 N is applied parallel to the surface of a horizontal table is just sufficient to make a block of mass 4.kg move on the table calculate the coefficient of friction between the block and the table

## Acceleration of a body on a rough surface

A black of mass 1.5kg placed on a rough horizontal surface is pulled by a constant horizontal force of 1.2kg wt. the cofficient of friction between the block and the surface is 0.3.  Find acceleration produced in terms of g.

(Posted by Ankur Srivastava)

Applied force, F=1.2 kg wt = 1.2g N (where g is the acceleration due to gravity)

Friction f=µmg=0.3 x 1.5 x g=0.45g N

The net force = ma

Therefore;

ma= F-f

=> 1.5 x a = 1.2 g -0.45g=0.8 g

or

a = (0.8/1.5)g

## Path of an object

If a man tossed a coin in a moving train and the coin fell back . Then in which type of motion train is moving? and how?

CHANDRIMA

For the person who tosses the coin the motion is vertically upward if he do so. But for an observer outside the train the path of the stone is a parabola.This is due to the horizontal velocity of the stone.

If the stone fell back, it means that the train is accelerated. If it were moving with a constant velocity, then the stone would’ve reached back to his hands only as both the train and the stone possess the same horizontal velocity.

## Tossing a coin in a moving train.

if a man tossed a coin in a moving train and the coin fell back then in which type if motion train is moving? and how?

Answer: This shows that the train is accelerated. When the coin was thrown, it had the same velocity of the train. If the train was not accelerated, the coin would have fallen on to the hands of the man itself. But the accelerated train moves a greater horizontal distance than by the coin.

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