- #1

UchihaClan13

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## Homework Statement

Air of density ρ, moving with velocity v strikes normally on an inclined surface (having area A) of a wedge of mass m kept on a horizontal surface. Collisions are perfectly elastic (No loss of kinetic energy). Minimum coefficient of static friction between wedge and the horizontal surface, for the wedge to be stationary, is[/B]

## Homework Equations

Force imparted to the wedge=

**ρ*A*v^2**

Forces exerted are broken down into their respective components[/B]

## The Attempt at a Solution

Breaking down the force (exerted by the air collisions)on the wedge into components we get,

**ρ*A*v^2costheta + mg= N(the normal force exerted by the ground surface on the wedge)****[/B][/B][/B][/B][/B][/B][/B][/B]**

**Here i assumed that the wedge will be in equilibrium in the y-direction**

and in the x-direction(after drawing the f.b.d of the wedge),one can see that

and in the x-direction(after drawing the f.b.d of the wedge),one can see that

**ρ*A*v^2sintheta - f**_{friction}= m*a(here a is zero since in the question it says so)**now comes the hardest part**

we know that

static friction is self adjustingt

so for the minimum coefficient of static friction,i first assumed that the friction force wouldn't be equal to the limiting friction and got stuck with an inequality

Fwe know that

static friction is self adjustingt

so for the minimum coefficient of static friction,i first assumed that the friction force wouldn't be equal to the limiting friction and got stuck with an inequality

F

_{friction}≤ [PLAIN]https://upload.wikimedia.org/math/9/3/9/939974a71dda1b83cce5ab82a2d2cec1.png(mg +**ρ*A*v^2costheta) hence i left this case**

and now took the frictional force as limiting friction yielding [PLAIN]https://upload.wikimedia.org/math/9/3/9/939974a71dda1b83cce5ab82a2d2cec1.png=[B][B][B][B][B]ρ*A*v^2sintheta/([B][B][B]ρ*A*v^2costheta + mg)

However my answer doesn't match with the actual answer

I think i am going wrong somewhere or i might have overlooked the "collisions are elastic" or i might have made a wrong assumptionand now took the frictional force as limiting friction yielding [PLAIN]https://upload.wikimedia.org/math/9/3/9/939974a71dda1b83cce5ab82a2d2cec1.png=[B][B][B][B][B]ρ*A*v^2sintheta/([B][B][B]ρ*A*v^2costheta + mg)

However my answer doesn't match with the actual answer

I think i am going wrong somewhere or i might have overlooked the "collisions are elastic" or i might have made a wrong assumption

Anyways,as usual

Help is much appreciated!:)[/B]

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