Question

find the acceleration of the wedge so that m on the slanted surface will be at rest also find the normal force on m​

Answer 1

Explanation:

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For no friction force there should be no relative motion between wedge and the block.

So relative to the wedge, the component of the pseudo force along the slope acting on the block must balance the component of gravitational force along the slope.

Pseudo Force is ma, where a is the acceleration of wedge.

∴macosθ−mgsinθ=0

⇒a=gtan30 0 = 3g

Answer 2

Answer:

Method 1 : Analysis of forces on m relative to ground

IF the motion of m is analyzed from ground, its acceleration is A and the forces acting on it are its weight mg and normal reaction N. Asm is at rest, moving with same acceleration as wedge in horizontal direction but in vertical direction, the block is at rest.

∑

F

y

=0⇒Ncosθ=mg........(i)

∑

F

x

=∑m

i

a

i

⇒Nsinθ=mA.........(ii)

On solving (i) and (ii), we get A=g

tanθ and N=

cosθ

mg

Method 2 : Analysis of forces on m relative to the inclined plane

If the motion of m is analyzed from the view point of an observer standing on the inclined plane (i.e., relative to the plane), its acceleration is 0 and the forces acting on it are : its weight. the normal reaction and a pseudo force of magnitude mA towards left.

mAsinθ=mAcosθ

⇒ A=gtanθ

Also: N=mgcosθ+mAsinθ

mgcosθ+mgtanθsinθ=

cosθ

mg

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