Acceleration of the inclined plane ?

[subho123]

acceleration of the inclined plane ?

Homework Statement

A block of mass m is placed on an inclined plane. the angle of inclination is θ. now i want to understand in which direction (horizontal) the plane should be accelerated so that the block on it doesn't move.

Homework Equations

The Attempt at a Solution

now all the time the block has a downwards acceleration because of one of the components of its weight which is mgsinθ. now the plane should be moved in such a way that a component of the force exerted on the plane should nullify mgsinθ.

If a force F is applied on the plane towards the inclined surface (parallel to base) then it has two components , Fcosθ (parallel to the the surface) & Fsinθ (against the weight). now it's actually increasing the accln of the block.

2ndly, if i want to find the accln (a) of the plane then i have to use then force F which is Ma (M is the mass of the plane not the block, which is not given). then i can i find a.

am i thinking right..or not...i think i am not getting the concept of it...please help me...

 

[proculation]

If you have an inclined plane, the best way to resolve that problem is to 'turn' your axis.

The X should be in the direction of the movement and the Y should be perpendicular to the plane. That way you remove the sinus and cosines.

 

[subho123]

sorry..i didn't get it..can u please explain it briefly...

 

[proculation]

The axis X and Y are arbitrary. They can be like a "cross" (normally) but you can put turn them like you want to simplify your equations.
here is a schema

 

[proculation]

red are axis.

blue are forces.

and green is theta.

 

[subho123]

i understand...thanks..but i want to know the horizontal direction of the force to be applied on the plane & also the accn the plane gets from the force satisfying that the block on the plane doesn't move. i want to get the concept that if the same force is exerted on the plane in opposite direction (i.e the plane gets the same accn but in opposite direction) then why we cannot stop the block from sliding down.

hope i have asked my question clearly

 

[proculation]

what is 'accn' ?

 

[subho123]

well "accn" means acceleration...:shy:

 

[proculation]

You're thinking it backwards.

Newton said F=MA.

You do not want to look for the acceleration. You want to look for the forces.

 

[subho123]

ok...actually i can calculate the acceleration of the plane so that the block doesn't move...but , i am confused with the direction the force should be exerted to ...i mean, is the direction an issue regarding the force that to be exerted on the plane so that the block doesn't move...?? more pricisely , will the force F(Ma) and - F( - MA) give the same result regarding the problem written above ?

 

[proculation]

Do you want the block to move ? I think no.

So: the Sum of the Forces = Mass X acceleration = 0

In X, and in Y.

It's call a static state.

Since it doesn't move, acceleration = 0. So the sums of the forces must be 0

You separate the forces in X and in Y with sinus and cosines. They all equal 0.
You resolve both equations to find the two unknown variables.

 

[rl.bhat]

A block of mass m is placed on an inclined plane. the angle of inclination is θ. now i want to understand in which direction (horizontal) the plane should be accelerated so that the block on it doesn't move.

If you refer the figure in the post#5, the inclined plane should accelerate towards right to keep the block at rest.
If M and m are the masses of plane and the block respectively, gthen the acceleration of the plane is
a = F/(m+M) where F is the force parallel to the base.

Since the block is free to move, due to inertia, the block will accelerate in the opposite direction of the force. The component of this acceleration along the plane in the upward direction is a*cosθ.
Τo keep the block at rest a*cosθ = mg*sinθ

 

[proculation]

A block of mass m is placed on an inclined plane. the angle of inclination is θ. now i want to understand in which direction (horizontal) the plane should be accelerated so that the block on it doesn't move.

If you refer the figure in the post#5, the inclined plane should accelerate towards right to keep the block at rest.
If M and m are the masses of plane and the block respectively, gthen the acceleration of the plane is
a = F/(m+M) where F is the force parallel to the base.

Since the block is free to move, due to inertia, the block will accelerate in the opposite direction of the force. The component of this acceleration along the plane in the upward direction is a*cosθ.
Τo keep the block at rest a*cosθ = mg*sinθ

So my schema was not so bad :P