# Block on inclined plane

• Parallel
In summary, gravity always acts downwards and if you want something to stay at rest, you need to use a vertical force in the opposite direction to balance the weight

#### Parallel

hello,i'm having some trouble with this problem.

a block with mass m,rests on a frictionless plane,inclined at angle alpha relative to the horizon.

what is the acceleration 'a' of the plane,if we don't want the block to slide down the plane?

here's what I've tried:
the x-axis will be parallel to the plane,so

x axis:
mgsin(/alpha) = macos(alpha)
==>a= g tan(alpha)

Is this o.k?

because it looks weird,if I don't want the block to slide,why am I "saying" in the equation it does?
or maybe because it's relative to an inertial frame?

thanks

Last edited:
It looks ok. In order for the block to rest, another force must act on in in the direction of the incline to balance the component of the weight along the incline. This very force must come from the acceleration of the block.

You can think about your result, too. If you put alpha = 0, then you get a = 0, which makes sense, doesn't it?

o.k

so now I'm thinking what if alpha=90 deg.

tangent doesn't like pi/2 :)

Yes, because it's undefined at pi/2. You could take a limit when alpha -> Pi/2, and you'd get infinity. Which would mean you'd need an infinite acceleration.

are you saying that,if I put a block on a vertical plane,there's no way I could keep this block at rest,by accelerating the plane?

Parallel said:
are you saying that,if I put a block on a vertical plane,there's no way I could keep this block at rest,by accelerating the plane?

Nope, at least not in this world.

do you have an intuitive explanation for this phenomena?

The only explanation you need is that gravity acts downwards all the time, and to balance it, you need a vertical force which acts in the opposite direction, which can't be accomplished if the force has no vertical component, i.e. if it only acts in the horizontal direction.

I got it.

thanks alot

## What is a block on an inclined plane?

A block on an inclined plane is a common physics problem where a block or object is placed on a sloped surface and the force of gravity is acting on it.

## What is the relationship between the angle of the inclined plane and the block's weight?

The angle of the inclined plane has a direct impact on the weight of the block. As the angle increases, the weight of the block increases as well.

## How does friction affect a block on an inclined plane?

Friction is an important factor in the motion of a block on an inclined plane. It opposes the motion of the block and can be calculated using the coefficient of friction and the normal force.

## What is the formula for calculating the force of gravity on a block on an inclined plane?

The formula for calculating the force of gravity on a block on an inclined plane is Fg = mgsinθ, where Fg is the force of gravity, m is the mass of the block, g is the acceleration due to gravity, and θ is the angle of the inclined plane.

## How does the height of the inclined plane affect the motion of the block?

The height of the inclined plane affects the motion of the block by increasing the potential energy of the block as it moves up the slope. This potential energy is then converted into kinetic energy as the block moves down the slope.