How Does an Elevator's Movement Affect a Block on an Incline?

[holezch]

Homework Statement

A block, mass m, slides down a frictionless incline making an angle theta with an elevator floor. Find its acceleration relative to the incline when:
a) elevator descends at a constant speed
b) elevator ascends at a constant speed
c) elevator descends with a constant acceleration c1) what is the force exerted on the block by the incline?

d) elevator descends with a decelerating acceleration

e) elevator cable breaks..

Homework Equations

The Attempt at a Solution

I think I may have an idea of what to do.. could someone what force would be in play if an object starts accelerating down a ramp because it;s in an elevator and that elevator starts moving down? (what is that? the wind?? I don't know :S)

thank you

 

[holezch]

unless the descending elevator exerts any "extra" force on the block, wouldn't the acceleration of the block just be the effect of gravity?

 

[holezch]

okay, for part a) I rotated the axis and said that the acceleration relative to the incline is gsintheta.. my reasoning was because the elevator the block is moving in is moving at a constant speed, so it doesn't affect the blocks movement (no idea why, just an intuitive guess..) so it's just the force of gravity that is the acceleration.. could anybody tell me why the constant speed wouldn't matter if I'm correct?

thank you

 

[silentwf]

For part a/b
Think: if the elevator ascends/descends with a constant speed, what's its acceleration?

Hint:
$$a = \frac {\Delta v}{t}$$

For parts c/d, the equation you'd want to use is
$$a_{t} = g sin\theta$$
And think about Newton's third law too, it should be enough to help you solve these two parts

last part..."FREE FALL BABY!" Umm... excuse me
You could simply put a coin on your hand and lower your hand at a=g, and you'll find out :)

 

[holezch]

For part a/b
Think: if the elevator ascends/descends with a constant speed, what's its acceleration?

Hint:
$$a = \frac {\Delta v}{t}$$

For parts c/d, the equation you'd want to use is
$$a_{t} = g sin\theta$$
And think about Newton's third law too, it should be enough to help you solve these two parts

last part..."FREE FALL BABY!" Umm... excuse me
You could simply put a coin on your hand and lower your hand at a=g, and you'll find out :)

okay so if the elevator moves with a constant speed, it has no acceleration? how do I find the "acceleration of the block relative to the incline"? the language kind of throws me off, I'm not entirely sure what I'm looking for.. thank you for the reply!

EDIT: OH! is that why there is no effect on the block from the movement of the elevator? because the elevator doesn't accelerate?

 

[holezch]

I think for part c) it is like this: gsintheta - asintheta.. the elevator goes down with an acceleration A, so everything inside the elevator is moving down with an acceleration A relative to the ground.. so the block exerts a force f = mA on the incline and by the 3rd law, the incline exerts the same force back on the block. the block slides down by gravity, rotating the axis we get gsintheta, and as it moves down the force exerted up by the incline retards its movement by some f = m(asintheta) so the acceleration would be gsintheta - asintheta
can someone confirm my answers please? see my first answer as well thank you!

 

[holezch]

and for the elevator going down with decelerating acceleration, following the same logic, you get gsintheta + asintheta.. then using that same logic again for the cable breaking, you get that the force exerted back on the block from the incline is gcostheta + gsintheta.. but since we know that it only slides down, the gcostheta cancels out (it has no vertical acceleration) and we are left with gsintheta - gsintheta = 0

 

[silentwf]

You should combined some of your posts lol
Ok, so any how, about your answer to part a/b, its correct
The reason is like this, according to Newton's first law, things in motion are always in motion, still things are still, unless a force acts upon them.
Now, since a = 0 for a/b, there is no force (since F=ma), so the block will not be affected.

As for parts c/d: think (sorry, I'm going to make you think) what it's like in an elevator. When it goes up, what do you feel? Do you feel lighter or heavier? What about when it goes down? Do you feel lighter or heavier?

 

[holezch]

You should combined some of your posts lol
Ok, so any how, about your answer to part a/b, its correct
The reason is like this, according to Newton's first law, things in motion are always in motion, still things are still, unless a force acts upon them.
Now, since a = 0 for a/b, there is no force (since F=ma), so the block will not be affected.

As for parts c/d: think (sorry, I'm going to make you think) what it's like in an elevator. When it goes up, what do you feel? Do you feel lighter or heavier? What about when it goes down? Do you feel lighter or heavier?

when the elevator goes down, the elevator floor exerts a force back on you in the opposite direction, so you get gsintheta - asintheta

 

[silentwf]

Yep. So then...all solved :)