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ok, in my physics class i was asked to give the relation of a trolley's acceleration depending on slope angle.
could someone give me the full relationship explanation please. i know that as you increase slope angle acceleration increases, but could someone please tell me the full mathamatical/scientific relationship?
Acceleration simply means a change in speed, whether faster or slower.
that has nothing to do with my question, i know what acceleration is.Quote:
Originally Posted by [SomeGuy]
what i want to know is, what is the relationship for a trolley's acceleration rolling down a slope depending on the slope angle. (oh, and assume the slope and trolley are frictionless)
Ok. If you tile the slope this way: \, it speeds up. Tilt it this way ---, it stays stationary. This way, /, speeds up.
The steeper the slope, the higher the velocity, the more acceleration.
I would draw the forces and build up from that. Newton's second law and all that.
Yes you basicaly just rewrote what i said i already knew. Im looking for all the jargon like the sine of the angle is directly proportional...Quote:
Originally Posted by [SomeGuy]
Ah, good idea, ill do that later and see what i get. ThanksQuote:
Originally Posted by Bonsay
Oh.
Okay, say the slope is at angle @ to the horizontal. There is a weight force of the trolley which acts vertically downwards, equal to Mg where M is the mass of the trolley. To find the component of this force in the direction of the slope, you need to multiply the force by sin@. Then to find the acceleration you divide this force by the mass of the trolley M, so a = Msin@g/M = gsin@.
As sin is strictly increasing between 0 and 90 degrees, increasing @ increases sin@ and hence the acceleration a = gsin@.
You may need to read up about Newton's second law and resolving forces if some of that is confusing.
Note that this ignores the frictional force. I can go into that if you want.
I think he already knows that :)Quote:
Originally Posted by [SomeGuy]
This should be your answer slash112
thanks guys, thats a massive help
thanks guys, thats a massive help
Quote:
Originally Posted by slash112
Double duplicates?Quote:
Originally Posted by slash112
Haven't seen that in a while.
woops, that must have been because i was using my phone to do it. dont know how though, if i clicked it twice it should come up with an error message.
EDIT: hold on a minute, they are minutes apart, how'd that happen?
Behind You!
(as in there is somebody behind you who did it...spooky)
well, i took the equation which i got from xei and Specialis Sapientia, but i didnt quite understand how they got to it, i did in a way so i was able to come up with a way i understand better. and it was right, so thanks you two.
So you've understood it now? Else I can try to draw a figure to help explain it better.Quote:
Originally Posted by slash112
yes i understand it now.Quote:
Originally Posted by khh
and just to be perfectly clear with that, i have always understood that acceleration is greater on a steeper slope (obviously), but it was how to get a=gsinx, but i understand now, well there is more than one way to get it.
Yeah, I figured that :pQuote:
Originally Posted by slash112
It was how to think to find it, specifically, I meant. Good you got it, though :p
How did you get it? I don't think there's really any other way than resolving the force parallel to the slope.
well, when i say a different way i mean different substitution of f=ma etc.
Yes you resolve the force in the direction parallel to the slope and then use F=ma. That's the only way of doing it...
right, ill re-word what i said.Quote:
Originally Posted by Xei
you substituted it in one way, i substituted it in another because i didnt fully understand yours at the time. but it doesnt matter anyway because it adds up to the same thing
ACTUALLY, Acceleration is a change in speed as the object begins to move faster. Deceleration is the change in speed as the object slows down. Accerleration is not the change in speed WHETHER FASTER OR SLOWER.... Only faster. :DQuote:
Originally Posted by [SomeGuy]
No, acceleration can be used either way, while deceleration is always a lowering of speed.Quote:
Originally Posted by davej
How do you figure that?
I will accelerate my car to a stop... Doesn't sound right ha ha :D explain how it can be used both ways.
In common speech it's as you said, but in physics the definition isQuote:
Originally Posted by davej
Δv / Δt
(change in velocity divided by the time used for the change)
hhmmm learned something new. that's interesting. never knew it could go both ways. I can wait to have some people in the car and say something like I had better accelerate before i get to the stop sign HA HA :D
make it easier for him to take in.
if something is getting slower it can be called decceleration or acceleration but with a negative value
Quote:
Originally Posted by slash112
Makes sense
If you really want to confuse them, then have a look at this:Quote:
Originally Posted by davej
Acceleration also can mean a change in direction. When you turn, you are technically accelerating.
acceleration is a change in the velocity vector. Think of the velocity vector an arrow. It's significance is that if the object was to continue in motion exactly as it is doing at a given instant, then it would travel the length of the arrow in the direction that the arrow is pointing in some unit time. obviously, changing the unit of time changes the length of the arrow.