Object sliding down an inclined plane

In summary, the conversation revolves around a physics problem involving an object with a starting velocity of 3 m/s on an inclined plane. The question is to find the velocity of the object when it reaches the bottom of the slope. The equations discussed include a=g(sin*alpha-mu*cos*alpha), v^2=v0^2-2a*h, and v^2=2as. It is determined that there is not enough information provided to solve the problem, but it is possible to solve it using a formula that includes all the variables. The discussion also touches on the power of using general formulas to solve problems and the fact that there is an actual numerical answer to the problem. The conversation ends with a suggestion for the student
  • #1
Antrox
13
0

Homework Statement


First of all, here is how it goes: an object with a starting velocity of 3 m/s reaches the height of 0.3m (inclined plane) and then it "stops" and slides down. What will be the velocity when it reaches the bottom of the inclined plane ?
(Sorry if the terms are wrong, English is not my native language :P).

Homework Equations


a=g(sin*alpha-mu*cos*alpha) ??
v^2=v0^2-2a*h ??
v^2=2as ??
i seriously don't know :/

The Attempt at a Solution


I seriously tried a lot of things. The problem is, I don't have enough data to calculate it (or do i?, I am fairly new so i don't know). No angle, no length, no time, no acceleration etc...
 
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  • #2
Antrox said:
an object with a starting velocity of 3 m/s reaches the height of 0.3m (inclined plane) and then it "stops" and slides down. What will be the velocity when it reaches the bottom of the inclined plane ?
You're right, there's not enough information. Have you quoted the whole question word for word?
Does it start at the bottom of the slope? If not, you'll need to know how high it starts.
Is there any friction?
 
  • #3
Its pushed from the bottom, starting speed of 3m/s and reaches the height of 0,3m. No info on friction.
 
  • #4
Antrox said:

Homework Statement


First of all, here is how it goes: an object with a starting velocity of 3 m/s reaches the height of 0.3m (inclined plane) and then it "stops" and slides down. What will be the velocity when it reaches the bottom of the inclined plane ?
(Sorry if the terms are wrong, English is not my native language :p).

Homework Equations


a=g(sin*alpha-mu*cos*alpha) ??
v^2=v0^2-2a*h ??
v^2=2as ??
i seriously don't know :/

The Attempt at a Solution


I seriously tried a lot of things. The problem is, I don't have enough data to calculate it (or do i?, I am fairly new so i don't know). No angle, no length, no time, no acceleration etc...

If you assume the object starts at the bottom of the slope and that there is friction on the slope, then you should have enough information to solve this.

Think about acceleration going up the slope compared with acceleration coming down the slope. The formula you have above is correct for one of these.
 
  • #5
I still don't quite get it, can you solve it ?
 
  • #6
Antrox said:
I still don't quite get it, can you solve it ?

Yes. You need to work through the equations and trust that the unknowns (angle and coeff of friction) will cancel out, which they do!

You have the necessary equations above.
 
  • #7
All 3 ? Or just the 2nd and 3rd ?
 
  • #8
Antrox said:
All 3 ? Or just the 2nd and 3rd ?

You only need ##v^2 = 2as##. And, of course, the formula for acceleration up and down.
 
  • #9
But i don't have s, only h (height)
 
  • #10
Antrox said:
But i don't have s, only h (height)
Which is exactly what you need. Put in unknowns for whatever you don't know (coefficient of friction, angle of slope) and see what happens.
 
  • #11
I don't get it xD
 
  • #12
Antrox said:
I don't get it xD

It's possible to solve physics problems when everything is unknown: initial speed, angle, coeff of friction, height gained. The solution, however, will be a function of all the variables. That, after all, is what the equations of motion are: general equations, where all quantities are unknown.

So, it must be possible to solve this problem. The answer will be a function of all the variables. So, it might be something like:

v (at bottom of slope) = velocity at start - gh*coeff of friction*tan(angle) - ... (some long complicated function)

There's nothing stopping you working out this formula, even if it gets very complicated.

But, it's possible that it doesn't get complicated at all! It's possible that things like angle and coeff of friction might cancel out and leave a simple formula.

How I started was this:

Let ##u## be the initial velocity at the bottom of the slope (u = 3m/s)

Let ##h## be the height gained (h = 0.3m)

Let ##\theta## be the angle of the slope

Let ##s## be the distance traveled up the slope

Let ##\mu## be the coefficient of friction.

Let ##g## be the acceleration due to gravity.

Let ##v## be the final velocity at the bottom of the slope.

I then worked out ##v## in terms of ##u, h, \theta, s, \mu \ and \ g##

But, ##\theta, s, \mu## all canceled out, leaving me with a nice equation for ##v## in terms of ##u, g \ and \ h##

Then, of course, I plugged ##u = 3## and ##h = 0.3## into the equation.

This is a good problem, as it shows the power of maths and general formulas to solve problems, even if you only know some of the variables.
 
  • #13
So there isn't a "real" solution to this ? Like, the velocity when the object reaches the bottom of the slope is 7 m/s (random number) ?
 
  • #14
Antrox said:
So there isn't a "real" solution to this ? Like, the velocity when the object reaches the bottom of the slope is 7 m/s (random number) ?

One answer to that question is that you'll never find out unless you try to solve the problem yourself.

But, yes there is an answer in terms of an actual number of m/s. If that's important to you!
 
  • #15
I seriously don't understand what formula to use. This isn't a homework or anything btw, i found this in a book and it got me interested so yeah. But seems like its un-solvable, atleast for me. I am only 15 tho, haven't studied about half of the things required to solve this :/
 
  • #16
Antrox said:
I seriously don't understand what formula to use. This isn't a homework or anything btw, i found this in a book and it got me interested so yeah. But seems like its un-solvable, atleast for me. I am only 15 tho, haven't studied about half of the things required to solve this :/
You worked out ##a = gsin(\theta) - \mu gcos(\theta)##

That is actually the acceleration on the way down. So, can you see what the deceleration is on the way up?

Then just use ##u^2 = 2as## for the motion up and ##v^2 = 2as## on the way down.

(I tend to use all positive quantites for a problem like this, as I find it easier. So, everything above is positive.)
 
  • #17
Yeah but, what is a then ?
I am very confused, sorry xd
 
  • #18
Antrox said:
Yeah but, what is a then ?
I am very confused, sorry xd

Maybe this problem is a bit hard.

On the way up, both gravity and friction are slowing the block, so we have:

##a_1 = gsin(\theta) + \mu gcos(\theta)##

On the way down, gravity is accelerating the block and friction is slowing it down, so we have:

##a_2 = gsin(\theta) - \mu gcos(\theta)##

Do you want to try to progress it from there?
 
  • #19
I understand that, but we DONT KNOW what the sin and cos of the angles are, that's the thing.
 
  • #20
Antrox said:
I understand that, but we DONT KNOW what the sin and cos of the angles are, that's the thing.
Neither do I. And I don't know what ##\mu## is either. You can't let an unknown angle stop you!

Seriously, just keep going. You'll get formulas with ##\theta## and ##\mu##for a while, but eventually you can get rid of them.
 
  • #21
The thing is, I still haven't studied about trigonometry and friction in school.
 
  • #22
If you know the answer to the velocity when the object reaches the bottom of the plane, please tell me.
If you don't know the answer, then never mind.
 
  • #23
Antrox said:
If you know the answer to the velocity when the object reaches the bottom of the plane, please tell me.
If you don't know the answer, then never mind.

On the way up, I got:

##u^2 = 2a_1s = 2(gsin(\theta) + \mu g cos(\theta))s##

On the way down:

##v^2 = 2a_2s = 2(gsin(\theta) - \mu g cos(\theta))s##

Then, I added those together to get:

##u^2 +v^2 = 2(2gsin(\theta))s = 4gsin(\theta)s##

Finally, I saw that:

##h = sin(\theta)s##

So:

##u^2 +v^2 = 4gh## or ##v^2 = 4gh - u^2##

You have to admit that's neat!
 
  • #24
That is pretty powerful, thanks so much ! <3
 
  • #25
Antrox said:
That is pretty powerful, thanks so much ! <3

An even better approach is using conservation of energy:

##KE_1 = PE + W_f## (Initial Kinetic energy = gravitational potential energy gained + work done by friction (on way up)

This becomes

##\frac{1}{2}mu^2 = mgh + W_f##

And

##KE_2 = PE - W_f## (the work done by friction is the same on the way down as on the way up)

So:

##\frac{1}{2}mv^2 = mgh - W_f##

Add these equations to get the same result as before.

This time you only need the unknown mass of the block.
 
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1. What is the force that causes an object to slide down an inclined plane?

The force that causes an object to slide down an inclined plane is gravity. The force of gravity acts on the object in a downward direction, pulling it towards the center of the Earth. This force increases as the angle of the incline increases.

2. How does the angle of the inclined plane affect the speed of the object?

The angle of the inclined plane affects the speed of the object by changing the amount of force acting on the object. The steeper the incline, the greater the force of gravity and the faster the object will accelerate down the plane. However, other factors such as friction and air resistance also play a role in determining the speed of the object.

3. What is the relationship between the mass of the object and its acceleration down the inclined plane?

The relationship between the mass of the object and its acceleration down the inclined plane is inversely proportional. This means that as the mass of the object increases, its acceleration decreases. This is because a greater mass requires a greater force to overcome its inertia and move down the incline.

4. How does the coefficient of friction affect the motion of the object down the inclined plane?

The coefficient of friction is a measure of the resistance to motion between two surfaces in contact. The higher the coefficient of friction, the greater the force of friction acting on the object. This force opposes the motion of the object down the incline, causing it to slow down.

5. Can an object ever reach a constant velocity while sliding down an inclined plane?

Yes, an object can reach a constant velocity while sliding down an inclined plane if the force of gravity is balanced by an equal and opposite force, such as air resistance. This is known as terminal velocity, and it occurs when the force of gravity can no longer accelerate the object any further. The object will continue to move at a constant speed until it reaches the bottom of the incline.

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