Does the angle of a ramp with the ground affect velocity?

[Mr Davis 97]

I have a question. If a put a marble at the top of a ramp, will the angle that ramp makes with the horizontal affect the velocity of the marble when it arrives at the bottom of the ramp? I am suspecting no, since the gravitation potential energy does not change as we change the angle of the ramp, so when the marble arrives at the bottom, all of that potential energy must be kinetic and thus the velocity must be the same. I think that changing the angle will only affect how long it takes to reach the bottom, since all we're doing ins modifying the parallel force component. Is all of this correct?

 

[phinds]

Do you understand that velocity is a vector?

 

[davenn]

If a put a marble at the top of a ramp, will the angle that ramp makes with the horizontal affect the velocity of the marble when it arrives at the bottom of the ramp? I am suspecting no,

I think that changing the angle will only affect how long it takes to reach the bottom

do you see your own contradiction there between your 2 statements ?

if it takes less time on a steeper ramp, then the velocity must be ... ? you fill in the blank

 

[nasu]

I have a question. If a put a marble at the top of a ramp, will the angle that ramp makes with the horizontal affect the velocity of the marble when it arrives at the bottom of the ramp? I am suspecting no, since the gravitation potential energy does not change as we change the angle of the ramp, so when the marble arrives at the bottom, all of that potential energy must be kinetic and thus the velocity must be the same. I think that changing the angle will only affect how long it takes to reach the bottom, since all we're doing ins modifying the parallel force component. Is all of this correct?

Granted that the height is the same, then you are right. This will mean that you start from the same height but you can go down either by a steeper and shorter ramp or by another, less steep but longer. And if there is no friction, of course. In the first case the time on the ramp will be shorter but the acceleration will be higher.
The velocity at the base of the ramps will be the same as for a free fall from the same height. The ramp just "extends" the time necessary to reach that speed.

On the other hand, if you have a ramp with variable angle, like the ones with a hinge at the bottom, then changing the angle will change the initial height and the above will not apply.

 

[phinds]

Why am I the only one here who believes velocity is a vector ?

 

[Vatsal Sanjay]

Why am I the only one here who believes velocity is a vector ?

No, you are not the only one. Mr Davis 97 must have corrected it to speed by now. I think he meant speed.
As per the answer to the question (modified); speed at the bottom will not be dependent on the angle of the ramp, provided that

• There is no friction.
• The height of the topmost point on the ramp from the ground is same. As Mr Nasu mentioned if you have a ramp with hinge at the bottom, then the length of the ramp will be constant and height ($lsin(\theta)$ ) variable.

It is a simple energy conservation thing, $$ mgh = \frac{1}{2} mv^2 $$

if it takes less time on a steeper ramp, then the velocity must be ... ? you fill in the blank

Time will change man. Assumed ideal case, $t = (\frac{2h/sin(\theta)}{gsin(\theta)})^\frac{1}{2}$ The length of the ramp is also variable in this case. You cannot simply relate the speed's magnitude with time.

 

[nasu]

Why am I the only one here who believes velocity is a vector ?

I see what you mean (and share your belief ) but it's too late to change the word in my post above.
Of course I mean that the speed at the base is the same.

 

[USeptim]

Do you understand that velocity is a vector?

Nice to know it. In Spanish we don't have this subtle difference between speed and directional speed (velocity) :).

 

[phinds]

Nice to know it. In Spanish we don't have this subtle difference between speed and directional speed (velocity) :).

Huh. I don't see it as a "subtle" difference at all. You can't solve vector problems with a scalar and most actual mechanics problems are vector problems. How do your engineers build bridges, for example ?

 

[berkeman]

speed at the bottom will not be dependent on the angle of the ramp, provided that

• There is no friction.

I don't think that's a requirement...

 

[nasu]

What if the angle is smaller than the friction angle? What will be the speed "at the base" then?

 

[berkeman]

What's a friction angle?

 

[jbriggs444]

Why am I the only one here who believes velocity is a vector ?

Putting my pedant cap on... If the transition between ramp and ground is sharp then although the object's speed at the bottom may be well defined, its velocity at the bottom will not be.

 

[nasu]

What's a friction angle?

The angle for which the friction force equals the tangential component of the weight.
The body is in equilibrium on the incline at this angle.
http://www.thefreedictionary.com/angle+of+friction

But this is just a name. It was a short way to say that if the angle is too small and there is friction, the body won't move down the incline. The friction is just too strong.
And this was just a way to show that with friction, the angle matters.

 

[Vatsal Sanjay]

I don't think that's a requirement...

Why do you think so? If I am not wrong, the work done by friction (or say the energy dissipated by friction); assumed kinetic will depend on the horizontal distance between the starting and ending points. Now if you wish to change ramp angle without changing height, you will need to change the base length of prism. is not it true? :P

 

[berkeman]

The angle for which the friction force equals the tangential component of the weight.
The body is in equilibrium on the incline at this angle.
http://www.thefreedictionary.com/angle+of+friction

But this is just a name. It was a short way to say that if the angle is too small and there is friction, the body won't move down the incline. The friction is just too strong.
And this was just a way to show that with friction, the angle matters.

The OP said it was a marble, not a block...

 

[berkeman]

Why do you think so? If I am not wrong, the work done by friction (or say the energy dissipated by friction); assumed kinetic will depend on the horizontal distance between the starting and ending points. Now if you wish to change ramp angle without changing height, you will need to change the base length of prism. is not it true? :P

What energy dissipated by friction? It's a marble rolling down a ramp. And the OP did stipulate that the marble starts at the same height for the different experiments with different angles for the ramps, so the PE is the same before the marble starts to roll.

 

[nasu]

The OP said it was a marble, not a block...

Yes, you are right. I did not pay attention.
For a marble I think it's harder to decide if friction matters or not. How do you see it when you say that friction does not matter?
Is the ball rolling without friction? Or just sliding? If it's just sliding, won't it start to roll for some friction?

 

[Vatsal Sanjay]

OP did stipulate that the marble

My bad. I must have noticed. :(

 

[Vatsal Sanjay]

Ok! I think I need to reframe my statement for marble case. There won't be any problem if the ramp is frictionless. The marble will simply slide down.
However, if there is friction. The is going to be a specific value of friction for which the ball will be in state of pure rolling (I can go into the mathematics of it, but I don't think there is a need for it), for which the friction will be static and not kinetic and, therefore, no loss of energy (rotational plus translational kinetic included of course!). But, there is another limit to the static friction that we will need to check as well (just for being sure).
Log story short, I think the friction might be kinetic and the rolling might not be "always" pure rolling. Is that wrong?

 

[CWatters]

Nice to know it. In Spanish we don't have this subtle difference between speed and directional speed (velocity) :).

"celeridad" and "velocidad" ?

To most non technical English speakers "Speed" and "Velocity" mean the same thing. It's only in the context of physics that they are considered different. It is an important difference.