Why Does Mass Affect Acceleration on an Incline?

[Delonge87]

Hi,

Just a quick question that I am stuck on. If the mass were increased on a trolley moving downhill, would the acceleration increase?

Since F = Ma...i'd say it would, but just to make sure :P

Thanks

 

[dextercioby]

What are the forces that act on the (growing in mass) body & what's the acceleration...??

Daniel.

 

[Zaimeen]

When the trolley moves down, the following expression gives you the acceleration

$$a = g \sin \theta$$, where $$\theta$$ is the angle of inclination

So, what can you say about the magnitude of the acceleration if you increase the mass?

 

[arildno]

This is a meaningless exercise, since the answer depends on the unspecified direction of the momentum (relative to the trolley) of incoming particles.

 

[gschjetne]

Is it possible that this is one of the lame questions where they suppose the mass would come from nowhere? In that case acceleration to gravity is expressed as $g = \frac{G m_\textit{Earth}}{r^2{}_{Earth} }$, $G = 6.67 \times 10^{-11}$
This doesn't involve the mass of the trolly, acceleration due to gravity is independent of mass.

 

[freemind]

In theory, if the trolley could reach relativistic speeds, then its mass could in fact come from "nowhere"...(just kidding )

 

[gschjetne]

Yeah, I have actually wondered how fast stuff really can go as a result of gravity...I suppose the answer lies in black holes. I did read Stephen Hawking's A Brief History of Time, but that was over a year ago. But now we're getting off-topic...

 

[ek]

If someone were pushing or pulling the trolley in addition to the force of gravity, the acceleration would decrease, as acceleration is inversely proportional to mass. But if it is just gravity acting on the trolley, adding mass will not change the acceleration which will always be gsinx.

Of course if you're taking into account friction, then the acceleration will go down, because friction force is uN, and if you have a greater mass there will be more friction and therefore a lower acceleration.

 

[xanthym]

With only gravity involved, adding mass increases two quantities (F & m) proportionally, and hence acceleration remains constant. When other factors (friction, etc.) affect that proportionality, acceleration will change.

~~

 

[VietDao29]

Hi,

=ek
Of course if you're taking into account friction, then the acceleration will go down, because friction force is uN, and if you have a greater mass there will be more friction and therefore a lower acceleration.

That's wrong! The accerlation will NOT go down. It is:
$$a = g\times(\sin{\theta} - \mu \times \cos{\theta})$$
$\mu$ is the coefficient of friction.
Viet Dao,

 

[Chronos]

Adding a coeffecient of friction changes the question. Are you looking for a mathematical or real world solution? That is disengenuous. Frankly, I think you are trying to show how brilliant you think you are compared to us pedestrians.

 

[Chronos]

To arildno: We agree on that point. What you did not say speaks volumes.

 

[VietDao29]

Frankly, I think you are trying to show how brilliant you think you are compared to us pedestrians.

Sorry, if I make you think that... But honestly, I am not... I never want to be outstanding here..., and I am not graduated yet. So comaperd to you, I am nothing. I am just a normal man living in a this planet. I know there are a lot of people who are more intelligent than me.
I post that just because they are talking about cases that have friction force. And... is that wrong? Am I wrong?
I am sorry if I ever make you guys think that I am trying to show how brilliant am I. Sorry...
Viet Dao,