Inclined Planes and Acceleration

[itinerantphysicist]

Inclined Planes and Acceleration
Hi, I'm new to this forum and basically to physics itself, as I have previously concentrated my attention on the mathematical areas of calculus and algebra. I'm currently a sophomore at an Australian Catholic high school and have been recently tasked with a non-assessable project to increase our understanding of physics in our junior and senior years in addition to our gradeable assignment tasks.

The project poses the following question: "A bearing ball is released down an inclined plane at angle theta. The inclined plane leads down to a flat surface. What is the relationship between the angle of the inclined plane and the distnace traveled along the flat surface after it comes off the inclined plane?"

The assignment asks that I prove this by utilising three ancient or modern ideas of motion in relation to gravity etc. I have decided to use Galileo's formula of a = g(sin theta) and his theory of diluted and constant gravity across a glat surface.

Does anyone know how I can apply Newton's Laws (ie F = Ma) and suggest any other basic theories (my teacher explained that any excessively complicated theories will not be accepted as proof!) which could help prove and demonstrate the relationship between the angle of the inclined plane and the distance traveled along the flat surface?

With Thanks,

K. Grimberg

 

[cookiemonster]

You haven't specified the problem enough.

However, assuming that the ball always starts from the same height on the ramp, the angle should have little to do with it. The only thing the angle does is determines how long it takes the ball to fall down the ramp; it does not change the velocity of the ball when it comes off the ramp. The only difference it poses is that the steeper ramp will exert less friction on the ball as it's coming down, which I'd call a pretty negligible difference (but maybe somebody will disagree). Once the ball's off the ramp, the balls will behave exactly the same.

Just a note: in a perfect magical physics world where friction doesn't exist, the ball will roll forever.

cookiemonster

 

[itinerantphysicist]

So, the angle has nothing to do with it because the velocity of the ball is the same at the end of the ramp?

 

[cookiemonster]

The first thing that needs to be done is specify the problem more specifically.

Does the ball start at the same height off the ground, regardless of the angle (this would mean that some ramps woud be longer)? Are you including friction in your model?

cookiemonster

 

[itinerantphysicist]

No specifics were provided on height or friction were provided. I suppose I can assume the height of the ramp is always the same.

 

[cookiemonster]

Then it's all up to friction.

If you're not considering friction, the ball will roll an infinite distance.

If you are considering friction, refer to my second post.

cookiemonster

 

[itinerantphysicist]

Using Newton's Second Law, how can I then apply F = ma to the fact that the ball will always rollthe same distance basically regardless of the inclination?

 

[HallsofIvy]

"tasked with a non-assessable project "
The teachers should be arrested for abusing the language!


"relationship between the angle of the inclined plane and the distnace traveled along the flat surface "

As pointed out above, you will have to make some assumptions as to friction. No friction and the ball will roll forever, regardless of angle. It is also true, as others have said, that the original height is the crucial point, not angle. However, since the problem specifically asked about "relationship between the angle and..." it probably would be better to assume the ball starts at a specific distance up the inclined plane. In that case, with d that distance and θ the angle, the height is d sin(θ). The acceleration down the inclined plane would be g sin(θ).

 

[itinerantphysicist]

According to Galileo, the speed of the ball at the end of the inclined plane is always the same. Can I assume this is the horizontal velocity and acceleration? How do I discover the speed?