Can a Single-Wheel Foam Roller Win a Physics Ramp Contest?

[microdoodle]

Homework Statement

I have this Physics Contest where you have to create an object that will roll down a 6 feet ramp which is positioned at a 7 degree angle above ground. The object can not have more than one contact with the ground(For example you cannot have two wheels touching the ground there can only be one). Also, the object can not be heavier than 5 pounds. The object must make two full revolutions by the end of the 6 feet ramp to be eligible.

Homework Equations

The Attempt at a Solution

So i am thinking about making a cylindrical object which has the maximum allowed radius and made of some type of material so it will be 5 pounds. What are your thoughts? Should the Circle be hollow and wide or thin and filled? Or do you believe it shouldn't be a cylinder at all? I would appreciate any comments on this experiment Thank you for your feedback

 

[Delphi51]

A marble or a doughnut will work . . . are there any objectives other than reaching the bottom in at least 2 turns?

 

[microdoodle]

A marble or a doughnut will work . . . are there any objectives other than reaching the bottom in at least 2 turns?

Well...The point of the competition is to win and i doubt a marble will win the contest unless it is 5 pounds. Reaching the bottom in two turns is not the objective its just a rule to limit the size of the object the objective is to have the fastest overall object. With that said do you think a sphere would come in first or a cylinder? I would greatly appreciate your feedback.

 

[Delphi51]

Oh - fastest! Now it is getting interesting.
I must confess that I am a retired high school physics teacher, and I loved the grade 12 mystery experiment of rolling things of various shapes down ramps. The students were supposed to use PE at the top = KE at the bottom to figure out how fast they were going, and predict how far they would fly when they rolled over the countertop edge at that speed. The predictions were a disaster - they never went as far as predicted, and some shapes were worse than others. They did spheres, cylinders and rings.

The reason the students did not predict correctly was that they did not quite know about a kind of energy that you do know if you are doing a college physics class. What is missing from
PE at top = 1/2*m*v^2 at bottom? I hate to give away the answer to the mystery, so please give it some thought! Once you know the missing form of energy, you will probably know its formula and how the formula varies with the shape of the rolling object. You will also be able to solve for the v at the bottom and see if the mass matters.

 

[Delphi51]

Have you thought of racing some marbles and things down a ramp to see which is best?
A socket from a set of mechanic's tools makes a pretty good hollow cylinder. And you can try various sizes to see if that makes a difference. Have fun!

 

[microdoodle]

Have you thought of racing some marbles and things down a ramp to see which is best?
A socket from a set of mechanic's tools makes a pretty good hollow cylinder. And you can try various sizes to see if that makes a difference. Have fun!

Thank You, So far I tried racing a hollow pipe and a pipe filled with weights with the exact same radius. The pipe filled with weights won. Because making objects takes a lot of time and my time is limited I want to know what will go faster...
Object A
Plastic object completely filled
5 inch radius
Thus because of a small radius the plastic pipe is a lot wider due to the 5 pound limit

Object B
Plastic object completely filled
10 inch radius
Thus because of a large radius plastic pipe is a lot thinner due to the 5 pound limit

Thank you for your feedback

 

[Dadface]

To give a clue what would reach the bottom first and why,an object which rolls down or the same object which slides down?

 

[microdoodle]

To give a clue what would reach the bottom first and why,an object which rolls down or the same object which slides down?

I don't clearly understand your question but the ramp is wooden and if an object slides it will create a lot of friction so i believe roll down is the answer?

 

[Delphi51]

Suppose the coefficient of friction was negligible - then would the roller or slider win?
We are giving you a CLUE here!

 

[microdoodle]

Suppose the coefficient of friction was negligible - then would the roller or slider win?
We are giving you a CLUE here!

roller

 

[Delphi51]

No, the roller will lose! It wastes energy in that other form I mentioned.
Also, I bet a marble or ball of any size - will beat your piece of pipe.

Other questions to work out - will mass affect the time for a frictionless slider? How about for a roller?

In case you need to lay in supplies before Sunday, you might want to make sure you have a light, soft foam ball and a small, dense marble or ball bearing.

 

[microdoodle]

No, the roller will lose! It wastes energy in that other form I mentioned.
Also, I bet a marble or ball of any size - will beat your piece of pipe.

Other questions to work out - will mass affect the time for a frictionless slider? How about for a roller?

In case you need to lay in supplies before Sunday, you might want to make sure you have a light, soft foam ball and a small, dense marble or ball bearing.

mass does affect the time so the heavier the weight the better and what do you mean by slider? Thank you for all of your help

 

[Delphi51]

mass does affect the time

For zero friction, the force along the ramp is mg*sin(A). Set that equal to ma, and you see the acceleration is g*sin(A) and does not depend on the mass. To understand that, imagine each molecule of the sliding mass going independently. They all go at the same acceleration.

The same thing happens for the rolling mass, though the math is more complex. Check it out by racing a marble vs a baseball.

So don't worry about the mass of your object - as long as it is under the maximum you are okay. Might as well make it small so it fits in your pocket!

 

[microdoodle]

For zero friction, the force along the ramp is mg*sin(A). Set that equal to ma, and you see the acceleration is g*sin(A) and does not depend on the mass. To understand that, imagine each molecule of the sliding mass going independently. They all go at the same acceleration.

The same thing happens for the rolling mass, though the math is more complex. Check it out by racing a marble vs a baseball.

So don't worry about the mass of your object - as long as it is under the maximum you are okay. Might as well make it small so it fits in your pocket!

Wow! Thank you for all of your help I would have never of thought that mass did not matter. now I don't have to spend a week constructing an object Thank You

 

[Delphi51]

Once you have the IDEA it will take you only a few minutes to convert your foam ball into a killer roller! They will all laugh when you bring out your foam ball, but you'll get the last laugh after it kills the competition. Write "physicsforums.com" on the side?

Have you thought of the reason why the roller goes slower than the frictionless slider and what its extra form of energy is?