How to Calculate the Time and Weight of a Ball Rolling Down a Ramp

[hover]

The title really says it all.
Lets say i have a ramp, 1 meter long, that is at a 32 degree tilt. I place a ball on the top of the ramp and let if role down the ramp (no friction). 1. How long should it take for the ball to get near the bottem and 2. Since the ball is falling what is the ball's weight on the ramp?

I am hoping that you guys will give me the equations to help me solve this on my own.

 

[berkeman]

Post moved to Homework Help forums -- please post homework and coursework questions in the appropriate Homework Help forum, not in the general forums.

And on this question, you need to show us what you have done so far. What equations have you considered using? Do you know how to apply the concept of "moment of inertia" to this problem?

http://en.wikipedia.org/wiki/List_of_moments_of_inertia

http://en.wikipedia.org/wiki/Moment_of_inertia

 

[Chronos]

In a free fall, the initial acceleration is, of course 9.8m/s^2. When you roll the ball down a ramp, it is no longer in free fall, albeit the gravitational attraction remains the same. It now becomes a vector problem. The downward force is known, the inclination of the ramp is known - looks pretty pythagorean. Note that the ball will achieve the same velocity at the bottom of the ramp as it would have had it free fallen vertically the same distance.

 

[berkeman]

Note that the ball will achieve the same velocity at the bottom of the ramp as it would have had it free fallen vertically the same distance.

I don't think that's true. As long as there is friction on the ramp, some energy gets stored in the rotational kinetic energy (depending on the moment of inertia). There is no such energy storage term in the free-falling ball case.

 

[Doc Al]

The OP did say "no friction".

 

[berkeman]

The OP did say "no friction".

Doh! But they also said "roll" (well, they said "role"), so it was a trick question! Oh well.

 

[Doc Al]

Good point! They should have said "ball sliding down a ramp".

What can you do?

 

[hover]

And on this question, you need to show us what you have done so far. What equations have you considered using? Do you know how to apply the concept of "moment of inertia" to this problem?

http://en.wikipedia.org/wiki/List_of_moments_of_inertia

http://en.wikipedia.org/wiki/Moment_of_inertia

Well that is what i really don't know. I really have no clue on what equations to use. What i do know what should be taken into consideration is the acceleration of gravity (9.8 meters/sec), the tilt of the ramp in degrees and the length of the ramp, but how would i formulate this into an equation?

I just finished getting numbers from 3 real experiments, so maybe those will help.

 

[Chronos]

It is a simple vector problem with G as the only force.

 

[hover]

Ok, so for the 3 real experiments i conducted, these are the results.

" test 1


ball rolling down slope with a 49.74 degree angle

height=14.5 inches
hypotenuse=19 inches

took .333 sec to hit ground


test 2

ball rolling down hill with slope of 37.24 degree angle

height=11.5 inches
hypotenuse=19 inches

took .4 to .4666 sec to hit ground


test 3

ball rolling down a hill with a slope of 21.61 degree angle

height=7 inches
hypotenuse=19 inches

took .6 sec to hit ground"

I still don't know how i would be able to calculate how long it would take for a ball to get to the bottem of the ramp.

 

[Chronos]

Measure the vertical displacement. Calculate the free fall time for that distance. Visualize how that must vary as the ramp angle increases, and the answer should become apparent.