# Ball rolling down a ramp

1. Jun 18, 2007

### 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.

2. Jun 18, 2007

### Staff: Mentor

3. Jun 18, 2007

### 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.

4. Jun 19, 2007

### Staff: Mentor

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.

5. Jun 19, 2007

### Staff: Mentor

The OP did say "no friction".

6. Jun 19, 2007

### Staff: Mentor

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

7. Jun 19, 2007

### Staff: Mentor

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

What can you do? :grumpy:

8. Jun 20, 2007

### hover

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.

9. Jun 21, 2007

### Chronos

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

10. Jun 23, 2007

### 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.

11. Jun 23, 2007

### 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.