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

In summary: For tests 1 and 2, the ball rolled down the ramp in .333 and .4 seconds, respectively. For test 3, the ball rolled down the ramp in .6 seconds. Based on these results, it appears that the ball will take the same amount of time to get to the bottom of the ramp regardless of the ramp angle. Additionally, since all of the tests were conducted with a gravitational acceleration of 9.8 meters per second squared, the ball's weight on the ramp will be 9.8 meters.
  • #1
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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:biggrin:.
 
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  • #3
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
Chronos said:
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.
 
  • #5
The OP did say "no friction". :wink:
 
  • #6
Doc Al said:
The OP did say "no friction". :wink:

Doh! But they also said "roll" (well, they said "role"), so it was a trick question! :grumpy: Oh well.
 
  • #7
Good point! They should have said "ball sliding down a ramp". :smile:

What can you do? :grumpy:
 
  • #8
berkeman said:
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.
 
  • #9
It is a simple vector problem with G as the only force.
 
  • #10
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
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.
 

What is the concept of a ball rolling down a ramp?

The concept of a ball rolling down a ramp is a basic example of the law of gravity and the effects of potential and kinetic energy. When the ball is placed at the top of the ramp, it has potential energy due to its position. As it rolls down the ramp, this potential energy is converted into kinetic energy, which allows the ball to move.

What factors affect the speed of a ball rolling down a ramp?

The speed of a ball rolling down a ramp can be affected by several factors, including the steepness of the ramp, the surface of the ramp, and the mass of the ball. A steeper ramp will result in a faster speed, while a rough surface or a heavier ball will slow the ball down.

How does the height of a ramp affect the distance a ball will roll?

The height of a ramp can affect the distance a ball will roll because it determines the potential energy the ball has at the top of the ramp. The higher the ramp, the more potential energy the ball has, and therefore, it will roll a greater distance before coming to a stop.

What is the relationship between the angle of the ramp and the force of gravity on the ball?

The angle of the ramp directly affects the force of gravity on the ball. As the angle of the ramp increases, the force of gravity pulling the ball down the ramp also increases. This is because a steeper ramp means the ball has to overcome a greater vertical distance, resulting in a stronger pull from gravity.

What is the difference between static and kinetic friction in regards to a ball rolling down a ramp?

Static friction is the force that keeps an object at rest from moving. In the case of a ball rolling down a ramp, static friction is what keeps the ball from moving until it is pushed or released. Kinetic friction is the force that opposes the motion of an object already in motion. In the case of a ball rolling down a ramp, kinetic friction is what slows the ball down as it rolls on the surface of the ramp.

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