How high does the frictionless ramp have to be for the ball....

In summary: If you have a picture, you can see that the ball has to have the same speed at the top of the loop as it does at the bottom. Otherwise, it will just slide back and forth.
  • #1
mailmas
46
0

Homework Statement


What minimum height does the frictionless ramp have to be for the ball to be able to travel along the ramp into a loop upside down and not fall?
Radius of loop = .3m

Homework Equations


PE + KE = PE + KE

The Attempt at a Solution


mgh_1=mgh_2 + 1/2 mv^2
h_1 = h_2 + v^2/(2g)

h_2 = .3m[/B]
Am I on the right track?
 
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  • #2
Is there a picture that goes with the question? If there is, please post it.
 
  • #3
kuruman said:
Is there a picture that goes with the question? If there is, please post it.
No :(
 
  • #4
If this is a "loop-the-loop" problem (as I suspect) then your solution is incorrect. If the ball starts at a height equal to the radius, then it can only rise to the same height of 0.3 meters on the other side and slide back. Energy conservation is part of the solution. The other part is that the ball must have enough speed at the top of the loop. How much speed is "enough" must be determined with a free body diagram, which is the remaining part of the solution. Even if you don't have a picture, you need to draw one in order to see what's going on.
 
  • #5
kuruman said:
If this is a "loop-the-loop" problem (as I suspect) then your solution is incorrect. If the ball starts at a height equal to the radius, then it can only rise to the same height of 0.3 meters on the other side and slide back. Energy conservation is part of the solution. The other part is that the ball must have enough speed at the top of the loop. How much speed is "enough" must be determined with a free body diagram, which is the remaining part of the solution. Even if you don't have a picture, you need to draw one in order to see what's going on.

Would speed be determined by: FN = mv^2/r - mg = 0
 
  • #6
mailmas said:
Would speed be determined by: FN = mv^2/r - mg = 0
Yes.
 

1. How does the angle of the frictionless ramp affect the distance the ball travels?

The angle of the frictionless ramp does not affect the distance the ball travels. In theory, the ball will continue to roll at a constant speed on a frictionless ramp regardless of the angle.

2. Is there a specific height that the frictionless ramp needs to be for the ball to reach a certain distance?

No, there is no specific height that the frictionless ramp needs to be for the ball to reach a certain distance. The distance the ball travels is determined by the initial velocity of the ball and the angle of the ramp, not the height of the ramp.

3. Does the weight of the ball affect the height of the frictionless ramp needed for it to reach a certain distance?

The weight of the ball does not affect the height of the frictionless ramp needed for it to reach a certain distance. However, a heavier ball may require a greater initial velocity to reach the same distance as a lighter ball.

4. How do other factors, such as air resistance or surface friction, affect the height of the frictionless ramp needed for the ball to reach a certain distance?

Other factors, such as air resistance and surface friction, can significantly affect the height of the frictionless ramp needed for the ball to reach a certain distance. These factors can slow down the ball and reduce its distance travelled, requiring a higher ramp height to compensate.

5. Can the height of the frictionless ramp be calculated using a specific equation?

There is no single equation that can be used to calculate the height of the frictionless ramp needed for a ball to reach a certain distance. The required ramp height depends on multiple factors, including the initial velocity of the ball, the angle of the ramp, and any external forces acting on the ball.

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