Smooth rolling ball rolls down hill, how far can it fly?

In summary, the conversation discusses solving a problem involving kinetic energy and gravity. The participants suggest using algebra and considering the geometry of the object, specifically the inertia of a solid ball, to determine the velocity at a certain point. It is noted that mass is not relevant in this type of problem and the correct answer is obtained through the equation.
  • #1
Addez123
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21
Homework Statement
A solid ball rolls smoothly from rest (At 6m) until it leaves the ramp (at 2m). How far horizontally from point 'a' does the ball hit the ground?
Hint: Smooth rolling means it does not slide.
Relevant Equations
v = ωr
a = αr
##K = \frac {1}{2}Iω^2 + \frac {1}{2}mv^2##
1570557570516.png

Figure of the problem.

There are many exercises like these, and I've read the whole chapter and I got no clue where to start here.
Kinetic energy from gravity is: E = mgh = 39.3m
I could try change v to ωr in the K equation but it will leave me nowhere because I don't have the mass nor the radius of the ball.
I'm obviously looking for the velocity at point v, assuming it has no vertical component (altho that's not specified either), but I have no way of getting it.

Anyone has a clue what to do here?
 
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  • #2
Do algebra. In the end what is requested is a distance...so write it down using r and v and m. Stuff will cancel.
 
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  • #3
Addez123 said:
I could try change v to ωr in the K equation but it will leave me nowhere because I don't have the mass nor the radius of the ball.

Given that gravity acts equally on all masses, the mass in a gravitational problem such as this is never relevant.

Not quite so obvious is that for rolling without slipping, only the geometry of an object is relevant. All solid spheres roll downhill under gravity at the same rate; all hollow spheres at the same rate; all solid cylinders at the same rate etc.

As @hutchphd suggests, if you do the algebra you'll see this for yourself - in this case for solid spheres.
 
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  • #4
@hutchphd @PeroK did the equation, it canceled out and I got the right answer.
It's true, all that matters is the Inertia of the solid ball.
 
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Related to Smooth rolling ball rolls down hill, how far can it fly?

1. How does the speed of the ball affect its flying distance?

The speed of the ball does not directly affect its flying distance. However, a faster rolling ball will have more kinetic energy and therefore more potential to travel further when it becomes airborne.

2. What factors influence the flying distance of the ball?

The main factors that influence the flying distance of the ball are the initial speed and angle of the ball, the shape and weight of the ball, the surface it is rolling on, and the presence of any external forces such as wind or friction.

3. Can the shape of the ball affect its flying distance?

Yes, the shape of the ball can have a significant impact on its flying distance. A more streamlined shape will experience less air resistance and may travel further compared to a less aerodynamic shape.

4. What is the maximum possible flying distance for a rolling ball?

The maximum possible flying distance for a rolling ball is dependent on various factors such as the initial speed and angle, the surface it is rolling on, and the presence of any external forces. Therefore, it is difficult to determine an exact maximum distance without specific information about these factors.

5. How does gravity affect the flying distance of the ball?

Gravity is the main force that pulls the ball towards the ground as it rolls down the hill. The angle of the hill and the speed of the ball also play a role in determining how gravity will affect the flying distance of the ball. A steeper hill or a faster ball will experience a greater pull from gravity and may travel further when airborne.

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