How High Will the Ball Bounce on an Inclined Plane?

In summary, when a ball falls onto an inclined plane at an angle α with respect to the horizontal, it will bounce elastically and reach a maximum height h. The vertical speed after impact can be calculated using the formula v_y = √(2gh)cos(2α). The angle of incidence and reflection are equal, and the vertical component of the final velocity can be determined by drawing a diagram and finding the angle between the initial and final velocity vectors.
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Faefnir
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A ball, which can be regarded as pointin all its effects, falls steady , subject only to the weight force, on an inclined plane of an angle α with respect to the horizontal from a height h computed from the impact point. The ball bounces elastically. Get the d height can reach the ball and the falling parabola characteristics after the impactAfter impact vertical speed:

$$ v_{y} = \sqrt{2gh} \cos (2 \alpha) $$Why ## \cos (2 \alpha) ##? There is a mathematical explanation for this? Yes, I know about vectorial speed components, but why exactly this corner?
 
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  • #2
What's the relationship between the angle of incidence and the angle of reflection when something bounces elastically off of a surface?
 
  • #3
angle of incidence = the angle of reflection
 
  • #4
Faefnir said:
angle of incidence = the angle of reflection
Right! So draw yourself a diagram of the initial and final (pre and post collision) velocity vectors, showing the angle between them. Then find the vertical component of that final velocity.
 
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What is an inclined plane?

An inclined plane is a simple machine that consists of a flat surface that is tilted at an angle. It is commonly used to make it easier to move objects from a lower to a higher level by reducing the amount of force needed.

How does an inclined plane work?

An inclined plane works by transforming the direction of the force needed to move an object. Instead of lifting an object straight up, an inclined plane allows the force to be applied at an angle, which requires less effort.

What is the relationship between the angle of the inclined plane and the force needed to move an object?

The force needed to move an object up an inclined plane is directly related to the angle of the incline. The steeper the angle, the more force is needed to move the object. As the angle decreases, the force needed also decreases.

How does friction affect the movement of an object on an inclined plane?

Friction is the resistance to motion between two surfaces. In the case of an inclined plane, friction can make it more difficult to move an object up or down the plane. The amount of friction depends on the roughness of the surfaces and the weight of the object.

What is the advantage of using an inclined plane?

The main advantage of using an inclined plane is that it reduces the amount of force needed to move an object. This makes it easier and more efficient to move heavy objects, especially when compared to lifting them straight up. Inclined planes are also simple and inexpensive machines.

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