Horizontal velocity over an uneven surface

In summary, at point p, a small ball with a mass of 1kg and an initial horizontal speed of 10 m/s is at a height of 8m. When it slides over an uneven frictionless surface, it reaches a point q at a height of 3m. The speed of the ball at point q is found using the equation Ui + KEi = Uf + KEf, taking into account the normal force exerted by the surface. Initially, it was thought that the horizontal velocity would not change, but this was incorrect as the normal force does have a horizontal component that affects the speed. After solving the problem, the speed was found to be 14 m/s.
  • #1
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Homework Statement


A small ball of m=1kg at height hp = 8m at point p, is given an initial horizontal speed vp = 10 m/s. It slides over an uneven frictionless surface. What is speed vq of the ball at height hq = 3m at point q?
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Homework Equations


Ui + KEi = Uf + KEf

The Attempt at a Solution


I figured out how to find the velocity at point q, but when I first did the problem, I thought that the horizontal velocity wouldn't change because there is no horizontal force acting on the ball. The surface is frictionless, so going back to kinematics, if you throw a ball at an angle, the horizontal velocity doesn't change because gravity only acts downward, so I thought it would remain at 10 m/s. But the speed actually increased to 14 m/s after I solved it using the total energy equation.
Why was my first way wrong?
 
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  • #2
In this case the ball isn't falling, but sliding. The surface exercises a normal force on the ball that is directed perpendicular to the surface (hence the name normal). That normal force has a non-zero horizontal component, so it increases v when the ball goes down, and it slows the thing down when going uphill. Roller coaster physics !

(Of course, at Q the normal force is straight up again).
 
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  • #3
Oh I see! I forgot about the normal force here. Thanks!
 

What is horizontal velocity?

Horizontal velocity refers to the speed at which an object is moving in a horizontal direction, such as left to right or right to left.

How is horizontal velocity affected by an uneven surface?

An uneven surface can affect horizontal velocity by causing changes in the object's direction or speed due to variations in friction and gravity.

Can horizontal velocity be calculated on an uneven surface?

Yes, horizontal velocity can still be calculated on an uneven surface using the same formula: velocity = distance / time. However, the result may not accurately reflect the object's true velocity due to the impact of the uneven surface.

How does horizontal velocity over an uneven surface compare to horizontal velocity on a flat surface?

Horizontal velocity over an uneven surface is typically lower than horizontal velocity on a flat surface due to the additional forces and changes in direction caused by the uneven terrain.

Why is it important to consider horizontal velocity over an uneven surface?

It is important to consider horizontal velocity over an uneven surface because it can affect the accuracy and precision of scientific experiments and measurements. It can also impact the safety of individuals and the performance of machines or vehicles moving on uneven surfaces.

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