Velocity down an inclined plane

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When a ball is released from the top of an inclined plane, its velocity increases as it descends, with V² being proportional to the displacement (S). In a theoretical scenario with an infinitely long inclined plane, classical physics suggests that the ball's speed could approach infinity, as there is no upper limit in Newtonian Mechanics. However, this only holds true at relatively low speeds; once the ball reaches a significant fraction of the speed of light (c), Newtonian equations become invalid. At that point, Special Relativity must be applied to accurately describe the ball's motion. Thus, while the velocity increases, it cannot reach or exceed the speed of light.
blade_chong
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Imagine u have a ball on top of an inclined plane. The ball is released, hence initial velocity is zero. Assume that air resistance and friction between the surface and ball is negligible. using kinematic equations, V2=2as, where a=gsinθ, θ is the angle of inclination of the plane and s is the displacement of the ball from the top of the plane. Therefore, V2=2(gsinθ)S. Does it mean that the velocity of the ball is always increasing on its way down since V2 is proportional to S? Does it also means that if u have a infinitely long inclined plane, the velocity of the ball will keep on increasing until the speed of light is attain? Please help me to clear my doubts. Thanks =)
 
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blade_chong said:
Does it mean that the velocity of the ball is always increasing on its way down since V2 is proportional to S?
Yes.
blade_chong said:
Does it also means that if u have a infinitely long inclined plane, the velocity of the ball will keep on increasing until the speed of light is attain? Please help me to clear my doubts. Thanks =)
Classically, the speed of the ball will approach infinity, there is no upper speed limit in Newtonian Mechanics. However, you should note that since the equations you have used are derived using Newtonian mechanics they are therefore only valid for relatively low speeds. Once the speed of the ball reaches a significant proportion of c, we have to abandon Newtonian Mechanics and use Special Relativity.
 
Hootenanny said:
Yes.

Classically, the speed of the ball will approach infinity, there is no upper speed limit in Newtonian Mechanics. However, you should note that since the equations you have used are derived using Newtonian mechanics they are therefore only valid for relatively low speeds. Once the speed of the ball reaches a significant proportion of c, we have to abandon Newtonian Mechanics and use Special Relativity.

it really helps me. thanks a lot for the reply. =)
 

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