Velocity down an inclined plane

[blade_chong]

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 =)

 

[Hootenanny]

Does it mean that the velocity of the ball is always increasing on its way down since V² is proportional to S?

Yes.

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.

 

[blade_chong]

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. =)