Velocity down an inclined plane

In summary, the velocity of the ball on an inclined plane will always increase as it travels down, as shown by the equation V2=2(gsinθ)S. This means that if the plane was infinitely long, the velocity of the ball would continue to increase until it reaches a significant proportion of the speed of light. However, it should be noted that the equations used are based on Newtonian mechanics and become invalid at high speeds, requiring the use of Special Relativity.
  • #1
blade_chong
33
0
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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  • #2
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.
 
  • #3
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. =)
 

1. What is the formula for calculating velocity down an inclined plane?

The formula for calculating velocity down an inclined plane is V = √(2ghsinθ), where V is the velocity, g is the acceleration due to gravity, h is the height of the incline, and θ is the angle of the incline.

2. How does the angle of the incline affect the velocity down an inclined plane?

The angle of the incline affects the velocity down an inclined plane by changing the component of gravity that acts parallel to the incline. The steeper the incline, the greater the component of gravity and therefore, the greater the velocity.

3. Can the velocity down an inclined plane ever be negative?

No, the velocity down an inclined plane cannot be negative. The velocity is always a positive value, as it represents the speed at which an object is moving down the incline.

4. How does friction affect the velocity down an inclined plane?

Friction can either increase or decrease the velocity down an inclined plane depending on the direction of the force. If the friction force acts in the opposite direction of the velocity, it will decrease the velocity. However, if the friction force acts in the same direction as the velocity, it can increase the velocity by providing a push in the same direction.

5. What are the units for velocity down an inclined plane?

The units for velocity down an inclined plane are meters per second (m/s). This is the standard unit for velocity in the SI system of measurement.

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