Two marbles are released to roll down two frictionless ramps. One marble rolls d

Question

Two marbles are released to roll down two frictionless ramps. One marble rolls down a short, steep ramp and the other marble rolls down a long, flat ramp. If they are released from the same heights, how will the speeds at the bottom of the ramps compare?

The marble rolling down the short, steep ramp will have the greatest speed.

The marble rolling down the long, flat ramp will have the greatest speed.

They will have the same speed at the bottom of the ramps.

There is not enough information to tell.

I want to say that it is the steep hill but since there is a lack of friction I believe they would both move at equal constant speed 10m/s^2?

Explanation / Answer

The marble rolling down the short, steep ramp will have the greatest speed.

If you increase the steepness of the ramp, then you will increase the acceleration of a marble which rolls down the ramp.

The force of gravity points straight down, but a marble rolling down a ramp doesn't go straight down, it follows the ramp. Therefore, only the component of the gravitational force which points along the direction of the marble's motion can accelerate the marble. The other component pushes the marble into the ramp, and the ramp pushes back, so there is no acceleration of the marble into the ramp. If the ramp is horizontal, then the marble does not accelerate, as gravity pushes the marble into the ramp and not along the surface of the ramp

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