Comparing Ball Trajectories on Different Ramps

[Grapz]

Homework Statement

There are two tracks side by side, same height above ground, one ball is placed on one track, and the other one on the other track. A spring is pulled back, and it hits both of the balls with the same force.
Both ramps end at the same place.
one track looks like this : ___________________________ its straight.
the other one looks like this : ------------\___/-------------

if it is hard to tell what the second one looks like, its just a straight ramp, and then it slopes down, and it becomes straight again, then it slopes up and goes back tot he normal height.

Whiich ball will end up first at the end of the track? If ball A is on the smooth ramp and ball B is on the second ramp, the one with the depression?

Homework Equations

conservation of energy

The Attempt at a Solution

I originally believed that both would arrive at the end of the ramp at the same time. but we did t his experimentally and ball B, the one with the depression, ends up at the end of the track faster than ball A.

Why is this?

 

[learningphysics]

Think about the horizontal velocity... how is it affected by the forces involved...

how will the horizontal velocity change as it goes into the depression and comes out...

suppose in the stralight line path the horizontal velocity is v...

in the curved path, does the horizontal velocity go above v... does it ever go below? You can answer this by examining how the normal force affects horizontal velocity.

 

[Grapz]

I know there's gravity acting on the ball and a normal force that's prependicular to the surface of the ramp. So when it is going down the ramp, there is a component in the y direction, which balances out the normal force, and a conponent in the x direction, which speeds up the ball.

THe velocity then doesn't accelerate any more when it reaches the straight part of the dpression. Then as it goes up the ramp the net force is opposing the direction of motion, so it will decrease the velocity.

So basically, from what I'm thinking although I'm not sure if its right. The horizontal velocity from when it reaches the ramp to when it gets out of the ramp is either always higher or equal to the horizontal velocity of the straight line path. Thus it arrives at the endf aster?

Can you tell me if my logic seems reasonable

 

[learningphysics]

Yes, that's exactly right. good job!

The normal force increases the horizontal velocity while it goes down into the depression. Then the normal forces decreases the horizontal velocity as it goes back up, until it gets back to the original horizontal velocity...

The horizontal velocity from when it reaches the ramp to when it gets out of the ramp is either always higher or equal to the horizontal velocity of the straight line path.

exactly.