Speed of box from ramp to floor

[HumanDrew]

Hey, so I just finished taking a physic's test and one of the question was interesting to me. I thought it was pretty simple but my friend did the problem a different way, so I'm wondering what's the correct way to do this problem. So a box is moving down a frictionless ramp and onto the floor. The floor has a coefficient of friction and you have to find the distance it travels before stopping. I said that the speed the box has at the bottom of the ramp is the same speed the box initially has on the floor. My friend says that the speed of the box from bottom of ramp decreases when it goes onto the horizontal floor because it's approaching the horizontal floor at an angle. He told me that the vertical component of the velocity at the bottom of the ramp would be gone once it reaches the floor and your initial velocity on the floor is just the horizontal component of the velocity at the bottom of the ramp. What's the correct way to do this problem? Thanks!

 

[berkeman]

Hey, so I just finished taking a physic's test and one of the question was interesting to me. I thought it was pretty simple but my friend did the problem a different way, so I'm wondering what's the correct way to do this problem. So a box is moving down a frictionless ramp and onto the floor. The floor has a coefficient of friction and you have to find the distance it travels before stopping. I said that the speed the box has at the bottom of the ramp is the same speed the box initially has on the floor. My friend says that the speed of the box from bottom of ramp decreases when it goes onto the horizontal floor because it's approaching the horizontal floor at an angle. He told me that the vertical component of the velocity at the bottom of the ramp would be gone once it reaches the floor and your initial velocity on the floor is just the horizontal component of the velocity at the bottom of the ramp. What's the correct way to do this problem? Thanks!

The horizontal velocity as it leaves the ramp is determined by how much KE it has, which is equal to the change in PE as the box slides down the frictionless ramp from top to bottom.

 

[anorlunda]

It is hard to say how much of the vertical component of momentum p will get converted to horizontal p. If the angle was 90 degrees, the block would just crash and stop at the bottom of the ramp, with zero vertical p converted to horizontal p. If there was even a small curvature where ramp meets floor, more of the vertical p would get converted to horizontal. But with a sharp corner I am tempted to say your friend is closer to being right.

 

[berkeman]

It is hard to say how much of the vertical component of momentum p will get converted to horizontal p. If the angle was 90 degrees, the block would just crash and stop at the bottom of the ramp, with zero vertical p converted to horizontal p. If there was even a small curvature where ramp meets floor, more of the vertical p would get converted to horizontal. But with a sharp corner I am tempted to say your friend is closer to being right.

Good point. We would need the angle of the ramp and the physical size of the box to start slowing it down with friction as the leading edge contacts the floor. Were those given in the problem?

 

[HumanDrew]

Good point. We would need the angle of the ramp and the physical size of the box to start slowing it down with friction as the leading edge contacts the floor. Were those given in the problem?

This is more of an introductory physic's class that's alegbra based so it shouldn't be too hard. But angle was given but the size of box was not

 

[Khashishi]

Hopefully your teacher accepts both answers. The question is not clear.