Jumping on a Moving Bus: Conservation of Momentum?

[nirvana1990]

Hello, I'm a little confused on what seems like a simple problem!

If you are on a moving bus (at a constant velocity) and you are standing in the aisle then you jump directly upwards, would you move backwards or forwards relative to the bus? Or would you stay in the same place relative to the bus?

Someone suggested to me that you would move forwards in order to conserve momentum. Is this correct?

 

[berkeman]

You do not move relative to the direction that the bus is moving -- you and the bus have a constant velocity in that direction. The combined linear momentum of you and the bus in the direction of travel does not change as you jump straight up relative to the bus.

 

[nirvana1990]

Thanks for replying so quickly!
So you don't move relative to the bus? But what if you were stood on top of the moving bus?!? Would you then move backwards relative to the bus; so you'd fall of the back? If so, why does it make a difference whether you are inside the bus or on top, and therefore not contained, in the bus?

 

[HallsofIvy]

Same thing except for air resistance. You would move relative to the bus, not the ground, but there would be a "wind" tending to blow you a little bit backwards. That's the difference- if you are "contained" in the bus, then the air around you is also contained in the bus and moving at the same speed (0 relative to the bus, bus speed relative to the pavement). If you are on top of the bus, the air is motionless (assuming no wind) relative to the pavement and so is moving at the buses speed, but backwards, relative to the bus. The situation is exactly the same as if you were standing on the ground and jumped straight up while a strong wind was blowing against you.

 

[meopemuk]

Thanks for replying so quickly!
So you don't move relative to the bus? But what if you were stood on top of the moving bus?!? Would you then move backwards relative to the bus; so you'd fall of the back? If so, why does it make a difference whether you are inside the bus or on top, and therefore not contained, in the bus?

The only difference is that when you are on top of the bus, there is air pressure (aka wind) blowing in your face. If bus is moving at 60 mph, there is a 60 mph wind, which is quite strong. So, when you jump, this wind tends to push you back. If there was no air resistance, then your jumps inside and outside would be equally uneventful.

Eugene.

 

[nirvana1990]

Is it because when you are in the bus everything inside is stationary relative to each other but if you're on top of the bus (or on a skateboard) all the air molecules etc. are not stationary relative to you or the bus. Is that the difference between being inside the bus and being on top of the bus?

 

[nirvana1990]

Oh ok I see thanks for the explanations!

 

[nirvana1990]

What if the bus is now accelerating, if you're inside the bus you would move backwards wouldn't you (to oppose the force)? So if you were on top of the bus would you also move backwards relative to the bus? Like if you were on a skateboard going downhill?

 

[LURCH]

What if the bus is now accelerating, if you're inside the bus you would move backwards wouldn't you (to oppose the force)? So if you were on top of the bus would you also move backwards relative to the bus? Like if you were on a skateboard going downhill?

Exactly right. If the bus is accelerating forward, and you try to jump strait up inside it, you'll be pushed backward by the acceleration "force", and if you're on the roof, you'll be pushed backward by the air resistance plus the acceleration, and land further back than you would if the bus were traveling at a constant speed.

 

[nirvana1990]

Phew I thnk I finally understand! Thanks everyone for your help!

 

[DyslexicHobo]

Newton's first law: an object in motion stays in motion until a force acts upon it. This can definitely be applied here.