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I seem to just not understand how relative velocities and accelerations work.

Here is a problem that I will use to ask my question:

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When the box lands, its moving 3m/s to the right, and the belt is moving 1m/s to the right. Therefore, the velocity of the box is 4m/s from an absolute point of view at the instant it lands on the belt. From the view of the belt, the velocity is 3m/s. Is this right?

So to determine the time to bring the package to rest, can't I just ignore the belt and do my work with a "ground" and a box with a velocity of 3m/s?

I know that that's wrong, I don't know how to think about this problem. Need help!

Edward Newgate
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1 Answers1

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The parcels are moving to the right at 3 m/s, and the belt is moving at 1 m/s in the same direction. The difference between these two is 2 m/s; you were wrong to state "the velocity of the box is 4 m/s from an absolute point of view". You could translate the problem into a frame of reference that is moving to the right at 1 m/s (i.e. become an observer sitting on the belt), and see how long it takes for the parcel to come to rest in that frame of reference.

While the time you calculate that way will be the time it takes the parcel to come to rest, if you want to know where the parcel is (relative to the world) you need to account for the distance your frame of reference moved during that time.

Moving at 2 m/s with a $\mu$ of 0.2, the force experienced is $\mu\cdot m \cdot g$ and the time take to come to rest is $\frac{mv}{\mu m g} = 1 \mathrm{\;s}$. In that time the belt moved 1 m, and the parcel moved $\frac12 a t^2 = 0.5\cdot 2 \cdot 1^2= 1 \mathrm{m}$ relative to the belt, for a total distance of 2 m.

Floris
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  • Why is it the difference between the two? I can't seem to grasp that. – Edward Newgate Jun 01 '15 at 04:21
  • If the parcel was moving at 1 m/s and landing on a belt going at 1 m/s, do you agree that the relative velocity difference is zero? – Floris Jun 01 '15 at 04:25
  • Also, if you could right the relative equations, that would be appreciated. – Edward Newgate Jun 01 '15 at 04:25
  • Yes, that makes sense. They are both moving at 1m/s but relative to each other they not not moving. Then, when the parcel is at 3m/s and the belt is at 1m/s, I would think that the parcel would speed up since the belt adds speed. It makes the platform move faster... but that logic doesn't work with the 1m/s example, so I don't really know how to think about this logically. – Edward Newgate Jun 01 '15 at 04:29
  • If you could direct me to further reading/videos, that might help. – Edward Newgate Jun 01 '15 at 04:33
  • Assume the belt is moving at a fixed velocity. The parcel comes in "too fast" and has to slow down to match the speed of the belt (think plane landing on aircraft carrier...) I can't think of another way to make this clear. – Floris Jun 01 '15 at 04:36