Power needed to keep conveyor belt moving at constant speed

[Janiceleong26]

1. The problem statement, all variables and given/known

Homework Equations

P=Fv
K.E = 1/2 mv²

The Attempt at a Solution

This is the examiner report:

the kinetic energy of the sand does increase by 1/2 mv² but this cannot be the only power involved (it would imply an infinite acceleration for every grain of sand landing on the belt)

Why infinite acceleration? Is it because the mass is too small?

 

[gneill]

Why infinite acceleration? Is it because the mass is too small?

It is assuming that every grain of sand (each of which has a non-zero mass) immediately goes from rest to v without passing through any intermediate speeds. This would require an instantaneous velocity change of a mass by a finite amount, which would be breaking (or at best ignoring) the actual laws of physics.

 

[Janiceleong26]

It is assuming that every grain of sand (each of which has a non-zero mass) immediately goes from rest to v without passing through any intermediate speeds. This would require an instantaneous velocity change of a mass by a finite amount, which would be breaking (or at best ignoring) the actual laws of physics.

Oh I see, thanks very much