(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Corn is falling vertically down on a conveyor belt at a constant rate of 1 kg/s. The corn instantanoulsy gets the forward speed of the belt of v = 5m/s. What is the power required for the belt to maintain its velocity.

2. Relevant equations

p=mv

dp/dt=F

F*v=P

Ekin=1/2*m*v^2

3. The attempt at a solution

Well, i thought that the simple way to solve this was to say that the belt needs to apply kinetic energy to the corns. How much? 1/2*1kg*(5m/s)^2, and that every second so the effect would be 25/2 W = 12.5W.

However, that is not the correct answer according to my lecturers soloutions. He says it is 25. Well, i can think of; from a momentum kind of view. dp/dt=v*dm/dt=F

F*v=P so 5m/s*1kg/s*5m/s = 25W. What am i missing here?

Another approach. Correct me if im wrong, but the energy needed to accelerate an object from f.x. velocity 0m/s to 5m/s is independant of the actual acceleration (even though its a non conservative force friction that is doing the acceleration?). To say, it deosn't matter if a large force is acting in a short time or a weak force in a long time? So

Faverage*Δt=Δp. From kinematics constant acceleration: x-x0=(v+v0)/2*t <=> if x0 and v0 is 0: x=v/2*t. Ok, so we multiply by this in the first equation to get the work: Fav*Δt*v/2=Δp. So if the acceleration time of the corn was 1 second, then i get the same result as i would get with energy considerations = 12.5W. Is this totally wrong?

Thanks for your help!

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# Homework Help: What is the power required for the belt to maintain its velocity

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