- #1
patricks1
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Member advised to use the homework template for posts in the homework sections of PF.
Hi, everyone, this is my first time posting.
I have a problem set that states "A machine at a packaging facility places stationary packages of mass m onto a horizontal conveyor belt that is moving packages steadily and horizontally at speed v. Once placed on the belt, the packages start moving at speed v; that is, they are rapidly accelerated."
It asks that I calculate the average mechanical power required by the belt by dividing the kinetic energy per package by the time interval between packages.
I have P = 1/2 m v^2 / T.
It then asks to compute the average force the belt is applying to packages.
I have F = mv/T
Then it says "power is force times velocity so the force answer can be turned into a power answer and compared to the power you computed above."
I get P = mv^2/T
Finally, the set asks "Do you have a discrepancy? If so, why? Which answer is more correct?"
I have wracked my brain for hours on this and cannot figure out why the two power formulae do not match. I've had one idea, but it's not really leading me to an answer; using the total time interval might be messing things up because power is only concerned with the time interval over which work is done. I thought if I knew the value for that time interval and plugged in the numbers the results of the formulae would match. However, I tried assigning values to the variable and plugging then in and the formula did not match. Can someone help please? Thank you!
I have a problem set that states "A machine at a packaging facility places stationary packages of mass m onto a horizontal conveyor belt that is moving packages steadily and horizontally at speed v. Once placed on the belt, the packages start moving at speed v; that is, they are rapidly accelerated."
It asks that I calculate the average mechanical power required by the belt by dividing the kinetic energy per package by the time interval between packages.
I have P = 1/2 m v^2 / T.
It then asks to compute the average force the belt is applying to packages.
I have F = mv/T
Then it says "power is force times velocity so the force answer can be turned into a power answer and compared to the power you computed above."
I get P = mv^2/T
Finally, the set asks "Do you have a discrepancy? If so, why? Which answer is more correct?"
I have wracked my brain for hours on this and cannot figure out why the two power formulae do not match. I've had one idea, but it's not really leading me to an answer; using the total time interval might be messing things up because power is only concerned with the time interval over which work is done. I thought if I knew the value for that time interval and plugged in the numbers the results of the formulae would match. However, I tried assigning values to the variable and plugging then in and the formula did not match. Can someone help please? Thank you!