Pe=mgh help

That rightt there is incorrect. Joule is the unit of energy, Watt is power.

[itex]1W=1Js^{-1}[/itex] is the correct conversion.

 

Yes. A watt is work over time. Watt= Kgm^2/s^3. All of the gravitational energy will be converted to kinetic while its falling, and since power it totall energy over time, it would be 980J/1s giving you 980W or about 1.31 horsepower.

 

not quite. watts per time is an entirely different unit. dont confuse joules/time with watts/time. and yes assuming your Eg=980J and the box takes 1 second to fall, the power would be about 1.3 horsepower. allthough a box of that height would take less than a second to fall. in order to take a full second to fall it must be 4.9m above ground. assuming of course you are on earth with gravity at 9.8m/s^2. and if the height is raised, yet the energy is still 980, then the mass must be lowered.

 

If you used up all that potential energy in one second, then you would have 980watts. But it would only last one second, because you've wasted (or more accurately, converted) all of the potential into something else.

Watts is a rate per time, a joule is independent of time. Just think of distance and velocity. If I traveled 25m, are you saying my velocity is 25m/s? Well, it doesn't neccessarily have to be.

 

a joule is not independant of time. the very deffenition of a joule has time in it. (Kgm^2/s^2) with s=seconds. watt really isnt rate per time. watt itself is a rate of how fast energy can be used, or as you said more accurately, converted.

 

if it has 980 joules and it expends that in 120 seconds then your talking about 8.16watts on average. [i say average because it will fall more slowly at first and more quickly later,assuming freefall the power would depend of the speed its falling].

as far as energy is concerned. your elevated box has 980 joules of potential energy. full stop. [period in usa].

Tension is a force. VERY different from energy.

the energy you would burn up holding the 50kg weight by a rope does not contribute to the potential energy of the box. its really just chemical energy in you cells being burned away, to, i guess, eventually produce heat. yes you are using your own energy and producing power, but not mechanical work!

AS FOR TIME BEING A FACTOR. yes time is what defines POWER, power is the RATE at which you do work. if you use 1 joule of energy in 1 second then your producing 1 watt of power.

 

There isnt anymore energy there becuase the formula for gravitational potential energy is Eg=mg(delta)y. the rate would only effect the power of an object. slowing it down means its less efficent so it would be a lower number of watts. it would instead be 980J/60s. which is 16.33 watts, or 16.33J/s. the energy from the box is still being converted from potential to kinetic just like before even if you slow it down. so the tension would not effect that. phlegmy brings up a good point, to remember force and work are different things. FORCE is mass X acceleration. ENERGY or work can be defined as Ek=force X displacement.

 

i think where you are getting confused here is the difference in watts and joules. its better to think of watts as a rate rather than a unit. it is a unit but it is a unit of rate. the number of watts is how many joules per second an object uses. this is how much work can something get done over time. a light bulb watt rating is to show you how much energy is used every second it is on. the light will consistantly use that much energy. if it is a 100w light bulb, it will consistantly use 100joules/second. just remember to think of watts as a rate of work.

 

Gravitational potential is independent of time, as it is conservative. While you make a point that any joule has time dependence from the acceleration from the force in general, this does not hold for gravity which we assume is constant. Power is a rate of change over time. Its a time derivative. How can it not be a rate per time?

Look to the physics and not just dimensional analysis.

 

good point. i should have worded that differently. i was just trying to clear up the difference between a watt and a joule. thank you for the correction.