The problem is: A leaky 10-kg bucket is lifted from the ground to a height of(adsbygoogle = window.adsbygoogle || []).push({});

12 m at a constant speed with a rope that weighs 0.8 kg/m. Initially the

bucket contains 36 kg of water, but the water leaks at a constant rate and

finishes draining just as the bucket reaches the 12 m level. How much work

is done?

Work = Force*Distance

Force = Mass*Acceleration

Mass = Volume*Density

So, Force = Volume*Density*Acceleration

don't know how relevent some of those are...

For work that does not have a constant force

Work = the definate intregral of [tex]\int[/tex] f(x)dx,

f(x) being the force.

Acceleration = 9.8 m/s^2

Density of Water = 1000 kg/m^3

I put the bounds of my integral as being [0,12]. x is the depth of the bucket

so x = 0 is the top and x = 12 is the bottom

36/12 = 3 kg/m water lost

Force = ((36-3x) + 10 + 0.8x)*9.8

Take the Integral of Force from 0 to 12

Answer = 3857.28 J

Does this look right?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integrals of Force

**Physics Forums | Science Articles, Homework Help, Discussion**