A leaky 10-kg bucket is lifted from the ground to a height of 12 m at a constant speed with a rope that weighs 0.5 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. Find the work done. (Use 9.8 m/s2 for g.) Show how to approximate the required work by a Riemann sum. (Let x be the height in meters above the ground. Enter xi* as xi.)

The work done is 3645.6 J or 3.6 kJ

Step-by-step explanation:

M1 = (0.5 kg/m)(12 - x m) = (6 - 0.5x) kg

At the height of x meters (0<=x<=12), the mass of the rope is,

M2 = (36kg/12m)(12 - x m) = (36 - 3x m) kg

At the height of x meters (0<=x<=12), the mass of the water is,

M3 = 10 kg

The mass of the bucket is 10 kg

Then, Total mass M is,

M = M1 + M2 + M3 = (6 - 0.5x) + (36 - 3x) + 10 = (52 - 3.5x) kg

From Force F = mass m * acceleration due to gravity g

Force = mass x gravity

F = 9.8(52 - 3.5x) Newtons

To get the work done W,

Follow the attached file,

The work done is 3645.6 J or 3.6 kJ

true

step-by-step explanation:

according to the national european world center, the engineering of the ford company on elon musk's flame throwers proved the globalization of the natural wallabies and therefore, results in the growth product domestication in almonds.