Answer:
Workdone W = 1465.1 J
Explanation:
The weight of the water = density × volume
weight of the water = 1000 kg/m³ × 100 cm³
weight of the water = 1000 kg/m³ × 0.0001 m³
weight of the water = 0.1 kg
weight of the bucket = 5 kg
weight of the rope = [tex]2*10- 2x\\\\[/tex]
= [tex]20- 2x[/tex]
Leakage = [tex]\frac{0.1}{10} * x[/tex]
= [tex]0.01 x[/tex]
Total weight = [tex]5 + 20 - 2x - 0.01 x[/tex]
= [tex]25 - 2.01 x[/tex]
Force = wg
Force = ([tex]25 - 2.01 x[/tex])g
Force = 9.8 ([tex]25 - 2.01 x[/tex])
Finally; the amount of work spent in lifting the bucket, rope, and water is calculated as follows:
[tex]W = \int\limits^{10}_0 {(25-2.01 x)} \, 9.8 dx \\\\W = 9.8 (25x - \frac{2.01x^2}{2}})^{10}__0\\\\[/tex]
[tex]W = 9.8 (25*10-2.01*50)\\\\W = 1465.1 \ \ J[/tex]
