Respuesta :
Answer:
The total work done is 5997.6 J
Solution:
As per the question:
Mass of the bag, m = 60 kg
Vertical distance, h = 9 m
Mass lost, m' = 12 kg
To calculate the amount of work done:
Lost mass is proportional to the square root of the distance covered while lifting:
m' ∝ [tex]\sqrt{h}[/tex]
m' = [tex]K\sqrt{9}[/tex]
where
K = proportionality constant
12 = 3K
K = 4
Mass of the floor containing bag at a height h:
[tex]m(h) = 60 - k\sqrt{h}[/tex]
Work done is given by:
[tex]W = \int_{0}^{h}m(h)gdh[/tex]
[tex]W = \int_{0}^{9}(60 - k\sqrt{h})gdh[/tex]
[tex]W = g([60h]_{0}^{9} + 4\times \frac{2}{3}[h^{\frac{3}{2}}]_{0}^{9})[/tex]
[tex]W = 9.8\times ([60\times 9 - 0] + \frac{8}{3}[9^{\frac{3}{2}} - 0^{\frac{3}{2}}])[/tex]
[tex]W = 9.8\times (540 + \frac{8}{3}\times 27) = 5997.6\ J = 5.9976\ kJ[/tex]
Answer:
The amount of work done in lifting the bag is -20109.6 N-m
Explanation:
Given that,
Mass of bag = 60 kg
Distance = 9 m
Loss of mass = 12 kg
The number of pounds lost is proportional to the square root of the distance traversed
Mass of the bag containing flour at height is
[tex]m(y)=60-k\sqrt{y}[/tex]
Put the value into the formula
[tex]60-k\sqrt{y}=12[/tex]
[tex]k=144[/tex]
We need to calculate the work done
Using formula of work done
[tex]W=\int_{0}^{9}{m(y)gdy}[/tex]
Put the value into the formula
[tex]W=\int_{0}^{9}{(60-k\sqrt{y})gdy}[/tex]
[tex]W=((60y-\dfrac{2k}{3}\times y^{\frac{3}{2}}})_{0}^{9})\times9.8[/tex]
Put the value of y
[tex]W=(60\times9-\dfrac{2\times144}{3}\times 9^{\frac{3}{2}})\times9.8[/tex]
[tex]W=-20109.6\ N-m[/tex]
Hence, The amount of work done in lifting the bag is -20109.6 N-m
