Answer:
work done lifting the bucket (sand and rope) to the top of the building,
W=67.46 Nm
Explanation:
in this question we have given
mass of bucket=20kg
mass of rope=[tex].2\frac{kg}{m}[/tex]
height of building= 15 meter
We have to find the work done lifting the bucket (sand and rope) to the building =work done in lifting the rope + work done in lifting the sand
work done in lifting the rope is given as,[tex]W_{1}=Force \times displacement[/tex]
=[tex]\int\limits^{15}_0 {.2x} \, dx[/tex] ..............(1)
=[tex].1\times 15^2[/tex]
=22.5 Nm
work done in lifting the sand is given as,[tex]W_{2}=Force \times displacement[/tex]
[tex]W_{2}=\int\limits^{15}_0 F \, dx[/tex].................(2)
Here,
F=mx+c
here,
c=20-18
c=2
m=[tex]\frac{20-18}{15-0}[/tex]
m=.133
Therefore,
[tex]F=.133x+2[/tex]
Put value of F in equation 2
[tex]W_{2}=\int\limits^{15}_0 (.133x+2) \, dx[/tex]
[tex]W_{2}=.133 \times 112.5+2\times15\\W_{2}=14.96+30\\W_{2}=44.96 Nm[/tex]
Therefore,
work done lifting the bucket (sand and rope) to the top of the building,[tex]W=W_{1}+W_{2}[/tex]
W=22.5 Nm+44.96 Nm
W=67.46 Nm
