A cable with a linear density of 2 kgm is used to lift an 80

Solution

Question:

A cable with a linear density of 2 kg/m is used to lift an 800 kg load of coal up a mineshaft 200 m deep. Find the work done in lifting the coal and cable.

Solution:

we need to find

W = F dx

where F is force and dx is small change in distance

we have a fixed load of 800kg and a variable load of cable

we have intially cable of lenght 200m and finally 0m

at a distance x from top means there is x m of cable left

F = 800*g + x*2*g

assuming g = 10 m/s^2(we can choose 9.8 m/s^2 also just to simplify calculations i am choosing 10)

F at a distance x is

F = 8000+20x N

W = fromm 200 to 0 (8000+20x) dx

    = 8000x+10x^2] from 200 to 0

    = 8000*200+10*(200)^2

    = 2000,000 J

   = 2000 kJ

we need to do 2000kJ of work with taking g=10m/s^2

if we took g = 9.8m/s^2 we get

   = 1960000

   = 1960 kJ

we get 1960kJ of work needs to be done