Question

An object with a mass of `6 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= 1+3cscx`. How much work would it take to move the object over #x in [(pi)/6, (pi)/4], where x is in meters?

Answer 1

`w=int_(pi/6) ^(pi/4)mu_k(x)*m*gdx`
`w=mgint_(pi/6) ^(pi/4)(1+3cscx)dx`
`w=mgint_(pi/6) ^(pi/4)dx+3mgint_(pi/6) ^(pi/4)cscxdx`

`=mgint_(pi/6) ^(pi/4)dx+3mgint_(pi/6) ^(pi/4)cscxdx`

`= mg[(pi/4-pi/6)](pi/6)-3mgln(csc(pi/4)+cot(pi/4)-ln(csc(pi/6)+cot(pi/6)))`
pl put m=6kg
`g=9.8ms^-2`
and values from trigonometrical table and calculate
`w= 6xx9.8*pi/12-3xx6xx9.8xxln((sqrt2+1)/(2+sqrt3))J`