Question

An object with a mass of `7 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= 4+secx`. How much work would it take to move the object over #x in [(pi)/8, (5pi)/12], where x is in meters?

Answer 1

`W~=5,288J`

Explanation:

`W=int _(pi/8) ^ ((5pi)/12) u_k(x)* d x=int _(pi/8) ^ ((5pi)/12) (4+sec x)* d x`
`W=[4x+ l n(sec x+tan x)] _(pi/8) ^ ((5pi)/12)`
`W=[(20pi)/12 +l n(sec (5pi)/12+tan (5pi)/12)]-[(4pi)/8+l n(sec (pi)/8+tan (pi)/8)]`
`W=[(5pi)/3+l n(3,864+3,732)]-[pi/2+l n(1,082+0,414)]`
`W=[(5pi)/3+ l n (7,596) ]-[pi/2+l n(1.496)]`
`W=[(5pi)/3+2,028]-[pi/2+0,403]`
`W=[7,261]-[1,973]`
`W~=5,288J`