Question

An object with a mass of `5 kg` is pushed along a linear path with a kinetic friction coefficient of `u_k(x)= x^2+2`. How much work would it take to move the object over #x in [2, 5], where x is in meters?

Answer 1

`=2250 J`

Explanation:

work done against the frictional force
W `=int_2^5u_k(x)mg*dx`
`=int_2^5(x^2+2)*5*10*dx` (Given mass m = 5kg and taking g `10ms^-2`)
`=50int_2^5(x^2+2)dx`
`=50[x^3/3+2x]_2^5`
`=50[(5^3/3+2*5)-(2^3/3+2*2)]`
`=50(117/3+6)`
`=50(135/3)50*45=2250 J`
Here
`{kg*ms^-2*m=N*m=J]`