Question

An object with a mass of `6 kg` is on a surface with a kinetic friction coefficient of `8`. How much force is necessary to accelerate the object horizontally at `7 m/s^2`?

Answer 1

Consider,

where `mu_k = 8.0` (which is like super glue!).

Recall Newton's second law,

`SigmaF_y = F_N - mg = 0`
`=>F_N = mg`

`therefore F_N = 6kg * (9.8m)/s^2 = 58.8N`

Hence,

`SigmaF_x = F_a - F_"fr" = ma`

`=> F_a - mu_k*F_N = ma`

`=> F_a = m(a+mu_k*F_N)`

`therefore F_a = 6kg * ((7m)/s^2 + 8.0*58.8N) approx 3kN`

That's some serious work we need to do!