Question

If an object is moving at `8 m/s` over a surface with a kinetic friction coefficient of `u_k=64 /g`, how far will the object continue to move?

Answer 1

The distance is `=0.5m`

Explanation:

The coefficient of kinetic friction is

`mu_k=F_r/N`

Let the mass of the object be `=mkg`

Then,

The normal force `N=mg`

The acceleration due to gravity is `g=9.8ms^-2`

Therefore,

`F_r=mu_kN=mu_kmg`

But according to Newton's Second Law

`F=ma`

Therefore,

`ma=mu_kmg`

The decelleration is `a=mu_kg`

Apply the equation of motion

`v^2=u^2+2as`

`0=8^2-2mu_kgs`

`mu_k=64/g`

The distance is

`s=64/(2*64/g*g)=1/2=0.5m`