Question

An object with a mass of `12 kg` is on a plane with an incline of `- pi/6`. If it takes `6 N` to start pushing the object down the plane and `3 N` to keep pushing it, what are the coefficients of static and kinetic friction?

Answer 1

Coefficient of Static Friction `mu_s=0.05891329277`
Coefficient of Kinetic Friction `mu_k=0.02945664639`

Explanation:

The given data:

`theta=(-pi)/6=-30^@`
mass `m=12" "`kg

Force needed to move the object down `F_s=6" "`N
Force needed to continue moving the object down `F_k=3" "`N

Compute the normal force `F_n`

`F_n=m*g*cos (pi/6)=12*(9.8)*cos (pi/6)=101.8445875" "`N

Compute for the Coefficient of Static Friction `mu_s`

`F_s=mu_s*F_n`
`6=mu_s(101.8445875)`

`mu_s=6/101.8445875`
`mu_s=0.05891329277`

Compute for the Coefficient of Kinetic Friction `mu_k`

`F_k=mu_k*F_n`
`3=mu_k(101.8445875)`

`mu_k=3/101.8445875`

`mu_k=0.02945664639`

God bless....I hope the explanation is useful.