An object with a mass of $12 k g$ $12 kg$ is on a plane with an incline of $- \frac{3 π}{8}$ $-(3 pi)/8$ . If it takes $25 N$ $25 N$ to start pushing the object down the plane and $15 N$ $15 N$ to keep pushing it, what are the coefficients of static and kinetic friction?

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Answer 1 · 2016-05-02T20:59:16

$μ_{s} = 2.97$ $mu_s = 2.97$ and $μ_{k} = 2.75$ $mu_k = 2.75$

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Here, $θ = \frac{3 π}{8}$ $theta = (3pi)/8$

As we can observe, for both the cases (static and kinetic), the force applied is given as:

$F_{s, k} = μ_{s, k} m g cos θ - m g sin θ$ $F_(s,k) = mu_(s,k)mgcostheta-mgsintheta$

so, putting $m = 12 k g$ $m=12kg$ , $θ = \frac{3 π}{8}$ $theta = (3pi)/8$ , and $g = 9.8 m s^{- 2}$ $g=9.8 ms^-2$

$F_{s, k} = 45 μ_{s, k} - 108.65$ $F_(s,k) = 45mu_(s,k)-108.65$ ( $F$ $F$ is expressed in Newtons)

$F_{s} = 25$ $F_s = 25$ gives:

$μ_{s} = 2.97$ $mu_s = 2.97$

and, $F_{k} = 15$ $F_k = 15$ gives:

$μ_{k} = 2.75$ $mu_k = 2.75$

An object with a mass of 12 kg12kg12 kg is on a plane with an incline of -(3 pi)/8 −3π8 -(3 pi)/8 . If it takes 25 N25N25 N to start pushing the object down the plane and 15 N15N15 N to keep pushing it, what are the coefficients of static and kinetic friction?