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

Question

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

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Answer 1 · 2016-05-15T10:06:32

Coefficient of Static Friction $μ_{s} = 0.05891329277$ $mu_s=0.05891329277$
Coefficient of Kinetic Friction $μ_{k} = 0.02945664639$ $mu_k=0.02945664639$

Explanation:

The given data:

$θ = \frac{- π}{6} = - 30^{\circ}$ $theta=(-pi)/6=-30^@$
mass $m = 12$ $m=12" "$ kg

Force needed to move the object down $F_{s} = 6$ $F_s=6" "$ N
Force needed to continue moving the object down $F_{k} = 3$ $F_k=3" "$ N

Compute the normal force $F_{n}$ $F_n$

$F_{n} = m \cdot g \cdot cos (\frac{π}{6}) = 12 \cdot (9.8) \cdot cos (\frac{π}{6}) = 101.8445875$ $F_n=m*g*cos (pi/6)=12*(9.8)*cos (pi/6)=101.8445875" "$ N

Compute for the Coefficient of Static Friction $μ_{s}$ $mu_s$

$F_{s} = μ_{s} \cdot F_{n}$ $F_s=mu_s*F_n$
$6 = μ_{s} (101.8445875)$ $6=mu_s(101.8445875)$

$μ_{s} = \frac{6}{101.8445875}$ $mu_s=6/101.8445875$
$μ_{s} = 0.05891329277$ $mu_s=0.05891329277$

Compute for the Coefficient of Kinetic Friction $μ_{k}$ $mu_k$

$F_{k} = μ_{k} \cdot F_{n}$ $F_k=mu_k*F_n$
$3 = μ_{k} (101.8445875)$ $3=mu_k(101.8445875)$

$μ_{k} = \frac{3}{101.8445875}$ $mu_k=3/101.8445875$

$μ_{k} = 0.02945664639$ $mu_k=0.02945664639$

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

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

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Explanation:

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An object with a mass of 12kg12 kg is on a plane with an incline of −π6 - pi/6 . If it takes 6N6 N to start pushing the object down the plane and 3N3 N to keep pushing it, what are the coefficients of static and kinetic friction?

1 Answer

Explanation:

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