An object with a mass of $10 k g$ $10 kg$ is on a plane with an incline of $- \frac{π}{4}$ $- pi/4$ . If it takes $12 N$ $12 N$ to start pushing the object down the plane and $4 N$ $4 N$ to keep pushing it, what are the coefficients of static and kinetic friction?

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An object with a mass of $10 k g$ $10 kg$ is on a plane with an incline of $- \frac{π}{4}$ $- pi/4$ . If it takes $12 N$ $12 N$ to start pushing the object down the plane and $4 N$ $4 N$ to keep pushing it, what are the coefficients of static and kinetic friction?

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Answer 1 · 2017-02-21T03:23:21

The static coefficient is 1.17; the kinetic coefficient is 1.06.

Explanation:

The object on an incline has one component of the force of gravity pulling it down the slope, usually referred to as $F_{∣ ∣}$ $F_(||)$ . As the diagram below shows, it is equal to $m g sin θ$ $mgsintheta$

![http://thecraftycanvas.com/library/online-learning-tools/physics-homework-helpers/incline-force-calculator-problem-solver/]!

In this problem, the applied force also acts down the incline, and only friction acts up the ramp to oppose these two forces.

The force of friction is given by $F_{f} = μ F_{N} = μ m g cos θ$ $F_f = muF_N = mumgcostheta$

Therefore the free body equation is

$F_{net} = μ m g cos θ - m g sin θ - F_{applied}$ $F_"net" = mumgcostheta - mgsintheta - F_"applied"$

Since there is no acceleration, $F_{net} = 0$ $F_"net"=0$ and the equation becomes

$μ m g cos θ - m g sin θ - F_{applied} = 0$ $mumgcostheta - mgsintheta - F_"applied"=0$

Inserting what we know, I will find $μ_{s}$ $mu_s$ first:

$μ_{s} (10) (9.8) cos (\frac{π}{4}) - (10) (9.8) sin (\frac{π}{4}) - 12 = 0$ $mu_s(10)(9.8)cos( (pi)/4) - (10)(9.8)sin ((pi)/4) - 12 = 0$

Since $cos (\frac{π}{4}) = sin (\frac{π}{4}) = .707$ $cos(pi/4) = sin(pi/4) = .707$

$μ_{s} (69.3) - (69.3) - 12 = 0$ $mu_s(69.3)-(69.3)-12=0$

$μ_{s} = 81.3 \div 69.3 = 1.17$ $mu_s=81.3-:69.3 = 1.17$

The calculation of $μ_{k}$ $mu_k$ is similar, using 4N in place of the 12 N applied force:

$μ_{k} (10) (9.8) cos (\frac{π}{4}) - (10) (9.8) sin (\frac{π}{4}) - 4 = 0$ $mu_k(10)(9.8)cos( (pi)/4) - (10)(9.8)sin ((pi)/4) - 4 = 0$

$μ_{k} (69.3) - (69.3) - 4 = 0$ $mu_k(69.3)-(69.3)-4=0$

$μ_{k} = 73.3 \div 69.3 = 1.06$ $mu_k=73.3-:69.3 = 1.06$

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An object with a mass of $10 k g$ $10 kg$ is on a plane with an incline of $- \frac{π}{4}$ $- pi/4$ . If it takes $12 N$ $12 N$ to start pushing the object down the plane and $4 N$ $4 N$ to keep pushing it, what are the coefficients of static and kinetic friction?

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Explanation:

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Explanation:

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