An object with a mass of 14 kg is on a plane with an incline of -(5 pi)/12 . If it takes 12 N to start pushing the object down the plane and 7 N to keep pushing it, what are the coefficients of static and kinetic friction?

1 Answer

4.07, 3.93

Explanation:

The force F required to push an object of mass m=9 kg downward on an inclined plane at an angle theta=-{5\pi}/12=-75^\circ & coefficient of static friction \mu_s is given as

F=\mu_s mg\cos\theta-mg\sin\theta

\mu_s=\frac{F+mg\sin\theta}{mg\cos\theta}

\mu_s=\frac{12+14\times9.81\sin75^\circ}{15\times9.81\cos75^\circ}
=4.07

Similarly, when the motion starts, then the force (F) required to keep the object moving on the plane is given as

F=\mu_k mg\cos\theta-mg\sin\theta

\mu_k=\frac{F+mg\sin\theta}{mg\cos\theta}

\mu_k=\frac{7+14\times9.81\sin75^\circ}{15\times9.81\cos75^\circ}
=3.93