A block is on a rough 30° inclined plane. The maximum external force down the incline for which the block remains at rest is 2 N, while the maximum external force up the incline for which it remains at rest is 10 N. Find the coefficient of static friction μ.

Question

G1 Physics · Accepted Answer

At impending downward motion: μmg cos30° - mg sin30° = 2. At impending upward motion: μmg cos30° + mg sin30° = 10. Adding gives 2μmg cos30° = 12; subtracting gives 2mg sin30° = 8. Thus mg = 8 N and μ = 6/[8(√3/2)] = √3/2.