Which statement about friction is true when a block is at rest on a plane and static friction is in effect?

Which statement about friction is true when a block is at rest on a plane and static friction is in effect?

• A. The friction balances the parallel component of weight, f_s = mg sin θ, as long as mg sin θ ≤ μ_s N.
• B. Kinetic friction always acts opposite the direction of motion.
• C. Friction is independent of the angle of the plane.
• D. Friction always equals μ_s N.

Answer: (A)

Static friction can take on whatever value is needed up to a maximum to prevent motion. On an incline, the weight has a component down the plane mg sin θ and a normal component N = mg cos θ. When the block is at rest, the friction force up the plane balances that downslope component: f_s = mg sin θ, provided this required friction does not exceed the maximum static friction μ_s N. If mg sin θ becomes larger than μ_s N, the block can’t stay at rest and would start to slide, at which point kinetic friction μ_k N comes into play and acts opposite the motion. So the statement is best because it states that friction balances the parallel component of weight as long as mg sin θ ≤ μ_s N. The other options are not correct in this static situation: kinetic friction is not in effect when the block isn’t moving; friction depends on the angle through both the downslope component and the normal force; and friction does not always equal μ_s N—only at the threshold of motion or if the maximum is reached.

Static friction can take on whatever value is needed up to a maximum to prevent motion. On an incline, the weight has a component down the plane mg sin θ and a normal component N = mg cos θ. When the block is at rest, the friction force up the plane balances that downslope component: f_s = mg sin θ, provided this required friction does not exceed the maximum static friction μ_s N. If mg sin θ becomes larger than μ_s N, the block can’t stay at rest and would start to slide, at which point kinetic friction μ_k N comes into play and acts opposite the motion.

So the statement is best because it states that friction balances the parallel component of weight as long as mg sin θ ≤ μ_s N. The other options are not correct in this static situation: kinetic friction is not in effect when the block isn’t moving; friction depends on the angle through both the downslope component and the normal force; and friction does not always equal μ_s N—only at the threshold of motion or if the maximum is reached.