What is the maximum static friction force for a block of mass 2 kg on a horizontal surface with μ_s = 0.4 and g = 9.8 m/s^2?

What is the maximum static friction force for a block of mass 2 kg on a horizontal surface with μ_s = 0.4 and g = 9.8 m/s^2?

• A. 5.00 N
• B. 6.30 N
• C. 8.50 N
• D. 7.84 N

Answer: (D)

Static friction can adjust to match the tendency of the block to move, up to a maximum value set by μ_s times the normal force. For a block on a horizontal surface, the normal force is just its weight: N = m g = 2 kg × 9.8 m/s^2 = 19.6 N. The maximum static friction is F_s,max = μ_s N = 0.4 × 19.6 N = 7.84 N. So the greatest frictional force that can hold the block in place without slipping is 7.84 N. If the push is smaller than this, static friction can balance it; once the push exceeds this value, the block will start to move and kinetic friction takes over.

Static friction can adjust to match the tendency of the block to move, up to a maximum value set by μ_s times the normal force. For a block on a horizontal surface, the normal force is just its weight: N = m g = 2 kg × 9.8 m/s^2 = 19.6 N. The maximum static friction is F_s,max = μ_s N = 0.4 × 19.6 N = 7.84 N. So the greatest frictional force that can hold the block in place without slipping is 7.84 N. If the push is smaller than this, static friction can balance it; once the push exceeds this value, the block will start to move and kinetic friction takes over.