Question

a block with mass m = 5kg is on an incline, l = 4 m long angled at 30° above the horizontal. coefficients of static and kinetic friction are: μs = 0.3, and μk = 0.2. how do we figure out if the box will move? a. if the force due to static friction is greater than kinetic friction it will not move b. if there is a net force down the slope, it will move c. if the force down the slope exceeds maximum static friction it will move d. if the force down the slope exceeds kinetic friction it will move e. im lost

Explanation:

Step1: Understand friction - motion relationship

The block will move if the force acting down - slope exceeds the maximum static friction force. Static friction opposes the impending motion. Once the applied force exceeds the maximum static friction, the block starts to move and kinetic friction takes over.

Step2: Analyze each option

• Option A: Comparing static and kinetic friction forces directly doesn't determine if the block moves. The key is the comparison between the force down - slope and maximum static friction.
• Option B: A net force down the slope is not the correct criterion initially. We first need to check if the force down - slope can overcome static friction.
• Option C: This is correct. When the force down the slope exceeds the maximum static friction ($F_{down - slope}>F_{s,max}=\mu_sN$), the block will move.
• Option D: We first need to consider static friction to determine if the block starts moving, not kinetic friction at the start.
• Option E: Not a valid physical answer for the problem.

Answer:

C. If the force down the slope exceeds maximum static friction it will move