1. A block of mass M = 10 kg is sitting on a surface inclined at angle θ = 45°. Given that the coefficient of static friction is μs = 0.5 between block and surface, what is the minimum force F necessary to prevent slipping? What is the maximum force F that can be exerted without causing the block to slip?
2. In the previous problem use θ = 15°. What is the maximum force pushing down the incline so that the block doesn't slip? What is the maximum force pushing up the incline so that the block doesn't slip?
3. A conveyor is dumping sand onto a cone shaped pile. Given that the coefficient of static friction between the sand grains is μs, what is the maximum angle θ?