55) Two masses (12 kg and 8 kg) are held together by a rope. A force of 15 N is applied to one of the block. What is the acceleration of the system (magnitude and direction), and what is the tension in the rope? 56) Two masses m1 and m2 are attached by a rope that slides around a pulley with no friction. Find expressions for the acceleration of the system and tension in the rope. 57) Three masses (m1,m2,m3) are in contact with each other and each is in contact with a horizontal surface. There is no friction between the masses and the surface. A force F pushes 58) Show that when you are applying a force to a block on a horizontal surface with friction between the block and the surface, it is always easier to pull. 59) A 40kg box is pushed by a force of 200N. The force is acting at an angle of 20 degrees above the horizontal. The coefficient of kinetic friction between the box and the floor is 0.4. What is the acceleration of the box? 60) A block is sitting on a wedge. The wedge has an angle theta from the horizontal. What is the maximum value of the angle (in terms of the coefficient of static friction) such that the block does not start to slide. 61) A box is sitting in the back of a truck. The coefficient of static friction between the box and the truck is 0.4. How fast can the truck accelerate without the box sliding in the back? Now suppose the block does start to slip at that maximum acceleration. The coefficient of kinetic friction between the box and the truck is 0.1. How far does the box slide on the truck in 1s. 62) Consider a wedge with angle theta from the horizontal. A block is sitting on the wedge. The coefficient of static friction between the block and the wedge is s. The wedge is accelerating with acceleration a. What is the minimum value of the acceleration such that the block does not slide down the ramp? Discuss the relevance of the case a=0. What is the maximum value of the acceleration such that the block does not slide up the ramp. 63) A car is going around a curve with speed v. The curve can be considered as a part of a circle of radius R. The coefficient of static friction between the tires and the road is s. What is the maximum speed the car can have before it starts to slip? Use real world numbers to estimate that maximum speed. 64) A car is going around the same curve. This time there is no static friction (it's super icy out) but the road is banked towards the inside of the turn with an angle 0. What is the maximum speed the car can have before sliding up the banked road? Use real world examples to estimate the maximum speed.