1) Consider a set of block as shown in the diagram. M1, M2, M3 are all attached by a wire. The wire goes around two identical pulleys. Consider the case M2>M1. Answer the following questions. a) If the system is release from rest with no friction, which block goes down and why? b) If the coefficient of static friction between block M3 and the table is s what is the smallest value of M2 that will result in acceleration of the system? For this case assume the wire travels over the pulleys without friction, and the pulleys do not rotate c) If M2 is greater than that value, it will drop. Find an expression for the acceleration of M2 in terms of the masses and the coefficient of kinetic friction k , between block M3 and the table. For this case assume the wire travels over the pulleys without friction, and the pulleys do not rotate. Remember to draw a free body diagram showing all forces for each mass. (This is a force problem) d) With the same conditions as (c) how fast is M2 moving after it has dropped a distance d? e) If the pulleys now have mass Mp and radius R, what is the value of the acceleration of M2? Consider the pulleys to be disks with I=1/2MR2 . Be sure to draw free body diagrams for the pulleys as well. Think about how the Tension will vary in different parts of the system. f) With the same conditions as (e) how fast is the M2 moving after M3 has moved a distance d to the right?

2)An airplane is located 300 Km and 60 East of North from the airport (initial point). The airplane traveled from its initial position to its final position in two stages. In the first stage of its travel, the airplane moves 100 Km at 30 North of West: (Consider the initial point as the origin of the coordinate system) (a) Draw a diagram of the Travel. (b) Determine the second stage displacement of the airplane in both magnitude and direction. (c) Express the first part of displacement of the airplane in terms of its x and y components. (d) Express the second part of displacement of the airplane in terms of its x and y components. (e) Express the final displacement of the airplane in terms of its x and y components.

3)A girl in the playground hits a ball at 25 degrees above horizontal with a speed 30 m/s. The total length of the playground is 80 m and there is an obstacle at a distance of 15 m from her. The height of the obstacle is 2 m. Please ignore air resistance and answer the following questions: (a) Draw the trajectory of the ball. (b) What are the vertical and horizontal components of the initial velocity of the ball? (c) How long does it take for the ball to reach the obstacle? (d) Does the ball clear the obstacle? If the answer is yes, Find the vertical distance by which the ball clears the obstacle. (e) Find the distance at which the ball hits the ground from her.

4)A boat crossing a river 200 meters wide. The boat's velocity relative to the water is 40 m/s and the direction of 30 degrees East of the North. The current in the river flows at a speed of 5 m/s to the East. a) Draw a diagram of this situation. b) What is the velocity of the boat relative to the shore in magnitude and direction? c) How long does it take for this boat to reach the shore? d) How far does the boat drift downstream as it crosses this river?

5)A 6 kg block is placed on a frictionless ramp making an angle of 30 degrees with horizontal. A one kg mass is attached to a rope. (The pully is frictionless). A man pushes up the heavier block with an 8 N force parallel to the ramp: a) Draw a free body diagram for the system. b) What is the final acceleration of the system? What is the direction of the movement? c) Assuming the system is not moving, with the same mass of block 1, what should be the weight of block 2?