1) Figure 1 A block of mass m1 is initially held in place on a surface a distance L away from the edge and is attached with a rope over a frictionless pulley to a second block of mass mg. The coefficient of kinetic friction between the block with mass m1 and the surface is DR, and the pulley has a radius R, see figure 1. If at time t = O the block m1 is allowed to move and begins sliding towards the edge of the table, compute the following in terms of m1,m2,L, my}? and g: Draw the freebody diagram for mass m1. Draw the free-body diagram for mass m2. Write Newton's equation in the x and y directions for mass m1. Write Newton's equation in the x and y directions for mass m2. Determine the acceleration of the boxes and the Tension in the rope. Determine the time it takes for block ml to reach the edge of the table. Determine the angular acceleration of the pulley. Determine the angular velocity ofthe pulley. Determine the number of revolutions the pulley makes when mass m1 reaches the edge of the table. Using the work energy theorem and placing the origin for the gravitational potential energy at the initial location of mass m2, write an equation relating the work done by the friction force to the total change in the energy of the system from the moment mass m1 is allowed to move until mass m1 reaches the edge of the table. 0. m .l- 2) Figure 2 Consider the situation depicted in Figure 2: A box of mass m = .250 kg slides down a frictionless rollercoaster. If at the beginning of the slide the box has an energy of E0 = 100] and a velocity of L3, = 0 ?, determine a) the initial height, h, of the box. Also, determine the velocities b) 123 and c} ya of the box. (Note: The initial energy ofthe system is ta ken with respect to a coordinate system with origin placed at ground level.) If at the end of the boxesjourney it comes to a complete STOP by slamming into a spring with springconstant k = 100 Nm, d) determine the amount the spring was compressed from it's equilibrium value, .515. (Note: The height of the box when it comes to a stop against the spring is 3 Eh.)