1. You hold a 2.4kg book against a wall by pushing at an angle 150 above the horizontal. What is the magnitude of the minimum force must you apply to keep the book stationary if the coefficient of static friction between the book and the wall is 0.45? Hint: Which direction does the friction force point if it is just enough to keep the book from sliding down the wall? How is the force of friction related to the normal force? How is the normal force related to the force you are applying? 2. Under what conditions is mechanical energy conserved? When me- chanical energy is not conserved, how can you calculate the change in mechanical energy of a system? Give an example of one situation in which mechanical energy is conserved (be sure to define your system) and one situation in which mechanical energy is not conserved. 3. Under what conditions is momentum conserved? Give an example of one situation in which momentum is conserved (be sure to define your system) and one situation in which momentum is not conserved. 4. What is the difference between an elastic collision, an inelastic collision and a perfectly inelastic collision?m1 m2 5. In the above figure, m1 = 1.4kg. The coefficient of static friction between block 1 and the table is As = 0.33. The coefficient of kinetic friction between block 1 and the table is /k = 0.21. The pulley is massless and frictionless, and the string doesn't stretch. a. Draw a free-body diagram for block 1 when the system is station- ary. b. Draw a free-body diagram for block 2 when the system is station- ary. c. What is the largest value of m2 for which the system will remain stationary? Hint: for a stationary system, the acceleration is 0 so the net force on each block must be 0. What must the tension in the string be to keep block 1 stationary? Then, considering the free-body diagram for block 2, what is my? 6. A 6000kg truck traveling at 20m/s decelerates to 5m/s over a distance of 130m. a. How much work is done on the truck while it slows down? Hint: use the work-energy theorem. b. What is the magnitude of the average force applied to the truck during this time if the force points opposite the direction of travel? 7. A 7.5kg block compresses a spring of spring constant 150N/m. If the block's speed is 1.8m/s when the spring is compressed 0.35m, what is the maximum compression of the spring? Assume no friction. N8. A 2.0kg block slides down a slope inclined 36 above the horizontal with a vertical height of 3.3m. If the block starts at rest and reaches a speed of 7.4m/s at the bottom of the slope, what is the coefficient of kinetic friction between the block and the slope? Hint: consider mechanical energy. What is the work done by friction? What is the force of friction? 9. A 0.45kg soccer ball has velocity 14m/si-17m/sj when a soccer player kicks it. If the ball is in contact with her foot for 0.08s and it leaves with velocity -11m/si+ 19m/sj, what is the average force (magnitude and direction) her foot exerts on the ball? Hint: First, what is the change in momentum of the ball? How does this relate to force? 10. A ball of mass m moving East at speed 3v collides head-on with a ball of mass 5m moving West at speed v. a. What are the final velocities of the balls if the collision is perfectly inelastic? b. What is the velocity of the mass 5m ball if the mass m ball travels West at speed 3v after the collision? F1 = 88N 550 670 F2 11. A uniform rod of length 0.76m is free to pivot about a hinge at its left end as shown above. Two forces are applied to the rod, with F1 applied 0.28m from the left end of the rod and F2 applied at the right end of the rod. a. What is the magnitude of the torque applied by F1? Cob. What is F2 if the rod is not rotating? c. If the rod begins rotating at 0.5 revolutions per second, what is its angular velocity in radians per second? d. In the situation described in part (c), what is the tangential ve- locity of a 5 x 10-kg ant clinging to the end of the rod farthest from the pivot point? e. In the situation described in part (d), what force must the ant apply to stay attached to the rod