Problem 10. Consider a curving waterslide which you can assume is frictionless. A large child slides down the slide into the water. A smaller child decides to hop straight off the slide into the water without going down the slide. (a) Upon reaching the water, is the kinetic energy of the smaller child (i) greater, (ii) less than or (iii) the same as the larger child. (b) Same choices but now consider the Speed of the smaller child. (c) During the time going from the t0p to the bottom how does the average acceleration of the smaller child compare to the larger one. You may use the same choices as in the rst two parts. Problem 11. A pendulum is created by attaching a bowling ball to the end of a L = 4 m cable coming from the ceiling. The ball is released with the cable making an angle of E) = 30 with the vertical. (a) Find the speed of the ball at the bottom of its swing (ignoring air resistance). (b) Describe in words the energy conversion process that occurs with and without air resistance. (c) If the ball is released with a speed of 'v = 4 m/s, what is the maximum height that it will reach when swinging up the other side. You can ignore air resistance again. Problem 12. A block of mass m = 2 kg is pushed against a spring of spring constant k = 30 N / m until the spring is compressed by a: = 0.1 m. The block is released and travels across a rough table with a coefficient of kinetic friction of M = 0.05. (a) Draw a free body diagram of the block when it is sliding across the table. (b) What is the maximum speed of the block? (c) How far does the block travel before stopping? (d) How much farther or shorter would a 1 kg block travel? Explain. Problem 13. A m = 10 kg block is released from a height of h = 3 m. It travels down a frictionless circular shaped m ramp to the bottom where it encounters a rough surface. h$l k It travels over this rough surface for 6 n1 followed by 3 In more on a frictionless surface. At this point the block ' g ( , compresses a spring by 0.3 m before stopping. The spring 6 m 3 m constant of the spring is 2250 N/m. Find the coefcient of kinetic friction for the rough surface. PROBLEM SET 5, WORK AND ENERGY Problem 3. 4704 J. Problem 4. (a) 90 J, (b) 120 J, (c) 0 J. Problem 5. 360,000 J, 101 m/s. Problem 6. 29.6 kW. Problem 7. 1.28 m. Problem 8. (b) 0 J, (c) 4.03 m/S. Problem 11. (a) 3.24 m/s, ((3) 2.65 m below pivot point. Problem 12. (b) 0.39 m/s, ((3) 0.15 m, (d) Twice the distance. Problem 13. 0.33. PROBLEM SET 5, WORK AND ENERGY Problem 1. As a simple pendulum swings back and forth, the forces acting on it are gravity, the tension in the supporting cord and air resistance. (a) Which of these forces, if any, does no work on the pendulum? (b) Which of these forces, if any, does negative work at all times during the motion. (c) Describe the work done by the gravitational force while the pendulum is swinging. Problem 2. Can kinetic energy be negative? Explain. Problem 3. Batman whose mass is 80 kg is dangling on the free end of a 12 m rcpe, the other end of which is xed to a tree limb above. By repeatedly bending at the waist, he is able to get the rope in motion, eventually making it swing enough that he can reach a ledge when the rope makes a 60 angle with the vertical. How much work was done by the gravitational force on Batman in this maneuver. Problem 4. A baseball outelder throws a 0.15 kg baseball at a speed of 40 m/s and an initial angle of 30. (a) What is the kinetic energy of the baseball at the highest point of its trajectory? (b) What is the kinetic energy when it hits the ground? (c) How much work is done by the gravitational force during its time in the air? Problem 5. How many joules of energy does a 100 Watt light bulb use per hour? How fast would a 70 kg person have to run to have the same amount of kinetic energy? Problem 6. A ski tow operates on a ski slope that is 300 m long at an angle of 15. The rope moves at 12 km/ hr and can move a total of 50 skiers. Assuming the average mass of the skiers is 70 kg, determine the power required to operate the tow. You may treat the slope as frictionless. Problem 7. On an essentially frictionless ice rink, a skater moves at 3 m/s. They encounter a rough patch of ice (with friction) that reduces their speed by 45% due to a friction force that is 25% of their weight. Find the length of the rough patch. Problem 8. A block of mass m starts from rest and slides down a rough incline of slope 6 = '30". It starts from a height of h = 1 m. The incline has a coefcient of kinetic friction of 0.1. (a) Draw a free body diagram for the block on the rough surface. (b) Find the work done by the normal force. (c) Find the speed of the block at the bottom of the incline. Problem 9. A person drops a ball from the roof of a building while a second person observes the motion of the ball from the ground. Will the people agree on the value of the gravitational potential energy? The change in potential energy? The kinetic energy? Explain your answers