1. The force due to a spring is variable and is guantified by F = k_x, where k is the spring constant M x is the displacement. Given the graph of the force versus displacement graph for a spring in Figure 5, determine; a. An expression for the work done by the spring using the area under the curve. xzo x=x, Figure 5: Force versus displacement of a spring. 2. Consider the ball example in the introduction when a ball is dropped from 3 meters. After the ball bounces, it raises to a height of 2 meters. The mass of the ball is 0.5 kg a. Calculate the speed of the ball right before the bounce. b. How much energy was converted into heat after the ball bounced off the ground? (Hint: Thermal Energy (TE) will now need to be included in your conservation of energy equation w you will now need to know the mass of the ball) c. Calculate the speed of the ball immediately after the ball bounces off the ground. 3. Both kinetic and potential energy are part of the thrill of roller coasters. For this exercise, you will examine the path of a roller coaster and describe what type of energy is at work. Use Figure 6 to answer the following questions: Figure 6: Different points in a roiier coaster's motion. a. Describe the kinetic and potential energy at each point of the roller coaster path. b. What happens to the roller coaster's kinetic energy between Points B and C? What happens to its potential energy between these points? 0. Why is it important for Point A to be higher than Point C? d. What causes the roller coaster train to lose energy over its trip