a) How much did the potential energy of this massspring system change when the spring was originally stretched 0.12 meters? b) What is the maximum speed the mass will attain in its oscillation? c) Where in the motion is this maximum speed attained? d) What is the frequency of oscillation of this massspring system? 6) Water flows over a dam at a rate of 66,000 kilograms/second at a hydroelectric plant. a) How much work does gravity do on this mass of water each second if the water falls 150 meters? b) If this hydroelectric plant is 100% efficient in converting the energy of falling water into electricity, how many megawatts of electric power does this plant produce? (A megawatt equals one million watts.) c) If there is a severe drought and water only flows over the dam at a rate of 10,000 kilograms/second, then how many megawatts of electric power does this plant now produce? 7) A 10, 000 kg railroad car is rolling on a horizontal railroad track at 1.20 m/s. The 10,000 kg car hits an 18,000 kg car, which is initially at rest, and the cars lock together. What is the final velocity of the coupled cars just after they lock together? 2) Mountain roads often have switchbacks, a road weaving back and forth across the face of a mountain slope, so that on any portion of the road there is usually only a gentle incline. Why are these switchbacks used? Do switchbacks require less work for an automobile climbing the mountain than if the automobile went straight up a mountain slope? Does the answer depend on the frictional force on the car's tires? 3) A 5.0 kilogram rifle fires a bullet with a mass of 20.0 gram (0.0200 kg). The bullet's speed is 300 meters/second after the gun is fired. a) What is the bullet's momentum after the rifle is fired? b) If external forces on the rifle can be ignored, what is the recoil velocity of the rifle? 4) A bowling ball is attached to a cable to make a pendulum with a length 14.0 meters. A physicist pulls the \"bowling ball pendulum\" a small angle from the vertical so that the center of the ball is raised to a height of 0.0300 meters above its initial position. He also gives the bowling ball an initial speed of V: 0.0200 m/s as he releases it. a) What will be the instantaneous speed of the pendulum at the lowest point of its swing? b) What will be the maximum height the bowling ball attains (measured from the lowest point of its swing) if the physicist's face is not in the way? c) How long does this pendulum take to complete one cycle, i.e. what is the pendulum's period? 5) A 0.20 kg mass is attached to a spring with a spring constant equal to 240 N/m, and this mass-spring system is oscillating on a horizontal surface that is nearly frictionless. The spring was originally stretched a distance of 0.12 meters from its equilibrium (unstretched) length