HW#23 Ch 8: Potential Energy and Conservation of Energy
Instructions: Use an energy approach to solve these problems. Show your work by writing formulas and showing substitutions to earn full credit. Some problems require FBDs.
1. A pebble is thrown at an angle of 30° above the horizontal at a speed of 8 m/s from a bridge 18 m above the surface of the water. What is the speed of the pebble as it strikes the water? Use an energy approach to solve the problem.
2. A lead weight is tied to the end of a 2.2 m massless string so that it swings freely as a pendulum. If it has a speed of 1.2 m/s when it is at its lowest point, at what angle does the lead weight make with the vertical when it is momentarily at rest?
3. A 30 g ball is shot from a spring gun whose spring has a force constant of 400 N/m. The spring can be compressed 6 cm. How high will the ball go (relative to the top of the unstretched spring) if the gun is aimed vertically?
4. What is the minimum g-force that one would experience on a roller coaster traveling in a vertical circular loop of radius R at a) the top of the loop, b) the side of the loop and c) the bottom of the loop?
5. Circular loops are rarely used in rollercoaster rides because of the intense g-forces that are experienced at the bottom of the loop, which are enough to make some people lose consciousness. Instead, a loop called a clothoid is used, an example of which is shown in the figure below. A clothoid maintains a constant centripetal acceleration throughout the loop by reducing the radius of curvature at the top of the loop, where the speed is the least. The Shockwave, which debuted in 1990 at Six Flags Great Adventure, featured a 90-foot initial drop and a 66-foot high vertical loop in the shape of a clothoid. a) What was the speed of the roller coaster at the bottom of the loop, neglecting friction? b) What would the radius of curvature have to be to maintain a g-force of 3.4g at the bottom of the loop? c) What would the radius of curvature have to be to maintain a g-force of 3.4g at the top of the loop?
