Conservation of Energy Problems One fundamental law in Physics is the law of the Conservation of Energy. The law tells us that. much like matter, energy is neither created nor is it destroyed, it simply changes form. We see this everyday especially with mechanical energy types like potential energy and kinetic energy. Potential Energy (U): The energy stored in an object based on its position. Kinetic Energy (K): The energy produced by an object in motion Knowing that energy is conserved we are able to make the following equation to help describe how energy can change its form, in ideal scenarios, between these two types. Conservation of Energy Formula Ut + Ki = U2 + K2 The equation tells us that the total initial energy stored and in motion, will equal the total energy at any point in a closed system. Directions: Using this formula, and the formulas for both gravitational potential and kinetic energies, solve each of the following problems, making sure to SHOW ALL WORK!! 1. An object which weighs 15 N is dropped from rest from a height of 6 meters above the ground. When it has free-fallen 1 meter its total mechanical energy with respect to the ground is what? 2. During a certain time interval, a 40-N object free-falls 12 meters. The object gains how many Joules of kinetic energy during this interval? 3. You drop a 2.00 kg book to a friend who stands on the ground at a distance D = 10.0 m below. If your friend's outstretched hands are at a distanced = 1.50 m above the ground, determine the following: A. Find the potential energy as the book is in your hands. B. How much work does the gravitational force do on the book as it drops to your friends hands? (Hint: Remember change in energy = work done on an object) C. What is the speed of the book when it reaches your friend's hands? D. If instead the book were thrown straight down at 2 m/s, what would be the final speed? 4. Watch the video below before beginning this problem. The height of the building Spider- Man (a.k.a. Peter Parker) starts off on is 18 meters high. The height of the building he wants to swing to is 3 meters high. Peter Parker is approximately 72 kg in mass. Determine... A. Spider-Man's speed when his feet touch the roof the second building. B. The approximate kinetic energy dissipated when Spider-Man struck the wall. 5. In the figure below, a frictionless roller coaster of mass m = 825 kg tops the first hill (A) at speed v = 17.0 m/s at height h = 42.0 m. Answer the following based on this information. A B A. How much work does the gravitational force do on the car from that point to point B? B. What is the speed of the car at point B? C. How much work on the car from A to C? D. What is the speed of the car at point C