NAME: DATE: PERIOD: PHYSICS - Conservation of Energy Notes Teacher Key - - Is Energy Conserved? - Determine the max height that a 5kg cannonball will reach if fired vertically with an initial velocity of 44.27 m/s. Determine the KE, PE, and work done by gravity at the following heights: 0m, 25m, 50m, 75m, and 100m Height PE KE E M Work by Gravity
Conservation of Mechanical Energy In our last example, the total MECHANICAL ENERGY that the cannonball had stayed constant The ball s energy was able to CHANGE FORMS from KE PE KE, however the total AMOUNT of ENERGY that the ball had DID NOT CHANGE. Mechanical energy was CONSERVED Why /how was it conserved? When certain FORCES act (or DO WORK) on an object, they result in a CONVERSION OF ENERGY from one form to another. Work done by these forces DOES NOT RESULT in a GAIN or LOSS of mechanical energy JUST A CONVERSION so total mechanical energy will be CONSERVED These forces are known as CONSERVATIVE FORCES Conservative Vs. Non-Conservative Forces Conservative Non-Conservative Any force that converts KINETIC energy to POTENTIAL energy. When CONSERVATIVE forces do WORK, there will be NO CHANGE in the total amount of MECHANICAL ENERGY that an object has. Examples: Gravity Spring (elastic) Electrostatic Magnetic Any force that converts KINETIC energy to HEAT (THERMAL) energy. When NON-CONSERVATIVE forces do WORK, there will be a DECREASE in the total amount of MECHANICAL ENERGY that an object has. Examples: Friction Air resistance
Conservative Force Facts WORK done by/against a CONSERVATIVE FORCE results in a CONVERSION of ENERGY from one form to another PE KE or KE PE. A system where ONLY CONSERVATIVE FORCES act is referred to as an IDEAL MECHANICAL SYSTEM NO FRICTION!!! Ex: Object in Freefall (ignoring air resistance), Pendulum (ignoring air resistance) When doing work against CONSERVATIVE FORCES, the amount of WORK done is INDEPENDENT of the PATH taken. Work against gravity only depends on final height Work against spring force only depends on x Conservation of Mechanical Energy - Example A 60kg student jumps from rest off a ladder and onto a trampoline that is 2m below. What is the total mechanical energy of the student before jumping? What form is this energy? As the student steps off the ladder, what force acts? Determine the velocity of the student as they are about to make contact with the surface of the trampoline. What form is the student s energy? As the students makes contact with the trampoline, what force acts? (For this part of the problem, ignore gravity) If the trampoline has a spring constant of 250 N/m, what is the maximum distance that the trampoline will stretch? What form is the student s energy?
Energy / Work Conservative Force The WORK done on an object is equal to a CHANGE in the ENERGY of the object. So if we know how much ENERGY an object gains, we can determine how much WORK is done on the object! The WORK done against CONSERVATIVE FORCES is INDEPENDENT of the PATH taken because there is NO FRICTION. To find the amount of WORK done against ANY CONSERVATIVE FORCE, simply look for the CHANGE in MECHANICAL ENERGY P.E. / Work - Pendulum Determine the amount of work required to lift this 6kg ball to a height of 5m from its initial resting position? Work done to raise the pendulum is equal to the amount of PE g that it gained since work is just a way for energy to change forms So if the pendulum were released from a height 5m above its normal resting position (point a), what velocity would it have when it passes point b? (Hint: Work PE KE)
Pendulum P.E. / Work Other curved path Determine the amount of work that a roller coaster must do in order to climb to the top of a hill before the big drop given the roller coaster car mass of 1,000kg and a hill maximum height of 10m? What is the PE of the roller coaster at the top of the hill? What is the KE of the roller coaster when it reaches the ground on the other side? What is the velocity? Cliff Diver - Example A 50 newton cliff diver climbs to a height of 50 meters above the water. How much PE does he gain in his climb? 50 m How much KE does he gain as he falls? 25 m What is his speed as he reaches the water? 0 m
Spring Toy - Example A spring toy with a mass of 0.02 kilograms has a spring with a spring constant of 120 newtons per meter. The toy is compressed 0.04 meter. What is the PE stored in the spring? What height should the toy spring to? What happens to the PE when the spring pops up? Rollercoaster - Example A 1700 kilogram rollercoaster operating on a frictionless track has a speed of 5 meters per second as it passes over the crest of a 35 meter high hill. What is the rollercoaster s PE at this point? What is the rollercoaster s KE at this point? 35 m What will its total energy be at the bottom of the hill? What will its speed be at the bottom of the hill?