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FIRST- LETβS DEFINE OUR TERMS Energy- The Ability to Cause Change Change is any kind of change, whether in shape, speed, heat, pressure, or light Kinetic Energy- The energy an object gains when it is in motion An object in motion has more energy (can cause more change) then an object at rest. Potential Energy- Stored energy An object at a high point, under strain (like a stretched spring), or able to react chemically has potential energy. CONSERVATION OF ENERGY The total energy of the universe is constant. Energy cannot be created or destroyed, it can only be TRANSFORMED. This means that the total energy (the kinetic energy plus the potential energy) in a system is constant. POTENTIAL ENERGY FROM GRAVITY The potential energy an object gains from being lifted against the force of gravity is called GRAVITATIONAL POTENTIAL ENERGY. More height equals more energy. For any object it can be calculated by multiplying the height off the ground (in meters) by the mass (in kilograms) and the acceleration due to gravity (Remember: F=ma) π·π¬ = π × π × π. π π¦ π¬ π OTHER TYPES OF POTENTIAL ENERGY Food has chemical potential energy that your body uses to do things like move, think, and stay warm Gasoline has chemical potential energy that engines turn into heat energy in order to do work A spring, a catapult, or a stretched rubber band have mechanical potential energy, energy stored in an object because it is under stress. KINETIC ENERGY As weβve seen in our lab activity, the kinetic energy of an object depends on its mass and itβs velocity. It can be calculated using the equation π²π¬ π π = × π × ππ The equation shows that as the mass increases, the kinetic energy increases by the same amount. Try adding numbers to see why. π π π π π΄πππ ππ ππππ πππππππππ π π π π π΄πππ ππ πππ πππππππππ π²π¬ = πππ = × π × ππ = πππ± π²π¬ = πππ = × ππ × ππ = πππ± SO- Doubling the mass doubles the kinetic energy if the velocity is the same. KINETIC ENERGY AND VELOCITY π From the equation π²π¬ = πππ , we showed that π doubling the mass doubles the kinetic energy. Any change in mass causes an identical change in kinetic energy. Velocity is different. A change in velocity causes a much greater change in kinetic energy. This is because the velocity is squared to find the kinetic energy. If you double the velocity, you quadruple the kinetic energy. PUTTING THE EQUATIONS TOGETHER The total energy of the ball is CONSTANT. So while at the top of the hill it only has potential energy, at the bottom it only has kinetic energy. AND THE TWO ARE EQUAL. Total Energy = PE + KE π × π × π. π π¦ π¬π = π π × ππ π PE at the top = KE at the bottom This means that if we know how high the hill is, we can find out how much kinetic energy it will have at the bottom. FINDING VELOCITY FROM KINETIC ENERGY With the kinetic energy of an object we can also determine its velocity. π π²π¬ = π × ππ π Divide both sides of the equation by the mass π²π¬ π π = π π π Multiply both sides of the equation by two π × π²π¬ = ππ π Then take the square root of both sides to go from the square of the velocity to the velocity alone. π × π²π¬ =π π HEREβS ALL FOUR EQUATIONS Gravitational Potential Energy: π·π¬ = π × π × π. π Kinetic Energy: π²π¬ = × π × ππ Velocity from Kinetic Energy: π= Mass from Kinetic Energy: π= π π π×π²π¬ π π×π²π¬ ππ SUMMARY -The total energy in a system does not change -The potential energy of an object is the stored energy -Gravitational potential energy is dependent on height and mass and is directly proportional to both. -Kinetic Energy is the energy an object gains from moving -Kinetic energy is dependent on mass and velocity. It is directly proportional to mass and directly proportional to the square of the velocity (the velocity multiplied by itself). -If you know the gravitational or mechanical potential energy of an object, you also know its maximum possible kinetic energy.