Energy Physics 4 th Six Weeks What is Energy? Energy is defined as the ability to produce a force. Energy is also defined as the ability to cause a change Energy is a fundamental building block of the universe. Energy exists in many different forms, and can change from one form to another. The SI unit for energy is the Joule whose symbol is J. The Joule is the amount of energy required to apply a force of 1 Newton over a distance of 1 Meter. 1 J = N x m Kinetic Energy Defined as energy in the form of motion. The amount depends upon both the mass of the moving object and its velocity. The more massive or the greater the amount of velocity of the moving object, the greater the amount of kinetic energy that it has. KE is in joules, mass in kg, and velocity in m/s KE is more dependent upon speed than mass. For example, doubling the speed increases the KE by 4. Tripling speed increases KE by 9, etc. FYI Remember that a Newton = kg x m/s 2 Also, remember that a Joule = N x m So, when a newton multiplies by a meter we have: Therefore which can also be rewritten as 1 Joule = kg x m 2 /s 2 Note: for our purposes dont stress out trying to cancel out units just rememberKE in J, mass in kg, and velocity (and speed) in m/s Example Problem #1 A 300 kg roller coaster cart reaches a height of 60 m before it descends to the bottom. If it reaches a speed of 34 m/s at the bottom of the ride, what is the kinetic energy of the roller coaster at the bottom of the ride? a distractor Stopping Distance Example Problem # 2 A 1000 kg race car has J of kinetic energy. What is the speed of the car? FYI Example Problem # 3 A race car has J of kinetic energy. If its speed was 72 m/s, what is the mass of the car? m = kg FYI Potential Energy Defined as the stored energy due to position and the potential to cause change. Gravitational Potential Energy (GPE), or PE g, is the amount of energy stored by objects above the Earths surface Although PE g can be calculated using a variety of units, When PE g is in joules, as it will be in our calculations, mass = kg Height = meters, and the gravitational constant is in m/s 2 Example Problem # 4 A 3 kg exercise ball is held 2 m above the ground. What is the gravitational potential energy of that ball? PE g = 3 kg x 9.8 m/s 2 x 2 m PE g = 58.8 kg x m 2 /s 2 PE g = 58.8 J Example Problem # 5 A 20 kg box has 588 J of PE g. How high up off of the floor is the box? h = 3 m Example Problem # 6 A toy is sitting 2 meters above the floor and has J of PE g, how massive is the toy? m = 7 kg Mechanical Energy, Energy Conversion, and the Law of Conservation of Energy Energy is most noticeable when it converts from one form to another. As energy changes from one form to another, the total amount never changes in a system, as it is transferred from one object to another. Mechanical Energy is the sum of the potential and kinetic energy within an object. Mechanical Energy = PE + KE Friction can often cause kinetic energy to convert to thermal energy, but still the total amount of energy in the system isnt destroyed it merely changes form. Law of Conservation of Energy states that energy cannot be created or destroyed. It can be transformed from one form to another, but the total amount of energy never changes. From the STAAR Reference Materials Practice Problem # 7 An object has J of KE near the bottom of a hill, and has J of PE. What was the total Mechanical Energy of the object? ME = J J ME = J Practice Problem # 8 An object is falling, and it currently has 360 J of PE and 1000 J of ME. How much KE does it possess? KE = ME - PE KE = 1000 J 360 J KE = 640 J Practice Problem # J = KE f J 200 J 150 J = KE f 50 J = KE f Mechanical Energy and Energy Transformation example 1. Where is PE highest? 2. Where is KE highest? A. E, F, B, G B. B, F, E, C C. D, E, B, F D. A, G, F, C 3. Which correctly shows a decrease in PE? 4. Which correctly shows an increase in PE? A D A. E, F, B, G B. B, F, E, C C. D, E, B, F D. A, G, F, C Energy Efficiency In an ideal situation, all of the energy available would be converted to useful output. An Ideal Machine is a hypothetical system where energy is not lost due to friction, deformation, or wear. Ideal Machines are 100% efficient However, in the real world, (usually due to friction) some energy is always lost to non-useful output making real machines less than 100% efficient. Efficiency is the ratio of useful output compared to the total energy input. Energy Efficiency Efficiency (%) = (Useful Energy Output / Total Energy Input) x 100 Ex: The spring on a wind-up car stores 10 J worth of potential energy when cranked tightly. Once released, the car moves forward with 8 J worth of kinetic energy. Therefore, the efficiency of the machine is 80%. Q: What happened to the remaining 20% of the energy that was put into the car? Did it disappear? A: Energy is never created nor destroyed. The missing energy was lost as heat due to friction of moving parts, air resistance, etc. Solving for Efficiency, Sample Problem # 10 If you put J of energy into a machine, and it puts out J of energy, how efficient was the machine? Key Equations GPE = Momentum, Force, & Energy commonalities A Newton of force = kg x m/s 2 1 Joule of Energy = kg x m 2 /s 2 One unit of Momentum = kg x m/s