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EQ: What type of energy describes the motion of a system? The Many Forms of Energy • The word energy is used in many different ways in everyday speech. • Some fruit-and-cereal bars are advertised as energy sources. Athletes use energy in sports. • Companies that supply your home with electricity, natural gas, or heating fuel are called energy companies. The Many Forms of Energy • Scientists and engineers use the term energy much more precisely. • Work causes a change in the energy of a system. • That is, work transfers energy between a system and the external world. The Many Forms of Energy • When work is done on a system, the energy of that system increases. • On the other hand, if the system does work, then the energy of the system decreases. Mechanical energy is the energy that is possessed by an object due to its motion or due to its position. The total mechanical energy of a system is the sum of the PE and KE of a system Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position What is causing the ball to move in the other direction? What would happen to the one side of the ball if the other ball was lifted higher to begin the motion? Why? https://www.youtube.com/watch?v=OuA-znVMY3I Hmm?! https://www.youtube.com/watch?v=GQGYXuSjo-E https://www.youtube.com/watch?v=OuA-znVMY3I Kinetic energy exists whenever an object which has mass is in motion with some velocity. Everything you see moving about has kinetic energy. The greater the mass or velocity of a moving object, the more kinetic energy it has. Formula: KE = ½ m 2 v Quantity Variable Unit Kinetic Energy mass velocity KE Joules (J) m v Kilograms (kg) Meters/second (m/s) Silvana Cruciata from Italy set a record in one-hour running by running 18.084 km in 1.000 h. If Cruciata’s kinetic energy was 694 J, what was her mass? Example continuation Givens: Δx = 18.084 km = 1.8084 × 104 m Δt = 1.000 h = 3.600 × 103 s KE = 694 J Unknown: mass Equation(s): manipulated Substitution: v =1.8084 × 104 m/3.600 × 103 s = 5.023 m/s m = 2(694)/(5.023)2 = 55.0127 Solution: m = 55.0 kg Ability to do work by virtue of position or condition. In other words, the amount of work the object capable of doing based on its position. A suspended weight A stretched bow Two Types of Potential Energy: Gravitational Potential Energy (GPE): The energy associated with an object due to the object’s position relative to a gravitational source. Elastic Potential Energy: The energy stored in a compressed or stretched spring. Formula: PE = m g h Quantity Potential Energy Mass height gravity Variable PE M ∆y g Unit Joules (J) Kilogram (kg) Meters (m) Meters/second (m/s2) In 1993, Javier Sotomayor from Cuba set a record in the high jump by clearing a vertical distance of 2.45 m. If the gravitational potential energy associated with Sotomayor at the top point of his trajectory was 1.59 x 103 J, what was his mass? m = 66.2 kg Formula: PEelastic = ½ Quantity Variable Unit Potential Energy Spring constant Distance compressed or stretched PE k x 2 kx Joules (J) Newton/meter (N/m) Meters (m) A 70.0 kg stuntman jumps from a bridge that is 50.0 m above the water. Fortunately, a bungee cord with an unstretched length of 15.0 m is attached to the stuntman, so that he breaks his fall 12.0 m above the water’s surface. If the total potential energy associated with the stuntman and cord is 3.43 x 104 J,what is the force constant of the cord? Example continuation: Givens: m = 70.0 kg h = 12.0 m x = 50.0 m − 12.0 m − 15.0 m = 23.0 m PEg = 0 J at river level PEtot = 3.43 × 104 J g = 9.81 m/s2 Unknown: k Equation(s): PEtot = PEg + PEelastic manipulated Petot = mgh + 1/2kx2 •The change in gravitational potential energy of an object is equal to the amount of work needed to change its height •Therefore: Work = DPE Fd = mgh •The KE of a moving object is equal to the work the object is capable of doing while being brought to rest •Therefore: W = DKE 2 Fd = ½mv A forward force of 11.0 N is applied to a loaded cart over a distance of 15.0 m. If the cart, which is initially at rest, has a final speed of 1.98 m/s, what is the combined mass of the cart and its contents? •Putting these two ideas together gives us the general Work-Energy Theorem: If no change in energy occurs, then no work is done. Therefore, whenever work is done, there is a change in energy. Closing Task • Show your knowledge of how kinetic and potential energy are converted from one form to the other by labeling the amount of KE and PE on the illustration at various points. Sketch it into your notebook