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Work, Power, and Energy Momentum Review Momentum = mass x velocity =mv If the boulder and the boy have the same momentum, will the boulder crush the boy? Hint: Which would have the larger speed? Review Videos Momentum and Projectile Motion in action: Jumping a Football Field Conservation of Momentum - Recoil: Dorm Chair Hit Work Work is the amount of force applied for a certain distance W=F*d The unit for Work can be found from force (N) and distance (m) or N*m But a N*m is also equivalent to a Joule (J) So the unit we use for Work is the Joule (J) When calculating work, we only use forces and distances that are in the same direction or orientation. BAD GOOD Force Force Displacement Displacement Work = Force x Distance F = 500 pounds (2000 N) D = 8 feet (2.5 meters) ----------------------------------W = 2000 N x 2.5 m = 5000 N-m ----------------------------------Alternative unit: Joule 1 N-m = 1 joule (J) Work = Force x Distance If the wall doesn't move, the prisoner does no work. Try this problem What is the work done by pushing a dumpster with 60N of force a distance of 3m? Try this Problem What is the work done by accelerating a 50kg block at 2m/s2 a distance of 6 meters? Power Power is the amount of work done over a specific period of time P=W/t The unit for power is the J/s or Watt (W) Power = Work/ Time 1 joule / second = 1 watt Try this Problem What is the power generated by moving a bucket of water 7m with an applied force of 4N for a total amount of time of 4s? Power can also be calculated using • P = F*v • You can see that this equation is equal to (F*d)/t with the following proof P = F * v = (F * d) / t F * d/t = F * d/t Graphing Work To find the amount of work done graphically you need to draw a Force vs. Distance graph Once you plot your points, find the line of best fit To determine the amount of work done for a particular range, take the area under the curve The area under the curve of a Force vs. Distance graph is = to the amount of WORK done The graph below shows the force applied to move a block 6m. Find the work done for the first 3m. the work done moving the block 6m. Energy Work can be found by not just F*d but also by finding the change in energy in the system. W E W KE 1 W ( mv 2 ) 2 1 W m( v ) 2 2 1 1 2 W mv f mvi2 2 2 Types of Energy Energy – energy involved with moving objects Kinetic • KE = ½ mv2 • Units are in Joules (J) Potential Energy – stored energy involved with the height of the object Gravitational • PEg = mgh • The height to which the object has risen is determined by using a reference level The position where PE is defined to be zero Units are in Joules (J) Potential Energy – stored energy of a spring Spring This is the amount of energy that compressed or stretched springs carry • PEsp = ½ kx2 Where ‘k’ is the spring constant in units of N/m • Spring constants vary and depend entirely upon the construction of the spring and ‘x’ is the distance that the spring is stretched or compressed from it’s equilibrium position • Units are in Joules (J) Gravitational Potential Energy Energy store by lifting. Energy = Work = F x d PEg = mgh m = mass g = acceleration of Gravity h = height What P.E. is gained when a 100 kg object is raised 4m straight up? ΔP.E. = mgΔh = (100 kg)(9.8 m/s2)4 m = 3920 J Calculate the work An object weighing 15 N is lifted from the ground to a height of 0.22 m. Find object's change in PE ΔP.E.= mgΔh mg = 15 N ΔP.E. = 15 N(.22m) ΔP.E. = 3.3 Nm = 3.3 J h = .22 m Conservation of Energy The Law of Conservation of Energy states that in a closed, isolated system, energy can neither be created nor destroyed • Energy is conserved The sum of kinetic energy and gravitational potential energy of a system is called mechanical energy. Total Energy: E = KE + PEg + PEsp Where there is no spring in the system, the mechanical energy of that sytem is: E = KE + PEg This means that since the energy in a system never changes, • If you increase KE you decrease PE • If you increase PE you decrease KE Important Note Any extra energy that may be lost is transferred to heat energy (Q) by any friction in the system The reference tables include this when it is written: E = KE + PE + Q • Ignore the on the reference table for this equation because internally, the total energy will never change Gravity supplies the energy to move objects like a roller coaster Watch what happens to the KE and PE over time…. Skiing is another example of conservation of energy If you ski down a steep slope and start at the top, your total mechanical energy starts as gravitational potential energy As you start skiing downhill, that potential energy is converted to kinetic energy As you ski down the slope, your speed increases as more of your potential energy is converted to kinetic energy Pendulums The simple oscillation of a pendulum also demonstrates conservation of momentum At the highest point where the pendulum is initially released, all the energy is in the form of potential energy But as the pendulum bob is swinging, its energy is in the form of kinetic energy This is the energy that gives the pendulum bob its velocity At the lowest point on the pendulum’s swing, the PE = 0 and the KE is maximized Three types of Energy Gravitational potential changes to kinetic and then work. Conservation of Energy Conservation of Mechanical Energy KEbefore + PEbefore = KEafter + PEafter Conservation of Energy Pendulums Brainiac Pendulums and Conservation of Energy and Conservation of Energy Science World Try this Problem A bike rider approaches a hill at a speed of 8.5m/s. The combined mass of the bike and rider is 85.0kg. Find the initial kinetic energy of the system. The rider coasts up the hill. Assuming there is no friction, at what height will the bike come to rest? Collisions Previously we has a conservation of momentum in collision situations pbefore = pafter Now, we also have a conservation of energy within collisions KEbefore = KEafter Collisions and KE KEAi + KEBi = KEAf + KEBf ½ mv2Ai + ½ mv2Bi = ½ mv2Af + ½ mv2Bf Spring Potential Energy As previously mentioned, the spring potential energy can be found by the equation: PEsp = ½ kx2 According to Hooke’s Law: The force exerted by a spring is equal to the spring constant times the distance the spring is compressed or stretched from its equilibrium position F = -kx Spring Constant and Energy in a Spring A spring stretches by 18cm when a bag of potatoes weighing 56N is suspended from its end. What is the PE stored in the spring? F = 56N x = 18cm = 0.18m k = ? F = -kx K=F/x K = 56N / 0.18m K = 310 N/m PEsp = ½ kx2 PEsp = ½ (310N/m)(0.18m)2 PEsp = 5.0 J