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Chapter 6: Energy and Oscillations. Brent Royuk Phys-110 Concordia University. Introduction. What do you know? Definition Forms Potential Kinetic The Unifying Idea Top-Down vs. Bottom-Up. Work. Definition The product of force and the distance moved due to that force W = F d
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Chapter 6: Energy and Oscillations Brent Royuk Phys-110 Concordia University
Introduction • What do you know? • Definition • Forms • Potential • Kinetic • The Unifying Idea • Top-Down vs. Bottom-Up
Work • Definition • The product of force and the distance moved due to that force W = F d • The component in the direction of motion • Work is a scalar • Units
Work • Note: No motion = no work • Carrying a book • Holding up a wall • Satellites • What if you push a car at constant speed? • Can work be negative? • So what is energy? • Work is a process, and energy is a property of a system.
Power • Definition: • MKS Unit • Another common power unit: 1 hp = 746 W • E = P t • kWh’s • Examples • A crane lifts 1.0 metric ton 25 m in 9.0 s. Find power in W, hp. • How much does it cost to leave a 100-W light bulb on for a month?
Kinetic Energy • Equation: • K is a form of energy: energy of ______ • Units? • Note v2 dependance. • In a certain sense, speed matters more than mass • Compare: A 50 g arrow at 40 m/s with a 1 g bullet at 400 m/s. • Try This Box 6.2 • The work-energy theorem • Application: Stopping distance
Try This • When a car brakes to a halt, the stopping distance depends on how fast the car is moving. Suppose that a 2003 Chrysler Town & Country minivan travels at some speed and then brakes to a halt. If the minivan were to travel twice as fast, how much farther would it take to stop? Assume that the brakes apply a constant force to decelerate the car. • twice as far • three times as far • four times as far • it depends on the original speed
Potential Energy • Potential energy is energy of ___________ • Any system that wants to move: something springy: springs, rubber bands, bent metal, item on a shelf, etc. • For gravity: PE = mgy • For spring:
Potential Forms • Electromagnetic Energy • Magnets, socks stick together, electricity that turns on lights • Radiant Energy • Any type of ER: radio waves, microwaves, light, x-rays, etc. • Chemical Energy • Comes from molecular arrangements- the energy you get when you burn things. • Nuclear Energy • This form only shows up when nuclei rearrange themselves, and this doesn’t happen on a large scale very often in everyday life.
Try This • Two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. Just before hitting the ground, the heavier marble has • as much kinetic energy as the lighter one. • twice as much kinetic energy as the lighter one. • half as much kinetic energy as the lighter one. • four times as much kinetic energy as the lighter one. • impossible to determine
Conservation of Energy • In systems involving only conservative forces, mechanical energy is conserved. E = U + K = constant • Variants Ko+ Uo = K + U K + U = 0 Ebefore=Eafter • If the forces are conservative, then the system will display path-independence.
Examples and Illustrations • A marble in a bowl • Roller coaster • A frictionless roller coaster leaves the top of a hill from rest. At the top of the next hill, it is 15 m lower. How fast is it moving? • Pendulum • Try This Box 6.4 • A skateboarder enters a ramp moving horizontally with a speed of 6.5 m/s and leaves the ramp moving vertically with a speed of 4.1 m/s. Find the height of the ramp, assuming no energy loss due to frictional forces. • The Bowling Ball of Death
Try This A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case. Assume air friction is negligible. • Case A: Thrown straight up. • Case B: Thrown straight down. • Case C: Thrown out at an angle of 45 degrees above horizontal • Case D: Thrown straight out horizontally In which case will the speed of the stone be greatest when it hits the water below? a. A b. B c. C d. D e. The speed will be the same in all cases
Try This A stone is launched upward into the air. In addition to the force of gravity, the stone is subject to a frictional force due to air resistance. The time the stone takes to reach the top of its flight path is • larger than • equal to • smaller than the time it takes to return from the top to its original position.
Periodic Motion • Periodic Motionis any motion that repeats itself. • The Period(T)is the time it takes for one complete cycle of motion. • What is the period of rotation of the hour hand on a clock? • The Frequency is the number of cycles per unit of time. • The period of the reoccurrence of Monday is one week. What is Monday’s frequency?
Simple Harmonic Motion • One particular type of periodic motion is SHM. • Hooke’s Law • F = - kx • A restoring force • A linear restoring force always produces SHM • Vocabulary • Equilibrium position • Periodic Motion vs. SHM • Displacement (x), Amplitude (A), Period (T), Frequency (f)
SHM • Generating the sine (or cosine) curve Animation courtesy of Dr. Dan Russell, Kettering University
Period Expressions • Mass on a spring: • Pendulum:
