Physics 101: Lecture 10, Pg 1 Physics 101: Lecture 10 Potential Energy & Energy Conservation l Today’s lecture will cover Textbook Sections Hour Exam 1: One week away! -exam time / conflicts -exam locations -how to study / exam review Sun. 8pm -sign up for conflict exam before Thurs. -if you have a double conflict, contact Prof. Bob Clegg,

Physics 101: Lecture 10, Pg 2Review  Work: Transfer of Energy by Force W F = |F| |S| cos  Kinetic Energy (Energy of Motion) K = 1/2 mv 2 Work-Kinetic Energy Theorem:  W =  K Preview Potential (Stored) Energy U

Physics 101: Lecture 10, Pg 3 Preflight 4 What concepts were most difficult to understand in preparing for this lecture? “everything” “nothing” “Work Energy- Theorem; What is it!?” “The equations were kind of confusing…” “Understanding what the symbols mean” “…confused as to the significance of the lower case ‘k’” Lecture / Lab / HW / Discussion order USA vs. Canada Olympic hockey was too awesomely distracting to think very hard about the pre-lecture, sorry. “the last problem the one with baseball on the moon. ” “signs for work... ” What is a conservative force anyway?

Physics 101: Lecture 10, Pg 4 Work Done by Gravity 1 l Example 1: Drop ball Y i = h Y f = 0 W g = (mg)(S)cos  S = h W g = mghcos(0 0 ) = mgh  y = y f -y i = -h W g = -mg  y mg S y x Y i = h Y f = 0 mg S y x

Physics 101: Lecture 10, Pg 5 Work Done by Gravity 2 Example 2: Toss ball up W g = (mg)(S)cos  S = h W g = mghcos(180 0 ) = -mgh  y = y f -y i = +h W g = -mg  y Y f = h Y i = 0 mg S y x

Physics 101: Lecture 10, Pg 6 Work Done by Gravity 3 Example 3: Slide block down incline W g = (mg)(S)cos  S = h/cos  W g = mg(h/cos  )cos  W g = mgh  y = y f -y i = -h W g = -mg  y h  mg S

Physics 101: Lecture 10, Pg 7 Work and Potential Energy l Work done by gravity independent of path  W g = -mg (y f - y i ) l Define U g =mgy l Works for any CONSERVATIVE force l Modify Work-Energy theorem

Physics 101: Lecture 10, Pg 8 Conservation ACT Which of the following statements correctly define a Conservative Force: A. A force is conservative when the work it does on a moving object is independent of the path of the motion between the object's initial and final positions. B. A force is conservative when it does no net work on an object moving around a closed path, starting and finishing at the same point. C. Both of the above statements are correct. D. Neither of the above statements is correct. correct

Physics 101: Lecture 10, Pg 9 Skiing Example (no friction) A skier goes down a 78 meter high hill with a variety of slopes. What is the maximum speed she can obtain if she starts from rest at the top? Conservation of energy:  W nc =  K +  U K i + U i = K f + U f ½ m v i 2 + m g y i = ½ m v f 2 + m g y f 0 + g y i = ½ v f 2 + g y f v f 2 = 2 g (y i -y f ) v f = sqrt( 2 g (y i -y f )) v f = sqrt( 2 x 9.8 x 78) = 39 m/s 26 0 = K f -K i + U f - U i

Physics 101: Lecture 10, Pg 10 Pendulum ACT l As the pendulum falls, the work done by the string is 1) Positive2) Zero3) Negative How fast is the ball moving at the bottom of the path? W = F d cos . But  = 90 degrees so Work is zero. h Conservation of Energy (W nc =0)  W nc =  K +  U 0 = K final - K initial + U final - U initial K initial + U initial = K final +U final 0 + mgh = ½ m v 2 final + 0 v final = sqrt(2 g h)

Physics 101: Lecture 10, Pg 11 Pendulum Demo With no regard for his own personal safety your physics professor will risk being smashed by a bowling ball pendulum! If released from a height h, how far will the bowling ball reach when it returns? h Conservation of Energy (W nc =0)  W nc =  K +  U 0 = K final - K initial + U final - U initial K initial + U initial = K final +U final 0 + mgh initial = 0 + mgh final h initial = h final

Physics 101: Lecture 10, Pg 12 Lecture 10, Preflight 1 Imagine that you are comparing three different ways of having a ball move down through the same height. In which case does the ball get to the bottom first? A. Dropping B. Slide on ramp (no friction) C. Swinging down D. All the same “they will all have the same speed at the bottom.” correct “The ball being dropped will reach the ground fastest since it doesn't have to travel as far.”

Physics 101: Lecture 10, Pg 13 Lecture 10, Preflight 2 Imagine that you are comparing three different ways of having a ball move down through the same height. In which case does the ball reach the bottom with the highest speed? 1. Dropping 2. Slide on ramp (no friction) 3. Swinging down 4. All the same correct Conservation of Energy (W nc =0)  W nc =  K +  U K initial + U initial = K final +U final 0 + mgh = ½ m v 2 final + 0 v final = sqrt(2 g h)

Physics 101: Lecture 10, Pg 14 Skiing w/ Friction A 50 kg skier goes down a 78 meter high hill with a variety of slopes. She finally stops at the bottom of the hill. If friction is the force responsible for her stopping, how much work does it do? Work Energy Theorem: W nc = K f -K i + U f -U i = ½ m v f 2 - ½ m v i 2 + m g y f – m g y i = g y i m = – 764 x 50 Joules = Joules Similar to bob sled homework

Physics 101: Lecture 10, Pg 15 Galileo’s Pendulum ACT How high will the pendulum swing on the other side now? A) h 1 > h 2 B) h 1 = h 2 C) h 1 < h 2 h1h1 h2h2 m Conservation of Energy (W nc =0)  W nc =  K +  U K initial + U initial = K final +U final 0 + mgh 1 = 0 + mgh 2 h 1 = h 2

Physics 101: Lecture 10, Pg 16 Power (Rate of Work) P = W /  t  Units: Joules/Second = Watt l How much power does it take for a (70 kg) student to run up the stairs in 151 Loomis (5 meters) in 7 sec? P = W / t = m g h / t = (70 kg) (9.8 m/s 2 ) (5 m) / 7 s = 490 J/s or 490 Watts

Physics 101: Lecture 10, Pg 17Summary  Conservative Forces »Work is independent of path »Define Potential Energy U n U gravity = m g y n U spring = ½ k x 2  Work – Energy Theorem  Chapter 6, problems 27, 31, 35