Energy Review Announcements 1 Exam 2 is coming up a Next lecture is exam review i No reading assignment or warmup quiz b Exam begins Tues Oct 7 10 15 am c Exam ends Mon Oct 13 end of day i Late fee if you pick up your exam after 5 pm d Covers Chapters 4 5 Homeworks 4 8 Ebefore Wnet Eafter E includes each object s total energy both kinetic potential Note I consider all exams to be cumulative Wnet includes the work done by all forces for which you don t have a potential energy formula Can have multiple work terms in eqn both positive and negative That is problems where you use Newton s 2nd Law to find acceleration then kinematics equations to find more details are fair game 2 Results of Table Tennis tournament Work done by a force on an object W F x Bank balances Tip Draw before and after pictures Colton Lecture 10 10 2 08 pg 1 Pulley ski jumping revisited What is the speed just at takeoff Colton Lecture 10 10 2 08 pg 2 Springs F x Hooke s Law Proportionality factor k spring constant Use conservation of energy Ebef Wnet Eaft Fspring kx negative sign force acts opposite displacement it pulls pushes back to resting point Work done to compress or stretch Defn of work W F x but can t use F is changing Better equation from calculus PEspring kx2 Question where is x 0 Then use conservation of energy to find work Colton Lecture 10 10 2 08 pg 3 Colton Lecture 10 10 2 08 pg 4 Clicker quiz If a spring is compressed by 20 cm the work done in the first 10 cm is a less than b the same as c more than the work done in the last 10 cm Bungee jumping Demo Bungee jump Video Royal Gorge Bridge Colorado 321 m http www youtube com watch v 8zSY9mQ8zvY Free fall region Hint two ways to think about this 1 Think of change in energy 2 Think of average force during the compression Demo Problem A spring stretches cm when a kg mass is added What is the spring constant k Colton Lecture 10 10 2 08 pg 5 Nonconservative forces Mechanical energy KE PE What happens when you put the brakes on in your car Colton Lecture 10 10 2 08 pg 6 Worked Problem Fred 50 kg including ice goes iceblocking on the grass Starting from rest he rides 40 m down a hill which has a 20 slope k 0 2 between the ice and grass On the way down Fred also brakes with his hands with an average force of 5 N backwards along the slope a What is his speed at the bottom b How far will will he go horizontally after he reaches the bottom Fred stops braking at the bottom Other forms of energy Where does frictional work go Microscopic picture Colton Lecture 10 10 2 08 pg 7 Colton Lecture 10 10 2 08 pg 8 Clicker quiz Fred goes down a hill with friction no braking The total vertical change is 20 m How does his speed at the bottom of a 20 slope compare to his speed at the bottom of a 30 slope a 20 would be faster b 30 would be faster c same speed at bottom Demo problem What is the spring constant of the spring inside the cannon cart Power The rate at which energy is produced or consumed P E t SI units 1Watt 1 J s 1 N m s 1 kg m2 s3 I think 1Horse power 746 W Or equivalently Power is the rate at which work is being done P F v Colton Lecture 10 10 2 08 pg 9 Empire state building Height 1 250 feet 443 meters Stories 102 There are 1 575 steps from the building s lobby to the 86th floor 374 m Paul Crake holds the record for racing these steps in 10 minutes 15 seconds What average power did he expend against gravity Assume m 80 kg Colton Lecture 10 10 2 08 pg 10 A car weighing 3000 N moves at a speed of 30 m s on level ground To do this it pushes backwards on the road with a 5000 N force Clicker quiz What is the power output of the car engine a 0 kW d 150 kW b 60 kW e 240 kW c 90 kW Where does this power go if the car moves at constant speed From work Switchbacks on mountain roads consider only work done against gravity Clicker quiz a They increase the work needed to go up a mountain b They decrease the work needed to go up a mountain c They keep the work needed the same From velocity Demo weight and light bulb Colton Lecture 10 10 2 08 pg 11 Clicker quiz a They increase the power needed to go up a mountain b They decrease the power needed to go up a mountain c They keep the power the same Colton Lecture 10 10 2 08 pg 12 Colton Lecture 10 10 2 08 pg 13