A 0 kg sled slides down a 30 hill after receiving a tiny shove (only enough to overcome static friction, not enough to give significant initial velocity, assume v o =0). A) If there is friction of µ k =0.1, what is the acceleration of the sled? B) If the length of the hill is 0 m, how long does it take the sled to reach the bottom of the hill if it starts from rest? Inclines & Friction 0 m 30 o
Random selection of suggested improvements Ok, I will email announcements I hope you earn one Thanks. I can move to less class discussion and more discussion from me on clickers (which would allow for more clickers and other problems). I currently don t have any control over the labs other than I ve been encouraging the TAs I know to email you earlier (and respond quicker) and I made them shift the labs around to better match up with our lectures. The lab manager has a major illness, so I have asked to be allowed to assist in guiding the TAs more. There are often extras at the end of the lecture notes. We don t have time for all of them during lecture. Ok Many want more. I tried that; it didn t. Me too, thoughts on how? Thanks to everyone for your feedback!
Statistics 71% of class thinks clicker questions help learning (which agrees with scientific research on education) 73% like having homeworks on WebAssign 81% like Webassign homeworks spread out Only % of the class did not like the Facebook page (rest like, neutral, or no opinion) Many think I should spend more time on problem solving. Ok, let s reduce clicker class discussion.
Main Ideas Today Work Done by a Constant Force Work-Energy Principle Kinetic Energy Potential Energy Extra Practice Problems: 5.1, 5.3, 5.9, 5.11, 5.37, 5.41, 5.43, 5.45, 5.47, 5.65, 5.69, 5.79, 5.83
A cable attached to a car lowers the car down the ramp (angle α). Which direction should friction point? A. B. C. D. E. not enough information given to decide Q49
Definition: Mechanical Work Work is what is accomplished by a force acting on an object (i.e., movement in the direction of that particular force) Work is a scalar quantity - no direction It can, however, be either positive or negative. Positive if the object moves at least partly in the direction of the force. Negative if moves at least partly in the opposite direction. Zero if moves in direction perpendicular to the force. Here we could discuss the work done by Tension, Friction, Gravity or the Normal Force.
What is the sign of the work of each force? Tension Gravity Normal force Friction Car Going Up the Ramp Positive Negative Zero Negative Car Going Down Negative Positive Zero Negative The work done by kinetic friction is always negative, since it always points in the direction opposite of motion.
Three blocks are connected as shown. The ropes and pulleys are of negligible mass. When released, block C moves downward, block B moves up the ramp, and block A moves to the right. After each block has moved a distance d, the force of gravity has done A. positive work on A, B, and C. B. zero work on A, positive work on B, and negative work on C. C. zero work on A, negative work on B, and positive work on C. The sign of the work done by gravity D. none of these depends on if the object moves up or down. Q54
Work Done by a Constant (or Average) Force x F Force F acting on an object causes the object to move a distance Δx does work W W = F x magnitude of displacement of object component of force parallel to displacement of object Units: N m = Joule (J) Or equivalently: Only concerned with movement in the direction of the force
Work Done by a Constant Force Ex: Person pulling a crate on the floor. F = F cosθ W = ( F cosθ ) x Δx What is the component of the force along the direction of motion? Ex: Person carrying bag of groceries at constant speed F = 0 Δx W = F x = 0
A person lifts a bag of groceries that weighs 15 N from the ground to a height of 1.5 m above the ground at a constant velocity. Calculate the work done by the person on the bag and the work done by gravity.
Energy Energy is always conserved - neither increased nor decreased. However, it can be converted to heat. (in Ch.11) F x Energy can be derived from W= and one of our formulas from Chapter. (you don t need to derive) Let s do that. We start by finding the work done when we change the speed of an object.
The Work-Energy Principle Relates net work done on an object to the change in its speed v o v f Constant net force changes velocity from v 1 to v over a distance Δx v = v + a x o F net = W net ma = m v v x o = Δx 1 x a = mv v v x o 1 x mv = F x W = 1 mv 1 o mv net o
The Work-Energy Principle The work done on an object by a net force is W = 1 mv 1 mv net o Translational kinetic energy (energy of motion) of an object: KE = 1 mv The net work done on an object is equal to the change in its kinetic energy W net = KE = KE f KE o
A system of objects: Just add up their individual kinetic energies v 1 m 3 v v 3 m 1 m 1 1 1 m v m v m v KE = + + system 1 We will do systems more in the next chapter when we discuss collisions! Examples: billard balls and football players 1 3 3
Kinetic Energy of a System v v Mass m Mass m What is the kinetic energy of the system of vehicles? Can KE(system) ever be negative? Ever zero? A) 0 B) ½ mv C) mv D) mv E) 3mv Q55
Fun Example : The Flash The Flash runs so fast that he can pluck bullets from the air (Flash s speed speed of bullets). Where does all of this energy come from? Food. The Flash eats for the same reason we do. KE = 1 mv The Flash s (and our) caloric intake requirements increase quadratically the faster we run. Twice as fast means four times the calories needed to fuel the running.
Let s estimate, like you should for your movie calculation. Flash s weight ~155 pounds or 70 kg Let s say he is running at 1% the speed of light (not his top speed) = 1860 miles/s or 3 million m/s KE = ½ (70 kg) (3,000,000 m/s) =315 trillion kg m /s (J) = 75 billion Calories (0.0004 Calories = 1 kg m /s ) That s 150 million burgers! And if he stops, he would need another 150 million burgers to speed up again!
Why does food give us energy? It s not the kinetic energy of the atoms shaking. A hot meal has the same calories as a cold meal. It s the potential energy locked in the chemical bonds. Remember that energy can never be created nor destroyed. Bonds are treated as "springs" with an equilibrium distance equal to the bond length. The chemical energy in our food can be used for other activities like moving and growing.
Cindy pushes her new 18 kg TV 0.0m at a constant speed and at an angle of 0 degrees from the rough carpet (µ k =0.50). A) What force does she apply? B) How much work does she do on the TV? C) What is the energy lost due to friction?
Test : Wednesday Feb 1, 7PM Same room as last test, Clark 101 Past test online (covered Wed. morning) If you have a Thursday lab, read your lab first 0 Multiple Choice Questions Covering: Projectile Motion, Newton s Laws, Free Body Diagrams, Friction, Work, Kinetic Energy, Potential Energy, Conservation of Energy and Applications of These
1.0 A)1 m B) m C)3 m D)4 m E)Impossible to determine Q56
Two iceboats (one of mass m, one of mass m) hold a race on a frictionless, horizontal, frozen lake. Both iceboats start at rest, and the wind exerts the same constant force on both iceboats. Q57 Which iceboat crosses the finish line with more kinetic energy (KE)? A. The iceboat of mass m: it has twice as much KE as the other. B. The iceboat of mass m: it has 4 times as much KE as the other. C. The iceboat of mass m: it has twice as much KE as the other. D. The iceboat of mass m: it has 4 times as much KE as the other. E. They both cross the finish line with the same kinetic energy.
A satellite is moving around the Earth in a circular orbit. Over the course of an orbit, the Earth s gravitational force A. does positive work on the satellite. B. does negative work on the satellite. C. does positive work on the satellite during part of the orbit and negative work on the satellite during the other part. D. does zero work on the satellite at all points in the orbit. Q58
Two iceboats (one of mass m, one of mass m) hold a race on a frictionless, horizontal, frozen lake. Both iceboats start at rest, and the wind exerts the same constant force on both iceboats. Q59 Which iceboat crosses the finish line with more kinetic energy (KE)? A. The iceboat of mass m: it has twice as much KE as the other. B. The iceboat of mass m: it has 4 times as much KE as the other. C. The iceboat of mass m: it has twice as much KE as the other. D. The iceboat of mass m: it has 4 times as much KE as the other. E. They both cross the finish line with the same kinetic energy.
Energy is a scalar, Velocity is not KE = 1 mv In two dimensions v = v + v x y (pythagorean theorem) In three dimensions v = vx + vy + v z I will not test you on three dimensions, but it could show up on the MCAT or DAT
More conservative examples: Springs (ignoring friction) Any example in Chapter -4 (ignoring friction) In this class, friction and air resistance are the main nonconservative forces we will use. In general, it is defined as nonconservative if you cannot get that energy back (like if you push something).
Clicker Answers Chapter/Section: Clicker #=Answer 1=E, =E, 3=D, 4=D, 5=B, 6=C, 7=A, 8=C, 9=E, 10=A, 11=C, 1=B, 13=C, 14=E, 15=A, 16=B, 17=C, 18=B, 19=D, 0=A, 1=B, =B, 3=A, 4=B, 5=A, 6=E, 7=C, 8=C, 9=B, 30=D, 31=C, 3=B, 33=D, 35=D, 36=A, 37=B, 38=C, 39=E, 40=B, 41=B, 4=C, 43=A, 44=A, 45=C, 46=D, 47=E, 48=B, 49=A, 50=A, 51=C, 5=C, 53=A Energy: 54=C, 55=E, 56=D, 57=E, 58=D, 59=E