Lecture 18: Work and Energy Work and Energy Definition of work Examples Today s Agenda Definition of Mechanical Energy Conservation of Mechanical Energy Conservative forces Physics 201: Lecture 10, Pg 1
Example A block of mass 2 kg is pulled up a frictionless incline by a tension T. The block starts at rest and after being pulled up the incline 4 m has a speed of 15 m/s. (a) What is the net work done on the block? (b) What is the force of tension? Physics 201: Lecture 10, Pg 2
Clicker Question 1: What is the work done by gravity as the block slides down the incline? (a) (b) (c) (d) (e) W = mgh W = mgh*sin( ) W = mgh*cos( ) W = -mgh W = -mgh*sin( ) h mg S Physics 201: Lecture 10, Pg 3
Clicker Question 2: What total work does gravity do as my book is moved up and then back to it s starting point? h h initial final (a) W = mgh (b) W = 0 (c) W= -mgh Physics 201: Lecture 10, Pg 4
Clicker Question 3: A frictional force F F resists the motion of the box below as it is moved to the right a distance d and then back to it s initial position. What total work does friction do on the block? initial d final d (a) W = 2F F d (b) W=0 (c) W = -2F F d Physics 201: Lecture 10, Pg 5
Conservative forces For conservative forces the work done does not depend on path taken, only the starting and finishing points matter Ex. gravity For conservative force work on a closed path is zero When I move my book up and then down to the initial position work done by gravity was zero This semester Conservative forces Gravity Springs Non-conservative forces Anything else! Conservative forces give object a potential energy!!!! Physics 201: Lecture 10, Pg 6
Work done by gravity Lets compute the work done by the gravitational force. final initial mg mg hf hi By moving the block up a distance h, it gains potential energy of mgh! U = -WC U = -(-mg(hf - hi)) = mg( h) Wg =- mg h Physics 201: Lecture 10, Pg 7
Gravitational Potential Energy W mg h U W U mg h U f mgh U 0 Physics 201: Lecture 10, Pg 8
The Work-Energy Theorem W tot = K W C + W NC = K W NC W NC = K W C = K + U Physics 201: Lecture 10, Pg 9
Conservation of Mechanical Energy If only conservative forces are doing work (ie W NC is zero), the total mechanical energy of a system is conserved. WNC = Ef - Ei =0 Einitial = Efinal E = K + U is constant!!! Both K and U can change, but E = K + U remains constant. Physics 201: Lecture 10, Pg 10
Clicker Question 4: A railroad car rides down a frictionless track in the x-direction then collides and sticks to another car at rest. Which below is true? (A) Mechanical energy is conserved during the collision (B) Linear momentum in the x-direction is conserved for the two railroad car system (C) Both (A) and (B) (D) Neither (A) or (B) (E) Neither (A) or (B) or (C) Physics 201: Lecture 10, Pg 11
Clicker Question 5: A ball is dropped from a height H. (Answer here for the time when the ball is in the air. Do not consider when it hits the ground. Also neglect air resistance.) Which below is true? (A) Mechanical energy is conserved for the ball (B) Linear momentum in the y-direction is conserved for the ball (C) Both (A) and (B) (D) Neither (A) or (B) (E) Neither (A) or (B) or (C) Physics 201: Lecture 10, Pg 12
Work by a Constant Force The work done by a force acting on an object that undergoes a displacement is equal to the area under the graph of F versus x F x Physics 201: Lecture 10, Pg 13
Work by a Non-constant Force The work done by a variable force acting on an object that undergoes a displacement is equal to the area under the graph of F versus x F F = -kx x1 x W = ½ (-kx1)(x1) W =-½k(x1) 2 WC = - U -kx1 U = ½ kx 2 U = ½k( s) 2 Physics 201: Lecture 10, Pg 14
Clicker Question 6: You grasp the end of a spring that is attached to the wall and is initially in its resting position. You pull it out until it is extended 0.1 m from its resting position, then push it in until it is compressed by 0.1 m from its resting position. Finally, you return the spring to its resting position. The spring constant is k = 20 N/m. The total work W done by the spring on your hand is (a) W < 0 (b) W = 0 (c) W > 0 Physics 201: Lecture 10, Pg 15
Example A 1.7kg particle moving along the x-axis experiences the force shown in the figure. The particle's velocity is 4.6m/s at x=0m. What is its velocity at x=2m? Physics 201: Lecture 10, Pg 16
Clicker Question 7: Two perfect billiard balls collide on a flat, frictionless pool table. Which below is true? (A) Mechanical energy is conserved for the balls (B) Linear momentum in the is conserved for the balls in the plane of the table (C) Both (A) and (B) (D) Neither (A) or (B) (E) Neither (A) or (B) or (C) Physics 201: Lecture 10, Pg 17
Clicker Question 8: A rifle bullet of mass m = 3.00 10-2 kg traveling at v b = 240.00 m/s collides with and embeds itself in a pendulum of mass M = 2.88 kg, initially at rest and suspended vertically by massless strings of length L = 2.00 m. As the bullet collides with the block, what is conserved for the block/bullet system? (The bullet/block collision is so fast the pendulum does not have time to swing up until after the collision) (a) Mechanical Energy (b) Linear Momentum (c) Both (a) and (b) (d) Neither (a) or (b) Physics 201: Lecture 10, Pg 18
Clicker Question 9: A rifle bullet of mass m = 3.00 10-2 kg traveling at v b = 240.00 m/s collides with and embeds itself in a pendulum of mass M = 2.88 kg, initially at rest and suspended vertically by massless strings of length L = 2.00 m. After the bullet is imbedded in the block and the pendulum begins to swing, what is conserved for the block/bullet system? (a) Mechanical Energy (b) Linear Momentum (c) Both (a) and (b) (d) Neither (a) or (b) Physics 201: Lecture 10, Pg 19
Clicker Question 10: A block slides down a rough inclined surface, eventually coming to rest. Which below is true? y x (A) Mechanical energy is conserved for the block (B) Linear momentum in the x-direction is conserved for the block (C) Linear momentum in the y-direction is conserved for the block (D) Both (A) and (B) (E) Neither (A) or (B) or (C) Physics 201: Lecture 10, Pg 20