Unit 08 Work and Kinetic Energy. Stuff you asked about:

Transcription

1 Unit 08 Work and Kinetic Energy Today s Concepts: Work & Kinetic Energy Work in a non-constant direction Work by springs Mechanics Lecture 7, Slide 1 Stuff you asked about: Can we go over the falling, sliding, and swinging question? I would like to see some examples in class on work. Not sure if i fully grasp the concept could you go over bridge question 3 More spring examples please Please go over more problems in class. I am not sure when to use which equation because the prelecture listed a lot of them. I need more help with understanding how the angle gets incorporated when solving these problems. I also did not understand the work on the box in the truck problem. I would like to go over Potential Energy (U); where Wc = Ui-Uf = -(Uf-Ui) = -delta U The difference between work and net work. more example problems Please explain the first bridge question! Please review the Work Done on Spring equation along with an example I do not feel confident on any of the prelecture topics. Please go over all of them! more practice problems with the spring please Review Bridge question one. Can we go over the skier problem from the prelecture Mechanics Lecture 7, Slide 2 1

2 Work-Kinetic Energy Theorem Work = FDx = ½ mv f2 ½ mv 2 o = DKE Units for both are Joules 1 Newton X 1 meter Mechanics Lecture 7, Slide 3 C B A m 2 a) Direction A b) Direction B c) Direction C d) All three forces will change the velocity of the cart by the same amount. A frictionless lab cart is free to move in the x direction. It can pushed in three different directions by a 5N force. Which will change the velocity of the cart the most? Mechanics Lecture 7, Slide 4 2

3 Work-Kinetic Energy Theorem The work done by force F as it acts on an object that moves between positions r 1 and r 2 is equal to the change in the object s kinetic energy: F DX cos(q) = ½ m f2 ½ mv o 2 W DK Units for both are Joules: 1 Newton X 1 meter Mechanics Lecture 7, Slide 5 Example 8.1 (Work on cart) A 2kg frictionless lab cart is pushed with a force of 5N for a distance of 1m. The force is horizontal. What is the kinetic energy of the cart after the push? What is the cart s velocity after the push? Mechanics Lecture 7, Slide 6 3

4 Example 8.2 (Work on cart) A 2kg frictionless lab cart is pushed with a force of 5N for a distance of 1m. The force has an angle of 30 o to the horizontal. What is the kinetic energy of the cart after the push? What is the cart s velocity after the push? Mechanics Lecture 7, Slide 7 Example 8.3 (Work on cart) A 2kg frictionless lab cart is moving to the right at 4m/sec. A horizontal 5N force pushes on the cart to the left for a distance of 2m. What is the kinetic energy of the cart after the push? What is the cart s velocity after the push? Mechanics Lecture 7, Slide 8 4

5 Bridge Question A hockey player does work on a hockey puck in order to propel it from rest across the ice. When a constant force is applied over a certain distance, the puck leaves his stick at speed v. If instead he wants the puck to leave with a speed 2v, by what factor must he increase the distance over which he applies the same force. A) 2 B) 2 C) 2 2 D) 4 E) 8 Bridge Question If instead he wants the puck to leave with a speed 2v, by what factor must he increase the distance over which he applies the same force. A) 2 I believe it would be half of the distance because it would then travel twice the speed. B) 2 W=Fd, so the distance would need to be multiplied by 2 to double the speed. C) 2 2 the velocity is squared. D) 4 Kinetic energy is proportional to V(squared), therefore to go twice the velocity (2v), you would need to go four times the distance (4d). E) 8 5

6 the whole pre-lecture was confusing. the apple has zero kinetic energy and thus 0 work because it started and stopped at rest; however a ball that is dropped does have work, when it too starts and stops at rest??? makes no sense The fact that work can be zero after something moves can be confusing. Mechanics Lecture 5, Slide 11 As the student lifted the apple, what kind of work did the student do on the apple? As the student lifted the apple, what kind of work did gravity do on the apple? A. Positive B. Negative C. zero As the student lifted the apple, what total work done on the apple? (Note that the term potential energy was not used.) Mechanics Lecture 5, Slide 12 6

7 Example 8.4 (Friction on a block) A 5kg block slides to the right with an initial speed of 4m/sec. The coefficient of kinetic friction between the block and table is m k =0.2. What is the block s speed after it has slid 2meters? How far will the block slide before coming to rest? Mechanics Lecture 7, Slide 13 If you push a box across the floor in the positive x direction for 1 meter at a constant velocity with a force of 10N, what is the work done by friction? A. +10J B. -10J C. 0J D. +20J E. Can t tell from the information provided Mechanics Lecture 7, Slide 14 7

8 If you push a box across the floor in the negative x direction for 1 meter at a constant velocity with a force of 10N, what is the work done by friction? A. +10J B. -10J C. 0J D. +20J E. Can t tell from the information provided Mechanics Lecture 7, Slide 15 If you push a box across the floor in the negative x direction for 1 meter at a constant velocity with a force of 10N, what is the net work done on the box? A. +10J B. -10J C. 0J D. +20J E. Can t tell from the information provided Mechanics Lecture 7, Slide 16 8

9 You push two boxes along a straight line from one side of a room to the other. Each box begins and ends at rest. The contact surfaces and areas between box and floor are the same for both, but one box is heavy and the other is light. Which of the following statements is correct? a) You do more work on the heavy box, and more net work is done on the heavy box. b) You do more work on the heavy box, but the net work done on both boxes is equal. c) You do the same amount of work on both boxes, and the same amount of net work is done on both boxes. d) You do more work on the light box, but more net work is done on the heavy box. e) You do the same amount of work on both boxes, but more net work is done on the heavy box. Mechanics Lecture 7, Slide 17 Question A box sits on the horizontal bed of a moving truck. Static friction between the box and the truck keeps the box from sliding around as the truck drives forward. a m S The work done on the box by the static frictional force as the truck moves a distance D to the left is: A) Positive B) Zero C) Negative Mechanics Lecture 7, Slide 18 9

10 Question a F m S D The work done on the box by the static frictional force as the truck moves a distance D is: A) Positive B) Zero C) Negative A) The box is moving along with the force of friction. The force and motion are in the same direction. B) Because there is no displacement there is no work. C) The static friction force must go the same direction as the acceleration. With that, the force and the distance are parallel to each other and the angle is 180 degrees, meaning that the work is less than zero. Physics 211 Lecture 7, Slide 19 Can break any path into tiny pieces WTOT W1 W2... W m g d l m g d l m g d l N m gdy... 1 m gdy 2 m gdy N m g D y N dl 1 dl N Dy mg dl 2 W mgdy g Mechanics Lecture 7, Slide 20 10

11 You are loading boxes so that they come to rest on to a truck and can use one of two methods. In the first method, the boxes are lifted directly on to the back of the truck. In the second method, the boxes are slid up a ramp at an angle q with rollers on it, which we can assume are frictionless, coming to rest in the truck. Using the physics definition how does the work done by you in the two methods compare? W 1 > W 2 2. W 1 = W 2 3. W 1 < W 2 4. depends on q Mechanics Lecture 7, Slide 21 Example 8.5 (Block on Ramp) A 5kg block is pulled up a distance of 2m along a frictionless ramp by a 20N force. How much work did force do on the block? How much work did gravity do? If it starts from rest, what is the velocity of the box after the 2m? 20 o Mechanics Lecture 7, Slide 22 11

12 Example 8.6 (Block on Ramp) A 5kg block starts from rest and is pulled up a distance of 2m along a frictionless ramp by a 20N force. After these two meters, the block is released and can slide up the ramp on it s own. How far up the ramp, L, will it go? 20 o Mechanics Lecture 7, Slide 23 A block having mass m moves along an incline having friction as shown in the diagram to the left. The spring is extended from its relaxed length. As the block moves a small distance up the incline, how many forces do work on the block? A. Two forces B. Three forces C. Four forces D. Five forces E. None of the above Mechanics Lecture 7, Slide 24 12

13 H Checkpoint Three objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string. Free Fall Frictionless incline Pendulum A) Free Fall B) Incline C) Pendulum D) All the same In which case does the object have the biggest net work done on it by all forces during its motion? Mechanics Lecture 7, Slide 25 Question Three objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string. What is the relationship between their magnitude of their velocities when they reach the bottom? H Free Fall Frictionless incline Pendulum A) v f > v i > v p B) v f > v p > v i C) v f = v p = v i Mechanics Lecture 7, Slide 26 13

14 Question Three objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string. What is the relationship between their horizontal component of their velocities when they reach the bottom? H Free Fall Frictionless incline Pendulum A) v xf > v xi > v xp B) v xp > v xf > v xi C) v xf = v xp = v xi Mechanics Lecture 7, Slide 27 Checkpoint A car drives up a hill with constant speed. Which statement best describes the total work W TOT done on the car by all forces as it moves up the hill? A) W TOT > 0 B) W TOT = 0 C) W TOT < 0 Let s ask this in a different way Mechanics Lecture 7, Slide 28 14

15 Question A car drives up a hill with constant speed. How does the kinetic energy of the car change as it moves up the hill? A) It increases B) It stays the same C) It decreases Mechanics Lecture 7, Slide 29 Work done by a Spring Physics 211 Lecture 7, Slide 30 15

16 Question you asked I am confused about the positive work and negative work and also the positive and negative forces for the spring problems. Easiest Method: 1) Use the formula to get the magnitude of the work 2) Use a picture to get the sign (look at directions) In this example the spring does ve work since F and Dx are in opposite direction. The axes don t matter. Physics 211 Lecture 7, Slide 31 Question A box attached at rest to a spring at its equilibrium length. You now push the box with your hand so that the spring is compressed a distance D, and you hold the box at rest in this new location. D During this motion, the spring does: A) Positive Work B) Negative Work C) Zero work Mechanics Lecture 7, Slide 32 16

17 Question A box attached at rest to a spring at its equilibrium length. You now push the box with your hand so that the spring is compressed a distance D, and you hold the box at rest in this new location. During this motion, your hand does: D A) Positive Work B) Negative Work C) Zero work Mechanics Lecture 7, Slide 33 Question A box attached at rest to a spring at its equilibrium length. You now push the box with your hand so that the spring is compressed a distance D, and you hold the box at rest in this new location. D During this motion, the total work done on the box is: A) Positive B) Negative C) Zero Mechanics Lecture 7, Slide 34 17

18 Example 8.7 (Box on Spring) 10cm 40cm A 20kg box is placed gently on a vertical spring which compresses it 10cm. I then compress the spring an additional 40cm with my hand. When I release the box and spring, how high will the box fly? Mechanics Lecture 7, Slide 35 A block having mass m travels along a horizontal frictionless surface with speed v. What is the LEAST amount of work that must be done on the mass to totally reverse its velocity? A. -mv 2 B. -mv 2 /2 C. 0 D. mv 2 /2 E. mv 2 Mechanics Lecture 7, Slide 36 18

19 Example 8.8 (Skier) 25 o 3.5m A 60kg skier starts from rest and goes down a 10.4m long 25 o slope. The coefficient of kinetic friction between the skis and the snow is m k =0.2. At the end of the slope, he flies off a 3.5m high cliff. What is his velocity just before he connects with the snow at the bottom of the cliff and skis coolly off for a hot chocolate? Mechanics Lecture 8, Slide 37 The Physics Donkey Because you re tired of hauling your TI-83 all over campus, you decide to bring your donkey and cart with you to COD. After physics class, you load all your books and stuff into the cart and tell the donkey to head off to Calc III. But the donkey replies (it s a talking physics donkey) There s no point in me trying. According to Newton s 3 rd Law, no matter how hard I pull on the cart, the cart will pull back on me with an equal and opposite force. The two forces add up to zero and the cart won t accelerate. Since the cart isn t moving now, and a=0, it will never move. The donkey lays down and takes a nap. Mechanics Lecture 5, Slide 38 19

20 Question Why is the physics donkey wrong? A. Because the donkey is less massive so the force of the donkey on the cart is always greater than the force of the cart on the donkey. B. Because the force of the donkey on the cart is greater than the force of the cart on the donkey for the brief instant of time when the donkey takes his first step. C. The donkey is correct that the forces are the same, but it doesn t matter in this case. D. Because the cart is more massive so the force of gravity is greater on the cart than on the donkey. E. The donkey is correct and the cart can not accelerate without an additional push. Mechanics Lecture 5, Slide 39 20