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Work and Energy Russ Ballard Science Department Kentlake High School Slippery Concepts • Mostly our definitions will work. • Sometimes they do not. • Think of pushing a heavy object that does not move. • Is work being done? March 16, 2005 Kentlake Science Department 2 Slippery Concepts • Can we have negative work? • How do we define work and energy? • Can we transform energy into different forms? March 16, 2005 Kentlake Science Department 3 Lecture Concepts 1. Work done by a constant force. 2. Work done by a variable force. 3. Work-Energy Theorem. March 16, 2005 Kentlake Science Department 4 Lecture Concepts 4. Potential Energy. 5. Conservation of energy. 6. Power March 16, 2005 Kentlake Science Department 5 Objective 1 • To be able to –Define mechanical work –Compute the work done in various situations. March 16, 2005 Kentlake Science Department 6 Work & Constant Force • The work done by a constant force in moving an object is equal to the product of the magnitudes of the displacement and the component of the force parallel to the displacement. March 16, 2005 Kentlake Science Department 7 Work & Constant Force • W = Fd (cos ) • SI units are N m or joule (J) ● • Work is a scalar quantity. March 16, 2005 Kentlake Science Department 8 Teaching Note • If you carry a book across the room is any work done? • Explain your reasoning. March 16, 2005 Kentlake Science Department 9 Example 5.1 • A student holds her physics textbook, which has a mass of 1.5 kg, out of a second story window. • a. How much work is done holding it? • b. How much work is done on it when it has fallen 3.0 meters? a. 0 b. +44J March 16, 2005 Kentlake Science Department 10 Draw Free-Body Diagrams F d W = Wmax F d W > 0 but < Wmax March 16, 2005 Kentlake Science Department 11 Draw Free-Body Diagrams F d W=0 F W<0 d F W = -Wmax March 16, 2005 Kentlake Science Department d 12 Coefficient of Friction • f k = μ kN • μ k = fk = mg sin = tan N mg cos March 16, 2005 Kentlake Science Department 13 Teaching Note in 5.3 • Friction does negative work • Weight does positive work • Net work is zero only when forces are equal and opposite. March 16, 2005 Kentlake Science Department 14 Example 5.3 • A 0.75 kg block slide down a ramp with uniform velocity. Base = 1.2 m, angle = 20o. • a. how much work is done by friction? • b. what is the net work done on the block? • c. discuss work done if ramp is adjusted to cause acceleration. • a. -3.2 J • b. +3.2J • c. component in x > friction. March 16, 2005 Kentlake Science Department 15 Objective 2 • To be able to –differentiate work done by a constant and variable force –compute work done by a spring force. March 16, 2005 Kentlake Science Department 16 Work and Variable Force • If you pull on a spring it pulls back. • The relationship to the distance pulled and pull of the spring is nearly linear. March 16, 2005 Kentlake Science Department 17 Work and Variable Force • Fs = -kx • Why is kx negative? March 16, 2005 Kentlake Science Department 18 Work and Variable Force • We will generally be limited to constant or average force situations. • Work done is stretching a spring • W= ½ kx2 March 16, 2005 Kentlake Science Department 19 Teaching Note • Constant acceleration is not present in variable forces. • Why? March 16, 2005 Kentlake Science Department 20 Teaching Note • If you use a bow vs. a spring. • It is not possible to derive an expression for the bow. • Why? March 16, 2005 Kentlake Science Department 21 Example 5.4 • A 0.15kg mass is suspended from a vertical spring and descends a distance of 4.6 cm, after which is hangs at rest. An additional mass of 0.50 kg is hung from the first. What is the total extension of the spring. • .20 m or 20 cm March 16, 2005 Kentlake Science Department 22 Problem Hint • The important quantity in computing work is the displacement difference x, or net change in length of the spring. March 16, 2005 Kentlake Science Department 23 Objective 3 • To be able to –explain the work-energy theorem –apply it in solving problems. March 16, 2005 Kentlake Science Department 24 Work-Energy Theorem • Kinetic energy KE = ½ mv2 • Units are the joule (J) • Energy of motion. March 16, 2005 Kentlake Science Department 25 Work-Energy Theorem • Wnet = KE • W = Fd = mgh = ½ mv2 = KE • Work is the measure of the transfer of kinetic energy. March 16, 2005 Kentlake Science Department 26 Teaching Note • Kinetic energy is a positive quantity. • In the previous problem you can find the acceleration. • Then use a kinematics equation to find the velocity. March 16, 2005 Kentlake Science Department 27 Example 5.5 • A shuffleboard player pushes a 0.25 kg puck, initially at rest, in a way that causes a constant horizontal force of 6.0 N to act on it through a distance of 0.50 m (neglect friction) • a. what are the kinetic energy and speed of the puck when the force is removed? • b. How much work would be required to bring the puck to rest? • a. 4.9 m/s • b. -3.0J March 16, 2005 Kentlake Science Department 28 Problem Hint • You have to calculate the actual KE. • You cannot use the change of velocity. March 16, 2005 Kentlake Science Department 29 Example 5.6 • In a football game, a 140-kg guard runs with 4.0 m/s and a 70-kg free safety moves at 8.0 m/s. • a. both players have the same kinetic energy • b. safety has twice as much • c. guard has twice as much • d. safety has four times as much • Explain your answer March 16, 2005 Kentlake Science Department 30 Example 5.7 • A car is traveling at 5.0 m/s speeds up to 10 m/s, with an increase of kinetic energy that requires work. Then the speed goes up 15 m/s, requiring work. • A. W1 > W2 • B.W1 = W2 • C. W2 > W1 March 16, 2005 Kentlake Science Department 31 Objective 4 • To be able to –explain how potential energy depends on position – compute values of gravitational potential energy. March 16, 2005 Kentlake Science Department 32 Potential Energy • Potential is stored energy. • Normally thought to be mechanical in nature. • Work is also a change in potential energy. March 16, 2005 Kentlake Science Department 33 Potential Energy • It has two expressions. • U = ½ kx2 • U = mgh • U= potential energy. • Units are joule (J) March 16, 2005 Kentlake Science Department 34 Example 5.8 • A 0.50kg ball is thrown vertically upward with an initial velocity of 10 m/s. • a. What is the change in the ball’s kinetic energy between the start and its maximum height? • a. -25 J March 16, 2005 Kentlake Science Department 35 Example 5.8 • b what is the change in the ball’s potential energy between the maximum height and the launch point? • b. +25 J March 16, 2005 Kentlake Science Department 36 Teaching Note • Potential energy is also a scalar quantity. • But it can be positive or negative. March 16, 2005 Kentlake Science Department 37 Teaching Note • You can pick the zero point. • Change in potential energy is independent of path. March 16, 2005 Kentlake Science Department 38 Objective 5 • To be able to –distinguish between conservative and nonconservative forces – explain their effects on the conservation of energy. March 16, 2005 Kentlake Science Department 39 The Conservation of Energy • When something is conserved it is constant. • The total energy in the universe is conserved or is constant. March 16, 2005 Kentlake Science Department 40 The Conservation of Energy • A force is said to be conservative if the work done on an object is independent of the object’s path. March 16, 2005 Kentlake Science Department 41 The Conservation of Energy • If it the path influences that the amount of work done then it is nonconservative. • A long path will result in the total work not equal to a change in potential energy. March 16, 2005 Kentlake Science Department 42 The Conservation of Energy • A conservative force allows all of the energy to be conserved to potential energy. March 16, 2005 Kentlake Science Department 43 The Conservation of Energy • Nonconservative force does not. • A force is conservative if the work done by or against it in moving an object through a round trip is zero. March 16, 2005 Kentlake Science Department 44 Conservation of Total Mechanical Energy • Etotal = KE + U • KEi + Ui = KEf + Uf • KE = - U This only works when nonconservative forces do no work. March 16, 2005 Kentlake Science Department 45 Example 5.9 • A painter on a scaffold drops a 1.50kg can of paint from a height of 6.0m • a. what is the kinetic energy of the can when it is at a height of 4.00m? • b. with what speed will the can hit the ground? (neglect air resistance). • a. 29.4 J • b. 10.8 m/s March 16, 2005 Kentlake Science Department 46 Example 5.11 • A 0.30kg mass sliding on a horizontal frictionless surface with a speed of 2.5 m/s, strikes a light spring, which has a spring constant of 3.0 x 103 N/m. March 16, 2005 Kentlake Science Department 47 Example 5.11 • a. What is the total mechanical energy of the system? • b. What is the kinetic energy(K1) of the mass when the spring is compressed a distance x1 = 1.0cm? (assume no energy loss). • a. 0.94 J • b. 0.79 J March 16, 2005 Kentlake Science Department 48 Total Energy and Nonconservative Forces • Friction is a nonconservative force. • If nonconservative forces are present mechanical energy is not conserved. March 16, 2005 Kentlake Science Department 49 Example 5.12 • A skier with a mass of 80-kg starts from rest and skis down a slope from an elevation of 110m. the speed of the skier at the bottom of the slope is 20 m/s • A. show that the system is nonconservative • B. how much work is done by the nonconservative force of friction? • a. 8.6 x 104 J vs. 1.6 x 104 J • b. -7.0 x 104 J March 16, 2005 Kentlake Science Department 50 Review of Concepts • Constant force work W = Fd cos • Variable force work requires advanced math. March 16, 2005 Kentlake Science Department 51 Review of Concepts • Kinetic Energy KE = ½ mv2 • Potential Energy PE = mgh March 16, 2005 Kentlake Science Department 52 Review of Concepts • Conservation of energy. • Total energy of the universe is conserved. • Total energy kinetic plus potential is constant. March 16, 2005 Kentlake Science Department 53 Review of Concepts • Mechanical systems have friction. • Friction causes a loss of mechanical energy. March 16, 2005 Kentlake Science Department 54 Review of Concepts • Power is work over time. • P = W = Fd = Fv t t • Efficiency relates output to energy (work) input. March 16, 2005 Kentlake Science Department 55 Formulas • Work W = Fd cos • Hooke’s Law Fs = -kx • Work (spring) W = ½ kx2 • Kinetic Energy KE = ½ mv2 March 16, 2005 Kentlake Science Department 56 Formulas • Work Energy Theorem Wnet = Kf – Ki = K March 16, 2005 Kentlake Science Department 57 Formulas • Elastic spring Potential U = ½ kx2 • Gravitational Potential Energy U = mgh March 16, 2005 Kentlake Science Department 58 Formulas • Conservation of Mechanical Energy ½ mvi2 + Ui = ½ mvf2 + Uf • Efficiency (percent) = Wout (x 100%) Win March 16, 2005 Kentlake Science Department 59 Credits • Problems –Prentice Hall College Physics Willson and Buffa • Diagrams –Holt Physics Serway & Faughn March 16, 2005 Kentlake Science Department 60