Chapter 7 Lecture Chapter 7: Work and Energy © 2016 Pearson Education, Inc. Goals for Chapter 7 • Overview energy. • Study work as defined in physics. • Relate work to kinetic energy. • Consider work done by a variable force. • Study potential energy. • Understand energy conservation. • Include time and the relationship of work to power. © 2016 Pearson Education, Inc. Introduction • In previous chapters, we studied motion. • We used Newton's three laws to understand the motion of an object and the forces acting on it. • Sometimes this can be hard. • We introduce energy as the next step. © 2016 Pearson Education, Inc. An Overview of Energy • Energy is conserved. • Kinetic energy describes motion and relates to the mass of the object and its speed squared. • Energy on earth originates from the sun. • Energy on earth is stored thermally and chemically. • Chemical energy is released by metabolism. • Energy is stored as potential energy in object height and mass and also through elastic deformation. © 2016 Pearson Education, Inc. A Study of Energy Transformation – Figure 7.4 • This transformation begins as elastic potential energy in the elastomer. It then becomes kinetic energy as the projectile flies upward. During the upward flight, kinetic energy becomes potential until at the top of the flight, all the energy is potential. Finally, the stored potential energy changes back to kinetic energy as the projectile falls. © 2016 Pearson Education, Inc. Internal Energy Can be "Lost" as Heat • Atoms and molecules of a solid can be thought of as particles vibration randomly on spring like bonds. This vibration is an an example of internal energy. • Energy can be dissipated by heat (motion transferred at the molecular level). This is referred to as dissipation. © 2016 Pearson Education, Inc. What is "Work" as Defined in Physics? • Formally, work is the product of a constant force F through a parallel displacement s. • Work is the product of the component of the force in the direction of displacement and the magnitude s of the displacement. © 2016 Pearson Education, Inc. Consider Only Parallel F and S – Figure 7.9 • Forces applied at angles must be resolved into components. • W is a scalar quantity that can be positive, zero, or negative. • If W > 0 (W < 0), energy is added to (taken from) the system. © 2016 Pearson Education, Inc. Applications of Force and Resultant Work – Figure 7.10 © 2016 Pearson Education, Inc. Sliding on a Ramp – Example 7.2 • Please refer to the worked example at the bottom of page 186. © 2016 Pearson Education, Inc. Work Done By Several Forces – Example 7.3 © 2016 Pearson Education, Inc. Work and Kinetic Energy • Unbalanced work causes kinematics. • Work-energy theorem: • The kinetic energy K of a particle with mass m moving with speed is During any displacement of the particle, the work done by the net external force on it is equal to its change in kinetic energy. • Although Ks are always positive, Wtotal may be positive, negative, or zero (energy added to, taken away, or left the same). • If Wtotal = 0, then the kinetic energy does not change and the speed of the particle remains constant. © 2016 Pearson Education, Inc. Work and Energy Related – Example 7.4 • Using work and energy to calculate speed. • Returning to the tractor pulling a sled problem of Example 7.3: • If you know the initial speed, and the total work done, you can determine the final speed after displacement s. © 2016 Pearson Education, Inc. A Pile Driver Application – Example 7.5 • Refer to the worked example on pages 191–192. © 2016 Pearson Education, Inc. Work Done By a Varying Force • In Section 7.2, we defined work done by a constant force. • Work by a changing force is sometimes considered. • On a graph of force as a function of position, the total work done by the force is represented by the area under the curve between the initial and final positions. © 2016 Pearson Education, Inc. Work Done By a Varying Force • In Section 5.4, we learned that force due to elongation/ compression of a spring followed Hooke's law: • As seen, this is a prime example of a varying force. The work done by a stretching/compressing a spring is equal to the area of the shaded triangle, or © 2016 Pearson Education, Inc. Work Done on a Spring Scale – Example 7.6 • Energy may be stored in compressed springs on a bathroom scale. • Refer to the worked example on page 194. © 2016 Pearson Education, Inc. Potential Energy In cases of conservative forces (gravity or elastic forces), there can be "stored" energy due to the spatial arrangement of a system, or •potential energy. Gravitational potential energy (Ugrav), near the surface of the © 2016 Pearson Education, Inc. Potential Energy • The change in the potential energy due to conservative forces is related to the work done by the net force: • If only conservative forces act, then by the work-energy theorem we can define the total mechanical energy: © 2016 Pearson Education, Inc. A Solved Baseball Problem – Example 7.7 • When the ball, with initial Conservation of total When the ball, with initial Conservationmechanical energy of total speed i is thrown straight upward, it slows down on the way up as the kinetic energy is converted to potential •energy (mgy>0). At the top, the kinetic energy is zero and potential energy is •maximum. On the way back down, the potential energy is converted back to kinetic energy, and © 2016 Pearson Education, Inc. Energy Stored in Spring Displacement – EnergyFigure 7.25 Stored in Spring Displacement – • Elastic stored energy stored • in a spring can be related to position. • (HookeElastic's storedlaw), the energy elastic stored in a spring can be related to position. • © 2016 Pearson Education, Inc. Potential Energy on an Air Track with Mass and Spring energy, we use this to find the final state at any position. • Using conservation of total mechanical energy: © 2016 Pearson Education, Inc. Conversion and Conservation – Figures 7.27 and 7.28 • As kinetic and potential energy are interconverted, dynamics of the system may be solved. Refer to the worked examples on page 202–203. © 2016 Pearson Education, Inc. could used conservation of total mechanical Conservative and Nonconservative Forces • In the previous section, we discussed that if we hadIn onlythe previous conservative section, forces we acting,discussed then that we if we had only conservative forces acting, then we energy. • If we have nonconservative forces which do work, we have to add this to the total energy: • Wother is the work done by nonconservative forces (e.g. friction). © 2016 Pearson Education, Inc. Problems With Nonconservative Forces – Example 7.12 Problems• With Nonconservative Forces – now we also include the work done an external, a This is the same problem as Example 7.8, but nownonconservative we also include force the F .work done an external, a • In addition to the spring force, there is a constant force F Wf = (Kf +Uf ) − (Ki +Ui ) W 1 m 2 1 kx2 1 m 2 1 kx2 f = ( 2 υf + 2 f ) − ( 2 υi + 2 i ) where Wf = Fx > 0 © 2016 Pearson Education, Inc. Conservative Forces II – Figure 7.35 The work done by a conservative force is independent of the path taken. • When the starting and ending points are the same, the total work is zero. © 2016 Pearson Education, Inc. • When a quantity of work ΔW is done during a time interval • When a quantity of work ΔW is done during a time interval • Units of watt [W], or P1 avwatt or work= 1 joule per unitper timesecond is: [J/s] • The rate at which work is done is not always constant. • Units of watt [W], or 1 watt = 1 joule per second [J/s] © 2016 Pearson Education, Inc. Power – Considers Work and Time to do It • Example 7.16: A marathon stair climb Example 7.16: A marathon stair climb • If the runner is initially at rest and ends at rest, the work done by the runner is equalgravity to on the the work runner. done by • © 2016 Pearson Education, Inc. .