Chapter 4 Work and Energy

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1 James T. Shipman Jerry D. Wilson Charles A. Higgins, Jr. Omar Torres Chapter 4 Work and Energy

2 Work being done by applied force (F ) through a distance (d ) Work = Force distance, W (J) = F. d where F is in Newton, d is in meters, work is in Joules Section 4.1

3 Find the Work being done? Section 4.1

4 Find the Work being done? d

5 B has a higher Kinetic Energy than A Kinetic Energy: Energy of Motion Which ball has a higher Kinetic energy? v=0 v

6 Kinetic Energy: Energy of Motion d 1 2 v v Section 4.2

7 Work = change in kinetic energy If the object is already moving at a velocity v 1, then work done is the change in kinetic energy d 1 2

8 Change in Kinetic Energy Example A 1.0 kg ball is fired from a cannon. What is the change in the ball s kinetic energy when it accelerates from 4.0 m/s to 8.0 m/s? Section 4.2

9 A has a higher potential Energy than B Potential Energy: Stored Energy Which ball has a higher potential energy?

10 Work= Change in Potential Energy h 1 h 2

11 Work and Potential Energy Example How much work is done in lifting 5.0 kg box 1.2m off the floor? 5kg

12 Conservation of Energy In changing from one form to another, energy is always conserved

13 Conservation of Energy: Finding Kinetic and Potential Energies A 0.10-kg stone is dropped from a height of 10.0 m. What will be the kinetic and potential energies of the stone at the heights indicated in the figure (neglect air resistance)? E T = E k + E p At the moment the stone is released E T = E p (E k = 0) At the moment the stone hits the ground E T = E k (E p = 0) Section 4.3

14 Solve for E p and E k at Various Heights At any height, the potential energy E p = mgh h = 10 m: E p =(0.10 kg)(9.8 m/s 2 )(10.0 m) = 9.8 J h = 7 m: E p = (0.10 kg)(9.8 m/s 2 )(7.0 m) = 6.9 J h = 3 m: E p = (0.10 kg)(9.8 m/s 2 )(3.0 m) = 2.9 J h = 0 m: E p = (0.10 kg)(9.8 m/s 2 )(0 m) = 0 J E T = E k + E p E k = E T E p Section 4.3

15 Solve for E p and E k at Various Heights Section 4.3

16 Conservation of Energy photogate photogate h 1 = 0.5m h 2 Cart mass (Kg) Height (m) Velocity (m/s) Potential Energy (Joules) E p = mg. h Kinetic Energy (Joules) E K = 1/2 mv 2 %Error 0.50

17 Potential energy (E p ) = mgdh Converted into kinetic energy (E k ) = ½mv 2 Since all the E p is converted into E k just before hitting the ground, we can use this to compute the speed or magnitude of velocity Therefore: ½mv 2 = mgdh ½v 2 = gdh (cancel m s) v 2 = 2gDh (solve for v) v 2gDh Magnitude of Velocity Section 4.3

18 Forms of Energy Thermal (heat) Energy related to the kinetic and potential energies on a molecular level Gravitational potential energy from an object s position, stored gravitational energy Electrical energy associated with the motion of electric charges Chemical energy molecular bonds Radiant energy Sun electromagnetic Nuclear energy rearrangement of nuclei Fission breaking apart of larger nuclei Fusion smaller nuclei are put together Section 4.5

19 Food Energy Section 4.5

20 Flaming Gorge Dam, Utah Section 4.6

21 Wind Farm near Tehachapi Pass, California Section 4.6

22 Solar Power Very promising future source of reliable and economic energy Although some solar power is in use now, many more applications are possible Section 4.6

23 Geothermal Energy Very site specific Depends on a large natural change in temperature being present and accessible Extensively used in Iceland Section 4.6

24 Puna Geothermal Plant, Hawaii Section 4.6

25 Tides Tidal energy is steady, reliable, and predictable Must be designed to handle bidirectional tidal currents Tidal currents have been generating electricity along the Rance River in France since the 1960 s Section 4.6

26 System Kinetic energy

27 System Potential energy Potential energy is stored energy due to attractive and repulsive forces between atoms in a molecule James T. Shipman Jerry D. Wilson Charles A. Higgins, Jr. Omar Torres

28 Potential Energy Potential energy is associated with the position of the object Gravitational Potential Energy is the energy associated with the relative position of an object in space near the Earth s surface The gravitational potential energy PE mgy m is the mass of an object g is the acceleration of gravity y is the vertical position of the mass relative the surface of the Earth SI unit: joule (J)

29 nergy: is the ability to do work. If work is done by a system (-w), the energy E of the system decreases If work is done on a system (+w), the energy E of the system increases system E + w - w Section 4.2

30 Potential Energy Depends only on the initial and final positions (difference in height, Dh) and is independent of path If we disregard any frictional loss, it takes the same amount of work (W ) to lift the mass (m), no matter the path Section 4.2

31 Work = Change in Potential Energy Work = W = E p = mgh = mgdh In the previous examples the h is actually Dh Work is done when there is a change in position Therefore the reference point for measuring heights is arbitrary (but must be internally consistent) Section 4.2

32 Reference Point: No matter which scale Dh is the same Section 4.2

33 Conservation of Energy Section 4.3

34 Homework (Exercises)

What is Energy? In science, energy is the ability to do work. Work is done when a force causes an object to move in the direction of the force.

What is Energy? In science, energy is the ability to do work. Work is done when a force causes an object to move in the direction of the force. Energy Energy is the ability to do work. (reminder=what is