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# Physics Work and Energy

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• When asking students to express their ideas, you might try one of the following methods. (1) You could ask them to write their answers in their notebook and then discuss them. (2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups. The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally. Kinetic energy comments will likely center around the velocity and probably not mention the mass of the object. Students may mention the different types of potential energy (gravitational, electrostatic, elastic, etc). Listen to ideas about these topics and then begin the lecture/discussion.
• Show students the steps and substitutions needed to derive the final equation for work. Make sure they see the use of F = ma in the first equation and the substitution for a  x from the 2nd equation into the third equation. Help students see the transformation of the 3rd equation into the 4th equation. Have them note that calculating the work no longer requires knowledge of the force but, instead, can be determined by the effect of the force or the change in velocity. Mention that a name has been given to the quantity 1/2 mv 2 . It is called kinetic energy. So, work is the change in KE. Then show them the next slide, which introduces the kinetic energy equation.
• Ask students to determine the units from the equation before showing this on the slide. Have them see that, since N are kg•m/s 2 , the units of N•m are equivalent to kg•m 2 /s 2.
• Discuss the many examples of moving objects doing work on other objects. For example, a moving baseball bat does work on a ball as it exerts a force on the ball, and the ball moves a distance in the direction of the force. Conversely, the ball does work on the bat as it exerts a force opposite to the direction the bat is moving. Work has a negative value in this case. A change in speed for an object allows it to do work on its environment.
• For the second problem, students should just use the change in KE (432 J – 300 J = 132 J). Sometimes they make the mistake of thinking that they can use the change in speed (2 m/s) in the equation for KE and end up with an answer of 12 J for the work done. This does not work because (12 - 10) 2 is not equal to (12 2 - 10 2 ).
• Hold a book above the desk. The book has the potential to move due to an interaction with Earth (gravity). Stretch a rubber band with a wad of paper held in it like a sling shot. The paper has the potential to move due to an interaction with its environment (the rubber band).
• This equation comes from W = Fd = ( ma ) d = mgh, so PE g is simply the work done in lifting an object. To help students understand the fact that the zero level is arbitrary, hold a book over the desk and ask them what they would use for h in order to calculate the PE . Then, maintaining the book at the same height, move it over the floor and ask the students once again what value they would use for h . Point out that, in general, our primary concern in physics involves changes in PE , not the actual amount of PE . The change in PE is always the same regardless of what zero level is assigned. Generally, the zero level is assigned to the lowest point the object will reach. For example, the desk if the book is held over the desk, and the floor if the book is held over the floor.
• Point out that  x in the diagram is the “Distance compressed.” This will be used in the equation for elastic potential energy (slide 10). Discuss the transfer of the elastic potential energy to the block when the deformed spring returns to its original configuration.
• Help students find the SI units as N•m or Kg•m 2 /s 2 or J. Now would be a good time to remind them that work, KE , and PE are all measured in joules (kg•m 2 /s 2 ).
• Point out to students that the zero level is at the table for gravitational PE . Also, they must use meters, not centimeters, in order to have joules as units in the final answers.
• Mass and KE are directly proportional. KE is directly proportional to the velocity squared. The net work done on an object equals the change in kinetic energy. Factors affecting gravitational PE are mass, acceleration due to gravity, and height above the zero level. All are directly related. Factors affecting elastic PE are the spring constant (directly related) and the displacement from equilibrium position (directly related to the displacement squared).
• ### Physics Work and Energy

1. 1. Work and Energy Section 2 What do you think? • You have no doubt heard the term kinetic energy. – What is it? – What factors affect the kinetic energy of an object and in what way? • You have no doubt heard the term potential energy. – What is it? – What factors affect the potential energy of an object and in what way?Mr. ThompsonsPublishing Company © Houghton Mifflin Harcourt Physics Class
2. 2. Work and Energy Section 2 Kinetic Energy Wnet = F ∆x = ma∆x Since v = v + 2 a ∆x 2 f 2 i v 2 − vi2 then Wnet = m( f ) 2 or 1 2 1 2 Wnet = mv f − mvi 2 2Mr. ThompsonsPublishing Company © Houghton Mifflin Harcourt Physics Class
3. 3. Work and Energy Section 2 Kinetic Energy • What are the SI units for KE? – kg•m2/s2 or N•m or JMr. ThompsonsPublishing Company © Houghton Mifflin Harcourt Physics Class
4. 4. Work and Energy Section 2 Work and Kinetic Energy • KE is the work an object can do if the speed changes. • Wnet is positive if the speed increases.Mr. ThompsonsPublishing Company © Houghton Mifflin Harcourt Physics Class
5. 5. Work and Energy Section 2 Classroom Practice Problems • A 6.00 kg cat runs after a mouse at 10.0 m/s. What is the cat’s kinetic energy? – Answer: 3.00 x 102 J or 300 J • Suppose the above cat accelerated to a speed of 12.0 m/s while chasing the mouse. How much work was done on the cat to produce this change in speed? – Answer: 1.32 x 102 J or 132 JMr. ThompsonsPublishing Company © Houghton Mifflin Harcourt Physics Class
6. 6. Work and Energy Section 2 Potential Energy • Energy associated with an object’s potential to move due to an interaction with its environment – A book held above the desk – An arrow ready to be released from the bow • Some types of PE are listed below. – Gravitational – Elastic – ElectromagneticMr. ThompsonsPublishing Company © Houghton Mifflin Harcourt Physics Class
7. 7. Work and Energy Section 2 Gravitational Potential Energy • What are the SI units? – kg•m2/s2 or N•m or J • The height (h) depends on the “zero level” chosen where PEg = 0.Mr. ThompsonsPublishing Company © Houghton Mifflin Harcourt Physics Class
8. 8. Work and Energy Section 2 Elastic Potential Energy • The energy available for use in deformed elastic objects – Rubber bands, springs in trampolines, pole-vault poles, muscles • For springs, the distance compressed or stretched = ∆xMr. ThompsonsPublishing Company © Houghton Mifflin Harcourt Physics Class
9. 9. Work and Energy Section 2 Elastic Potential Energy • The spring constant (k) depends on the stiffness of the spring. – Stiffer springs have higher k values. – Measured in N/m • Force in newtons needed to stretch a spring 1.0 meters • What are the SI Units for PEelastic?Mr. ThompsonsPublishing Company © Houghton Mifflin Harcourt Physics Class
10. 10. Work and Energy Section 2 Classroom Practice Problems • When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table. – What is the gravitational potential energy associated with the mass relative to the table? • Answer: 9.81 J – What is the spring’s elastic potential energy if the spring constant is 400.0 N/m? • Answer: 2.00 JMr. ThompsonsPublishing Company © Houghton Mifflin Harcourt Physics Class
11. 11. Work and Energy Section 2 Now what do you think? • What is kinetic energy? – What factors affect the kinetic energy of an object and in what way? – How are work and kinetic energy related? • What is potential energy? – What factors affect the gravitational potential energy of an object and in what way? – What factors affect the elastic potential energy of an object and in what way?Mr. ThompsonsPublishing Company © Houghton Mifflin Harcourt Physics Class