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Worksheet Problem 5 A kinematic formula derived in Chapter 2 for conditions of constant acceleration relates speed, acceleration, and displacement: 2a (x – x 0 ) = v 2 – v 0 2. a)Multiply both sides of this equation by m/2. b)Explain the resulting formula in terms of the work- energy theorem.

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Worksheet Problem 6 This is a type of question popular on driver’s license exams: If a car initially traveling 30 mi/h skids to a stop in 100 ft, how far will it skid before coming to a stop if its initial speed is 60 mi/h? a)What force is responsible for the net force on the skidding car? b)How does the stopping time depend on initial speed? c)To what quantity is stopping distance proportional? d)What is the answer to the driver’s license exam question? e)Explain the result without referring to work or kinetic energy.

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Gravitational Potential Energy Energy of height § 7.1

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Potential Energy The energy of relative position of two objects gravity springs electric charges chemical bonds

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Potential Energy Energy is stored doing work against a potential Potential energy increases when “the potential” does negative (< 0 ) work lifting a weight stretching a spring

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Gravity Does Negative Work Source: Young and Freedman, Figure 7.2b.

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Work from Potential Energy When a potential does work on a body: The body’s potential energy decreases The body’s kinetic energy increases Or, more than one potential can operate at once

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CPS Question When a cute furry animal moves downward in free-fall: A.Its gravitational potential energy increases. B.Its kinetic energy increases. C.Both A and B. D.Neither A nor B.

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Gravity Does Positive Work Source: Young and Freedman, Figure 7.2a.

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CPS Question When a disgusting scaly thing moves upward in free-fall: A.Its gravitational potential energy increases. B.Its kinetic energy increases. C.Both A and B. D.Neither A nor B.

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Worksheet Problem 7 A small rock with a mass of 0.20 kg is released from rest at point A at the top of a hemispherical bowl of radius R = 0.5 m. The rock slides rather than rolls. The work done by friction when it moves from A to B is –0.22 J. What is the speed v of the rock when it reaches point B? A B v R

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CPS Question As the rock slides down the trough, the normal force on it depends on A B v R A.The local slope of the trough. B.The rock’s speed. C.Both of these.

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Mechanical Energy The energy available to do work Kinetic + potential = K + U

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Gravitational Potential Energy Gravitational potential energy = the work to raise an object to a height Gravitational U = mgh

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Conservation of Mechanical Energy If the only force doing work is gravity, mechanical energy does not change. E 1 = E 2 K 1 + Ug 1 = K 2 + Ug 2 1/2 mv 1 2 + mgy 1 = 1/2 mv 2 2 + mgy 2

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Worksheet Problem 8 A 50-g egg released from rest from the roof of a 30-m tall building falls to the ground. Its fall is observed by a student on the roof of the building, who uses coordinates with origin at the roof, and by a student on the ground, who uses coordinates with origin at the ground. What values do the students find for: a)Initial gravitational potential energy U grav 0 ? b)Final gravitational potential energy U grav f ? c)Change in gravitational potential energy U grav ? d)Kinetic energy just before impact K f ?

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Worksheet Problem 9 Your cousin Throckmorton, m = 20 kg, plays on a R = 1.5-m swing. What is his change in gravitational potential energy as he swings from an angle = /6 from vertical down to = 0? a)If the height of the swing pivot is 0, what is Throckmorton’s height h at = /6? At = 0? b)What is his change in height h? c)What is his change in potential energy DU grav ? d)What is his speed at the bottom?

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