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qz3sol_1243Hs11 - N a Write down the definition of work in...

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TA: Tomoyuki Nakayama Wednesday, January 26, 2011 PHY 2048: Physic 1, Discussion Section 1243H Quiz 1 (Homework Set #2) Name: UFID: Formula sheets are not allowed. Do not store equations in your calculator. You have to solve problems on your own; memorizing final algebraic expressions from homework assignments and just plugging numbers into them will not give you full credit. Leave all your work. ________________________________________________________________________________ The figure below right shows a cord attached to a cart that can slide along a frictionless horizontal rail aligned along an x axis. The left end of the cord is pulled over a pulley, of negligible mass and friction and at cord height h = 3.00 m, so the cart slides from x 1 = 5.00 m to x 2 = 2.00 m. During the move, the tension in the cord is a constant 50.0
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Unformatted text preview: N. a) Write down the definition of work in integral form, and then express the integrand in terms of T, x and h . The definition of work is W T = ∫ 1 2 T · dx = ∫ 1 2 Tcos θ dx where θ is the angle between T and positive x direction. Let φ the angle between T and negative x direction. The integrand is Tcos θ = -Tcos φ = -T x/ √ (x 2 + h 2 ) b) What is the change in the kinetic energy of the cart during the move? According to the work-energy theorem, the change in the kinetic energy of an object is equal to the work done on the object. The definition of work yields Δ K = W T = -T ∫ 1 2 x/ √ (x 2 + h 2 )dx Changing the variable from x to s = √ (x 2 + h 2 ), we get Δ K = -∫ 1 2 Tds = -Ts| 1 2 = -[ √ (x 2 2 + h 2 ) - √ (x 1 2 + h 2 )] = 111 J...
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