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qz5sol_7193f10

# qz5sol_7193f10 - sign The x component is negative The...

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TA: Tomoyuki Nakayama Monday, October 4, 2010 PHY 2048: Physic 1, Discussion Section7193 Quiz 5 (Homework Set #6) Name: UFID: Formula sheets are not allowed. Calculators are allowed. Do not store equations in your calculator. You need to show all of your work for full credit. ________________________________________________________________________________ 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 = 2.00 m, so the cart slides from x 1 = 4.50 m to x 2 = 1.50 m. During the move, the tension in the cord is a constant 30.0 N. a) When the block is at x = 3.00 m, what is the x component of the tension? (Pay attention to the
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Unformatted text preview: sign!) The x component is negative. The cosine of the angle between the string and the horizontal is cos θ = x/ √ (x 2 + h 2 ) Therefore, when the block is at x, the x-component of the tension is T x = -Tcos θ = -Tx/ √ (x 2 + h 2 ) At x = 3 m, the T x is T x = -Tcos θ = -30×3/ √ (3 2 + 2 2 ) = -25.0 N 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 x dx = ∫ [-Tx/ √ (x 2 + h 2 )]dx Changing the variable from x to s = √ (x 2 + h 2 ) and integrating from x 1 to x 2 , we get Δ K = -∫ Tds = -T[ √ (x 2 2 + h 2 ) - √ (x 1 2 + h 2 )] = 72.7 J...
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