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 xcomponent 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 workenergy 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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 Summer '08
 Field
 Energy, Force, Kinetic Energy, Work, frictionless horizontal rail, Discussion Section7193 Quiz

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