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# hw14 - Overton Mays – Homework 14 – Due 4:00 am –...

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Unformatted text preview: Overton, Mays – Homework 14 – Due: Feb 25 2005, 4:00 am – Inst: Turner 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Hint: W = ~ S · ~ F . Consider a force ~ F with components F x = 27 N, F y = 58 N, and F z = 90 N, as illustrated in the figure below. Work is done when a particle moves up the vertical z-axis a distance of 4 m . ~ F F y ˆ F z ˆ k & ~S F x ˆ ı θ The figure is not drawn to scale. What is the angle θ between the body di- agonal which represents the force ~ F and the front-left edge of the block which represents both the z-component F z of the vector ~ F and the vector ~ S the particle traversed? Correct answer: 35 . 4071 ◦ . Explanation: Basic Concept: ~ X · ~ Y = k ~ X k k ~ Y k cos θ . (1) Note : ~ S · ~ F = ( S ˆ k ) · ( F x ˆ ı + F y ˆ + F z ˆ k ) = S F z = (4 m)(90 N) = 360 Nm . Solution: Using Eq. 1, we have θ = arccos ˆ ~ S · ~ F k ~ S k k ~ F k ! = arccos S F z | S | q F 2 x + F 2 y + F 2 z = arccos • (4 m)(90 N) (4 m)(110 . 422 N) ‚ = arccos(0 . 815056) = 35 . 4071 ◦ . 002 (part 1 of 1) 10 points An applied force varies with position ac- cording to F = k 1 x n- k 2 , where n = 3, k 1 = 4 . 4 N / m 3 , and k 2 = 86 N. How much work is done by this force on an object that moves from x i = 6 . 24 m to x f = 18 . 3 m? Correct answer: 120 . 662 kJ. Explanation: Basic Concepts: W = Z ~ F · d~s Solution: The work done by a varying force is W = Z x 2 x 1 ~ F · d~s. which adds up all the little ~ F · ~s parts along the path, taking into account the changing force. Here all the motion is in theˆ ı direction so ds = dx . W = Z x f x i F · dx = Z 18 . 3 m 6 . 24 m £ (4 . 4 N / m 3 ) x 3- (86 N) / · dx = • (4 . 4 N / m 3 ) x 4 4- (86 N) x ‚fl fl fl fl 18 . 3 m 6 . 24 m = µ 4 . 4 N / m 3 4 ¶ £ (18 . 3 m) 4- (6 . 24 m) 4 /- (86 N)(18 . 3 m- 6 . 24 m) = 120662 J = 120 . 662 kJ ....
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hw14 - Overton Mays – Homework 14 – Due 4:00 am –...

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