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Unformatted text preview: Bautista, Aldo Homework 6 Due: Oct 11 2005, 4:00 am Inst: Maxim Tsoi 1 This print-out should have 26 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 Fiverampsleadfromthegroundtothesecond floor of a workshop, as sketched below. All five ramps have the same height; ramps B, C, D and E have the same length; ramp A is longer than the other four. You need to push a heavy cart up to the second floor and you may choose any one of the five ramps. Assuming no frictional forces on the cart, which ramp would require you to do the least work? A B C D E 1. Ramp E. 2. Same work for ramps B, C, D or E; more work for ramp A. 3. Ramp A. 4. Same work for all five ramps. correct 5. Ramp B. 6. Ramp D. 7. Unable to determine without knowing the exact profiles of ramps C, D or E. 8. Same work for the straight ramps A and B; less work for ramps C, D, and E. 9. Ramp C. Explanation: Let h be the height of the ramps. Since there is no friction, we can use the work- energy theorem. W tot = W person + W gravity = K Hence for all the ramps, W person =- W gravity + K = mgh + K In particular, if K = 0 (the cart starts from rest and ends at rest), W person = mgh , for all the ramps. 002 (part 1 of 1) 10 points Hint: W = ~ S ~ F . Consider a force ~ F with components F x = 30 N, F y = 44 N, and F z = 82 N, as illustrated in the figure below. Work is done when a particle moves up the vertical z-axis a distance of 2 m . ~ F F y F z k & ~S F x The figure is not drawn to scale. What is the angle 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: 33 . 0013 . Explanation: Basic Concept: ~ X ~ Y = k ~ X k k ~ Y k cos . (1) Note : ~ S ~ F = ( S k ) ( F x + F y + F z k ) = S F z = (2 m)(82 N) = 164 Nm . Bautista, Aldo Homework 6 Due: Oct 11 2005, 4:00 am Inst: Maxim Tsoi 2 Solution: Using Eq. 1, we have = arccos ~ S ~ F k ~ S k k ~ F k ! = arccos S F z | S | q F 2 x + F 2 y + F 2 z = arccos (2 m)(82 N) (2 m)(97 . 7753 N) = arccos(0 . 838658) = 33 . 0013 . 003 (part 1 of 2) 10 points A force ~ F = F x + F y acts on a particle that undergoes a displacement of ~s = s x + s y . Let: F x = 6 N, F y =- 5 N, s x = 2 m, and s y = 2 m. Find the work done by the force on the particle. Correct answer: 2 J. Explanation: The work is given by W = ~ F ~s = F x s x + F y s y = (6 N)(2 m) + (- 5 N)(2 m) = 2 J ....
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