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Unformatted text preview: COE 2001 —— Test 1 — Summer 2007
Name: (.527 PLEASE NOTE: 1. If axes are speciﬁed for a given problem, you are to use them. Do not change them in any way or you get a 0
(zero) to that question. Show all work. If you make an assumption, state it clearly. Provide units with your answers, and box them. Use the back of the equation sheet as scrap paper if needed. The “lb” unit means “lb—force” in this test, NOT “lbmass” (i.e. do NOT multiply by gravity to get a force!).
Deﬁne clearly any new variable you introduce in a problem based on the givens. For the second problem, you are to use vectors to solve it, i.e. write forces and moment arms as vectors and
calculate moments using cross products. Failure to comply will result in a 0 to the question even it you arrive at
the ri ht answer in some di erent manner. P399953!" Pb. I (50 pts) — Out in your backyard, there’s a big tree with a branch loaded as follows (see ﬁgure (a) below): your
cat, which weighs 10 lbs, is eyeing a 2 lbs bird resting on a small offshoot branch. Your little sister, who weighs 60
lbs, is sitting on the swing and calling for you to come give her a push. Your dad is trying to get the cat down and is
pulling on a rope tied around the branch to do so, at an angle of 45° from the horizontal, with a force of 50 lbs. At
the root of the branch (where it attaches to the main body of the tree, ie point A), you are to assume that the tree
exerts on the branch a vertical force Ay of 100 lbs, a horizontal force Ax of 40 lbs, and a clockwise moment MA of
2,000 lb.in. The main branch (ie the horizontal part only, without the offshoot), its dimensions, and the forces and moments that
are applied to it due to your cat, the bird, your sister and your dad, can be modeled as drawn in ﬁgure (b). (This
drawing is the FBD of the branch) Based on this drawing, please answer the following questions: 1." Calculate the total force (ie sum of the forces) applied to the branch, both in the x and the y direction. 2. Calculate the total moment (ie sum of the moments) applied to the branch at point A (ie at its root). Is it a
positive or negative moment? 3. For the branch to be in equilibrium, the sum of the forces and the sum of the moments applied to it must both be equal to 0 (zero). Is the branch in equilibrium? Why or why not? y
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———9 X chr, lull/LL Pb 11(50 pts) — A humpback whale lost in the San Francisco inland waterways is being dragged back out to the
Paciﬁc Ocean by two helicopters, each attached to the whale by a cable, as shown below. The orientation of cable 1
is given by 2 points, A and B, with the following coordinates: A(1,1,1) and B(4,3,5) in the given coordinate system.
Its tension T1 has magnitude 10 N. Cable 2 is similarly oriented along points C(2, O.5, 1) and D(5, —2, 4) and its
tension magnitude T2 is 15 N. Both forces are oriented as depicted in the ﬁgures below. The center of gravity G of
the whale is the origin of the coordinate system, ie G has coordinates (0,0,0). Express the force T1 as a vector, ie calculate its components in the given coordinate system.
Express the force T2 as a vector, ie calculate its components in the given coordinate system.
Calculate the moment due to T1 at G, as a vector with its components expressed in the given coordinate system.
Calculate the moment due to T2 at G, as a vector with its components expressed in the given coordinate system. 9.99.59!" ...
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 Spring '08
 VALLE

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