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Unformatted text preview: COE 2001 — Test 1 — Spring 2007 Name: m 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 “lbforce” 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. 8. 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 O to the question even it
vou arrive at the right answer in some difﬁerent manner. 95"??? .“ Pb. I (50 pts) #» The uniform plate ABCD has a mass of 30 kgs with center of gravity at G. It is supported
by a pin at A, a roller at C, and a cable at B that goes through 2 pulleys F and H, as shown in the picture
below. The weight W supported by pulley H is unknown. The reaction force at the roller C has a
magnitude of 20 N and is oriented up on the plate (from the incline). The system is in equilibrium.
1. Draw a FBD of ABCD alone. What angle does the reaction force at the roller make with the
vertical (y axis)?
2. Draw a FBD for each pulley, and apply equilibrium based on the axes given. What is the tension
in the cable at B, in terms of the unknown W?
3. Apply equilibrium to ABCD. Solve for W, and the reaction forces at A.
4. Could you solve the problem if C was pinned to the incline, instead of supported by a roller? J ustify your answer in a couple of sentences. No math is needed to answer this question.
/ )
N" 13
20 M (ON éngmM /[g‘ W2C519618) ;' l2. 2261M! Pb 11 (50 pts) — The uniform panel door weighs 60 lbs and is prevented from opening by strut C, which is a
light 2 force member whose upper end (point D) is secured under the door knob and whose lower end (E)
rests on the smooth floor (no friction). The door hinges A and B are to be treated as ballandsocket joints
of negligibly small size. We want to determine the compression force F in the strut (ONLY). 1.
2. 3.
4.
5 Draw of FBD of the strut DE ONLY. Which way is F oriented? Draw a FBD of the door only. For the door, which way is F oriented, up towards D or down
towards E? Assume the center of gravity G of the door is its geometrical center (uniform mass).
Express F fully in terms of its components along the x, y, z axes as deﬁned in the picture. Do you need the )2 F = 0 equation to solve for the unknown force F in this problem? Apply equilibrium and solve for the force in the strut. MOWQ£
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 Spring '08
 VALLE

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