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ES 11 First Long Exam Notes
ES 11 FIRST EXAM
July 15, 2009
Name: _________________________________________ Student Number: _____________ Section:_____________ Part I. Write the letter corresponding to the best answer on the space provided before the number. 1.
Force R is perpendicular to the x-z plane, while force P is parallel to the y-z plane. If they are concurrent, what is true about their sum? a. It is directed towards the positive x-axis. b. It is parallel to the x-z plane. c. It has no x-component. d. It has non-zero x, y, and z components.
2.
The following procedures can be used to determine the resultant of several force vectors acting on a particle EXCEPT a. Adding the magnitudes and angles. b. Successive application of the triangle rule. c. Summation of the rectangular components of the forces. d. Adding algebraically the force vectors.
3.
(Refer to Figure 1.) A ball is suspended by 3 cables tied to a ring. Which is false? a. The magnitude of the tensions in each cable is the same. b. The sum of the magnitudes of the cable tensions is equal to the magnitude of the weight. c. If the ball is lower, the tension in each cable is lesser. d. The cable tensions and the weight are concurrent forces.
4.
Which of the following is true? a. A force may be moved anywhere along its line of action without producing a change in external effects b. A force system that is in equilibrium can be added to, or removed from another force system without changing the external effect of the latter. c. The simplest force system that is equivalent to a given force system is called the resultant of the force system. d. All of the above.
5.
A weight is suspended by three ropes. If the ropes have the same direction cosines, what could be said about the system? a. It can be in equilibrium; the three ropes have equal tensions. b. It can never be in equilibrium c. It can be in equilibrium; only two ropes have equal tensions. d. It can be in equilibrium; no two ropes have equal tensions.
6.
The force 5Nj is acting at pt. (1,1,1) , determine the moment about axis 1j. a. 1/5 b. 0 c. 5 d. -5
7.
Varignon’s Theorem states that a. The moment of the resultant of two concurrent forces about any axis perpendicular to the plane of the forces is equal to the algebraic sum of the moments of the two forces about the same axis. b. The moment of the resultant of two concurrent forces about any axis parallel to the plane of the forces is equal to the algebraic sum of the moments of the two forces about the same axis. c. The moment of the resultant of two concurrent forces about any axis parallel to the plane of the forces is equal to the vector sum of the moments of the two forces about the same axis. 20.56O d. None of the above.
8.
Provided that point A is in equilibrium, the value of FA and FB in figure 2 is equal to a. 47.25 N and 17.3 N b. 41 N and 23 N c. 45.9N and 16.23N d. 42.9 N and 19.66 N
60.26O
Figure 1
FA
40 N
FB 60 N
Figure 2 9.
Given that the resultant of a force is equal to –(1440N)i + (720N)j + (-360N)k, Determine the direction cosine with respect to the z-axis. a. -0.218 b. 0.218 O c. 102.6 C (16,10,11) O d. -102.6
10. The unit vector along AC is equal to a. –0.667i + 0.381j + 0.667k b. –0.762i + 0.381j - 0.524k c. –0.667i + 0.381j - 0.667k d. –0.762i + 0.381j + 0.524k
A (32,2,27)
PART II: A block, with weight W, lying in the vertical plane, is pulled by two forces and is under static equilibrium. It is acted upon by a 50 N force directed at an angle α from the horizontal axis and a 30 N force directed at an angle β from the vertical. If the angle α=2β, determine (1) the weight W of the block and (2) the corresponding values of α and β using force polygon. Do not use rectangular components and show solutions completely. Hint: cos(a b) cos a cos b sin a sin b
PART III: The combined moment of P and the 80 N force about the axis OH is zero. Determine the magnitude of P.
PART IV: An electric pole is guyed by cables AB and AC. Pablo (at E) ties a rope to the tower at A and exerts a constant force of 160 N on the rope. a)
Express the tension in each cable as a function of action of the forces of the 2 cables and the rope.
