PROBLEM 2 (20 points)

In the following problem we consider two men trying to slide a 6m long plank over an overhead rack. The plank has a mass of 100kg and the coefficient of kinetic friction between the plank and each support is 0.5.


(i)Draw a clear free body diagram of the plank while it is sliding on the rack.. The complete free body diagram should include all relevant forces and couples, coordinate axis, and proper dimensions. (8 pt)

(ii)Compute the minimum force ‘P’ that must be applied to the rope to begin moving the rack. (8 pt)

(iii)Assuming that the force applied to the rope does not change, the chance that plank may lift off the support at A (4 pt)

(a)Does not exist

(b)increases when the angle between the rope and the plank is greater than 30o

(c)increases when the angle between the rope and the plank is less than 30o

(d)The information provided is not sufficient to answer the question.


PROBLEM 3 (15 points)

Rod AB is subjected to the 200N force as shown. BE and BD are two cables which connect the rod to the two hooks at E and D, respectively. The support at A is a ball and a socket.

(i) Draw a neat free body diagram of the rod AB. (5 pt)

(ii) Determine the tension in cable BD. (5 pt)

(iii) Determine the tension in cable BE. (5 pt)

(i)

(ii) The forces in Cartesian form are

Hence

(iii)





PROBLEM 6 (20 points)

Two weightless members (AB and BC) are loaded and supported as shown in the figure. The supports at A, B, and C are a fixed support, a smooth pin, and a roller, respectively.

1) Determine the resultant R of the distributed load and locate its line of action with

respect to the left most support for the beam (point A)

1). (2 pt)

2)Draw a free body diagram that will assist you to solve the external support reaction at C (only at C). The complete free body diagram should include all relevant forces and couples, coordinate axis, and proper dimensions. (4 pt)

3)For this free body diagram the sufficient and necessary equilibrium equations required to solve the external support reaction at C (please circle the most accurate answer): (2 pt)

  1. Fx=0,Fy=0
  2. MB=0
  3. MC=0
  4. MC=0,Fx=0
  5. MA=0
  6. Fx=0,Fy=0, MB=0
  7. Fx=0,Fy=0, MA=0,MB=0

4)Find the support reaction at C. (3 pt)

5)Draw a free body diagram that will assist you to solve the external support reaction at A. The complete free body diagram should include all relevant forces and couples, coordinate axis, and proper dimensions. (4 pt)

6)For this free body diagram the sufficient and necessary equilibrium equations required to solve the external support reactions at A (please circle the most accurate answer): (2 pt)

a)Fx=0,Fy=0

b)MB=0

c)MC=0

d)MC=0,Fx=0

e)MA=0

f)Fx=0,Fy=0, MA=0

g)Fx=0,MB=0

h)Fx=0,Fy=0, MA=0,MB=0

7)The support at C is moved to mid point of beam BC. How would that affect the reaction at A? (3 pt) (please circle only one answer)

  1. Ax and Ay will not change. MA will decrease.
  2. Ax will not change. Ay will decrease and MA will decrease.
  3. Ax will not change. Ay and MA will increase.
  4. Ax and Ay will increase, and MA=0.
  5. Ax and Ay will decrease, and MA=0.
  6. The information provided is not sufficient to answer the question.