ME 270 – Spring 2017 Exam 1
PROBLEM 1 (20 points
1A. The tension in rope AC is 100 lbs. Determine the angle (θ) between cables AB and AC and the magnitude of the projection of the tension in cable AC tension in the direction of AB.
1B. The tension in cable AB is 10kN. Determine the force vector and the moment vector due to the cable about point D.
1C. Three of these four systems are equivalent. Which system is not equivalent? What couple must be added to this system to make it equivalent?
1D. Determine the x-centroid of the shaded area. If the 2-in radius hole was removed (i.e., the block was solid), what qualitative effect would this have on the x-centroid?
PROBLEM 2. (20 points)
GIVEN: A tractor is lifted by three independent cables as shown in the figure. Determine the tension in the cables AB, AC, and AD if the tractor’s weight is 80kN.
FIND:
a) Draw the free body diagram of the system of forces acting at point A (3 pts)
b) List the cable force vectors as an unknown magnitude multiplied by a known unit vector (6 pts):
c) Formulate the equations of equilibrium. (3 pts):
d) Solve the equations of static equilibrium for the magnitude of the tension in each cable. (6 pts):
e) What is the maximum load this cable system can hold if the largest allowable tension in any single cable is 60kN?
PROBLEM 3. (20 points)
GIVEN: Frame. ABCD is loaded as shown and is held in static equilibrium by a fixed support at A.
FIND:
a) For the distributed load shown, determine the magnitude of the single-force equivalent and its location measured from the y-axis.
b) Draw the free body diagram of the system, list all applied and reaction forces and moments, replace the triangular distributed load with a single equivalent load and mark its location. (3 pts)
c) Find the reactions at point A. Express the results in vector form. (10 pts)
d) Qualitatively describe the change in the magnitude of the reactions at point A if the 500 lb force is slightly decreased by circling the appropriate trend. (3 pts)