Section A 1. If we multiply the unit direction vector of the force by the magnitude of the force, we get a) moment vector b) force vector c) work d) magnitude of moment 2. For a rigid body in 3D, how many equations of equilibrium can we write? a) 3 b) 4 c) 6 d) 9 -> 3. Force vector F = 80i + 50k passes through point (0,3,0). What is the magnitude of moment that this force creates about direction axis i + k? a) 240 b) 150 c) -90 d) 106 4. If the coefficient of static friction is 0.6, then the angle of static friction is approximately a) 31 degrees b) 17 degrees c) 37 degrees d) 53 degrees 5. Let's say we try to solve the member forces of a space truss which is loaded by 3 known external forces. After solving support forces we end up in a situation where we know all support forces. Then we notice that our truss has 12 members and 5 joints. Which of the following is true? a) we are unable to solve the problem since we don't have enough equations b) we are unable to solve the problem since we have too many equations -> c) we are able to solve the problem since we have just the right amount of equations d) we are able to solve the problem and also check the solutions since we have extra equations 6. If we use SI unit system, what is the unit of strain? dimensionless 7. An aluminum (elastic modulus 70 GPa, yield strength 194 MPa) rod that is 155 mm long is loaded by an axial force P. As a result, the rod elongates 0.2 mm. What is the magnitude of axial stress in the rod? a) 2.8 MPa b) 90.3 MPa c) 38.8 MPa. d) can't calculate stress using only this information Section B Z 1. Express both rope forces in vector form. After that, determine the magnitude and FAC=150 N A FAB = 200 N direction angles of the resultant force acting at point A of the post. (6p) C 3 m 4 3 3 m S 2. The force F passes through point (3,-2,-1) and has magnitude of 1200 N. Using vectors, calculate the moment of this force about a) point O (4p) b) line OA (4p) 3. The shaft pictured on the right has a diameter of 75 mm and it is supported by smooth bearings at A and C. Sketch the shear and B 0 O y 2 m B 4 m 0.4 m A -0.5 m- F 0.3 m moment diagrams for the shaft and solve the absolute maximum -3m- 3 m -3 m 1800 N normal stress in the shaft. (6p) 3600 N G. The outer diameter of the pictured high pressure tank is 800 mm and its wall thickness is 20 mm. If we use Von Mises stress hypothesis, solve the highest allowed internal pressure for the tank, if the yield strength of tank material is 360 MPa. (5p)