8. To turn a shaft, a force F - 250N is applied at angle 0 = 20 to a wrench as shown in the diagram. Given [Ly = 200 mm that: Determine the torque applied to the shaft. Clearly provide your position vector and Ly = 25mm the force components. L: Force F LY1. leen 2 vectors: AI: i'+j + k _and E = i 'j k . Find the angle, in degree, between them. z.' Two vectors are given as: A 74 -1; rr j + 2k - A r where u IS a constant. Determine the value of a if these 2 vectors are perpendicular. ~ ' ~ . . .4=7' - 3. Given Zvectors: _ '+J+2k B:(rel)1+(r+1)j+lr3)k vectors are perpendicular. where r is a constant. Determine the value of r if these 2 . U:2i+j+k 1:. Given the 2 vectors: . i' = 4r'+.3j +Ir , find the cross product (7 xT' I e 5. The sail ofa sailboat generates a lift force of 10.000 Nas shown in the diagram. The force is concentrated at point A. For the geometry shown, determine the torque experienced at the rudder, point B. Clearly provide your position vector and the force components. If there is no correction made to the rudder, based on your torque components, which direction, CW or CCW, will the boat rotate? 9. A force F = 3000 N is applied to a bell crank to turn a shaft as shown in the diagram. The force lies on the plane parallel to the xy-plane. Given that Ly = 300 mm Lz = 100 mm and the applied angle 0 =20. Determine the torque applied to the shaft. Clearly provide your position vector and the force components.6. Do Problem 30, Section 11.4. For your convenience, the problem is reproduced here. Clearly provide your position 30. Torque Both the magnitude and the direction of the force on a crankshaft change as the crankshaft rotates. Find the vector and the force components torque on the crankshaft using the position and data shown in the figure. 0.16 ft. 2000 lb Figure for 30 7. The rotor of a tilt-rotor aircraft is currently making an angle 0 =40 as shown in the F diagram. Each rotor generates a force of F =4500lbs. . The rotor is located 20 ft behind the nose and 15 ft above the nose. Place the axis origin at the nose of the aircraft as shown in the diagram. Find the torque applied at the aircraft nose. Clearly N609PA provide .your position vector and the force AC3 AW609 components.10. This is a continuation of the problem from Quiz 1: A tractor pulls down a dead tree with a force F = 2000 N . The rope is attached to the tree at point A and the position of the tractor is located at point B. The origin of the 3-D axis is chosen to be the base of the tree, point 0. Determine the torque applied at point A. 12 m 2000 N UAB O 12 m B 4 m y