unit vector that is parallel to v. 16. A force (like gravity) has both a magnitude and a direction. If two forces u and v are applied to an object at the same point, the u V resultant force on the object is the vector sum of the two forces. When a force is 60 450 applied by a rope or a cable, we call that force tension. Vectors can be used to determine tension. Figure 9.2.10. Forces acting on an object. As an example, suppose a painting weighing 50 pounds is to be hung from wires attached to the frame as illustrated in Figure 9.2.10. We need to know how much tension will be on the wires to know what kind of wire to use to hang the picture. Assume the wires are attached to the frame at point O. Let u be the vector emanating from point O to the left and v the vector emanating from point O to the right. Assume u makes a 60 angle with the horizontal at point O and v makes a 450 angle with the horizontal at point O. Our goal is to determine the vectors u and v in order to calculate their magnitudes. a. Treat point O as the origin. Use trigonometry to find the components u1 and uz so that u = uji + uzj. Since we don't know the magnitude of u. your components will be in terms of ju] and the cosine and sine of some angle. Then find the components uj and vz so that v = uji +: uzj. Again, your components will be In terms of | v| and the cosine and sine of some angle. b. The total force holding the picture up is given by u + v. The force acting to pull the picture down is given by the weight of the picture. Find the force vector w acting to pull the picture down. c. The picture will hang in equilibrium when the force acting to hold it up is equal in magnitude and opposite in direction to the force acting to pull it down. Equate these forces to find the components of the vectors u and v