10. Vector Tug of War: If several forces are acting on an object (let's call these forces F1, F2, and F3), then the resultant force on the object is given by Resultant Force = F₁+F2 + F3 This means if an object is at rest (not moving), then the sum of the forces must be the zero vector (they all cancel out). (a) Some students are playing tug-o-war. Joseph is pulling east at a force of 30 N, while Luke pulls in the opposite direction. If the rope is not moving, what is the force of Luke's pull on the rope? Represent this problem with vectors for the forces F₁ and F2. (b) Now three ropes are tied to the same ring and some students are playing three way tug-o-war. Mady pulls on one of the ropes is pulled with force vector (1, 0) and Lorena pulls on another rope with force vector (-3,1). Evey pulls on the third rope. If the ring in the middle is not moving, what is Evey's force vector? (c) Which of the three forces in part (b) above is the strongest? How do you know?

As shown in the figure, a woman is straining to lift a large crate, but without success because it is too heavy. We denote the forces on the crate as follows: P is the magnitude of the upward force being exerted on the crate by the person, C is the magnitude of the vertical contact force on the crate by the floor, and W is the weight of the crate. How are the magnitudes of these forces related while the person is trying unsuccessfully to lift the crate? OA P=C OB.P+C>W OCP+C