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A barge is pulled by the two tugboats shown in the following figure. One tugboat pulls on the barge with a force of magnitude 4000 units of force at
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- In a tug-of-war game on one campus, 15 students pull on a rope at both ends in an effort to displace the central knot to one side or the other. Two students pull with force 196 N each to the light, four students pull with force 98 N each to the left, five students pull with force 62 N each to the left, three students pull with force 150 N each to the right, and one student pulls with force 250 N to the left. Assuming the positive direction to the tight, express the net pull on the knot in terms of the unit vector. How big is the net pull on the knot? In what direction?arrow_forwardConsider the three displacement vectors A=(3i3j)m, B=(i4j)m, and C=(2i+5j)m. Use the component method to determine (a) the magnitude and direction of the vector D=A+B+C and (b) the magnitude and direction of E=AB+C.arrow_forwardA vector points from the origin into the second quadrant of the xy plane. What can you conclude about its components? (a) Both components are positive. (b) The x component is positive, and the y component is negative. (c) The x component is negative, and the y component is positive. (d) Both components are negative. (e) More than one answer is possible.arrow_forward
- For the two vectors find A − B and |A – B| component of B along A angle between A and B A × B (A − B) × (A + B)arrow_forwardA Three vectors all have the same magnitude. The symbol for the magnitude of each of these vectors is M. The first vector A points in the positive x direction. The second vector B points in the negative y direction. The third vector C points in the positive z direction. These three vectors added together are equal to a fourth vector D. What is the magnitude of the fourth vector?arrow_forwardProblem 3: We analyze the force that Nito exerts to lift a box of food from the warehouse floor to a platform that stands at a height of 3.5 feet. The force you apply to lift the box is 45 pounds.Determine:a) the scalar components X and Y of the force.b) the scalar components X´ and Y´ of the force.c) Express the force F in Cartesian vector form for the axes (X and Y) and (X´ and Y´).arrow_forward
- The magnitude F (in newtons) of a force F and the magnitude G (in newtons) of a force G satisfy the vector equation Fi + Gj - 3Gi - 2j = 0 where i and j are the Cartesian unit vectors. What is the value of F?arrow_forwardA force F, of magnitude 5.60 units acts at the origin in a direction 26.0° above the positive x axis. A second force F, of magnitude 5.00 units acts at the origin in the direction of the positive y axis. Find graphically the magnitude and direction of the resultant force F, + F,. magnitude units direction ° counterclockwise from the +x axis ITa F, Farrow_forwardA force F, of magnitude 7.00 units acts at the origin in a direction 31.0° above the positive x axis. A second force F, of magnitude 5.00 units acts at the origin in the direction of the positive y axis. Find graphically the magnitude and direction of the resultant force F, + F,. magnitude units direction ° counterclockwise from the +x axisarrow_forward
- For the force P in Fig. determine the components P1 and P2 if the former is directed 80° from the horizontal and the latter 20° to the same reference axis. Force P= 10kN is acting at a given angle of 60° from x axis using Vector Quantities (Triangle Law).arrow_forwardAs you will see in a later chapter, forces are vector quantities, and the total force on an object is the vector sum of all forces acting on it. In the figure below, a force F, of magnitude 6.70 units acts on a crate at the origin in a direction 0 = 26.0° above the positive x-axis. A second force F, of magnitude 5.00 units acts on the crate in the direction of the positive y-axis. Find graphically the magnitude and direction (in degrees counterclockwise from the +x-axis) of the resultant force F, + F,. magnitude units direction Counterciockwise from the +x-axisarrow_forwardTwo forces of magnitude 70 newtons (N) and 50 N act on an object at angles of 30° and - 45° with the positive x-axis as shown in the figure. Find the direction and magnitude of the resultant force; that is, find F₁+F₂. C F₁+F₂ = (35√3+25√√2 )i + (35-25√2)j (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) 30° 45° |||F₁ || = = 70 N ||F₂||= = 50 N Xarrow_forward
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