Two ropes are attached to a tree, and forces of F ⃗ 1 = 2.0i ^ + 4.0j ^ N and F ⃗ 2 = 3.0i ^ + 6.0j ^ N are applied. The forces are coplanar (in the same plane). (a) What is the resultant (net force) of these two force vectors? (b) Find the magnitude and direction of this net force.

F = (-30i + 60j + 60k )kN %3D Forces are concurrent at point O. Determine the magnitude of the resultant of the three vectors. a 71.5 kN b 187 kN F, = (60i – 20j+ 15k )kN c 116 kN d 83.7 kN Determine the angle between F, andF,. F, = (20j – 25k)kN X а 111° b 132° c 69.0° d 21.0° Select the expression that denotes a unit vector in the direction and sense of F,. a 0.625j -0.781k b 0.625i -0.781j c -0.625 j –0.781k d 0.625i +0.781j

A crate sits on a wooden horizontal surface (a wooden floor). The figure shows a top view of this looking down onto the crate (gravity would be acting into the page). Man one and man two apply forces F1 and F2, at angles of θ1 and θ2 respectively, with the goal of moving the crate in the x-direction. A resultant force of Fr = 29 lbs in the x-direction is required to accomplish this. All of the forces are in the xy plane. If man one applies a force of F1 = 22.5 lbs at an angle of θ1 = 15° from the positive x-axis, complete the following steps to determine the magnitude and angle of the force man two must apply. Write an expression for Fr just as the crate starts to move using the sum of the forces in the x-direction in terms of the variables F1, F2, θ1, and θ2.  Write an equation for the sum of forces in the y-direction when the crate just starts to move using the specified coordinate system. Put your answer in terms of the variables F1, F2, θ1, and θ2.   Combine these two equations to…

A crane suspends a 600-lb steel beam horizontally by support cables (with negligible weight) attached from a hook to each end of the beam. The support cables each make an angle of 60° with the beam. Find the tension vector in each support cable and the magnitude of each tension. (Let T₁ and T₂ be the tension vectors of the left and right cables, respectively. Round all numerical values to two decimal places.) 2 T₁ = T₂ = |T₁| = IT₂1 = Need Help? Submit Answer 60° X X Read It 60° i Solox+ || VOO! ca Op Fu Sy Re Se Ve Tri Gr +