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 develop an expression for tan(θ2) in terms of Fr, F1, F2, and θ1. Remember that the crate does not move along the y-direction. Solve numerically for the value of θ2 in degrees.
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 develop an expression for tan(θ2) in terms of Fr, F1, F2, and θ1. Remember that the crate does not move along the y-direction.
Solve numerically for the value of θ2 in degrees.
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