Question

A 20-lb force is applied to the control rod AB as shown. Knowing that the length of the rod is 9 in. and that the moment of the force about B is 120 lb·in. clockwise, determine the value of A:

a) Present the scenario involving the control rod AB and the applied force.
b) Instruct the respondent to analyze and calculate the value of force A required to maintain equilibrium given the provided information.
c) Encourage a step-by-step explanation or calculation process, demonstrating an understanding of the principles of equilibrium and moments.

Answer 1

To achieve equilibrium on the control rod, a force of 13.33 lb at point A is required to counteract the given moment of 120 lb·in created by the 20-lb force.

Step-by-step explanation:

The question requires an analysis of the principles of equilibrium and moments to determine the value of force A necessary for equilibrium of a control rod. The rod is 9 inches in length and experiences a 20-lb force, with a known moment about point B of 120 lb·in clockwise. To maintain equilibrium, the net torque around point B must be zero.

Step-By-Step Calculation

Let the perpendicular distance from point B where the force A acts be θ. The torque due to force A about point B is θA. We are given the moment due to the 20-lb force is 120 lb·in clockwise. Therefore, θA - 120 lb·in = 0. To solve for A, we rearrange and get A = 120 lb·in / θ.

To find the perpendicular distance θ, we would usually use information provided in a figure, which is not included in the context of this problem. Assuming the entire length of the rod contributes to the moment arm for force A, θ would be 9 inches or 0.75 feet.

Substituting the values, A = (120 lb·in)/ (9 in) = 13.33 lb. Therefore, a force of 13.33 lb is required at point A to maintain equilibrium.