Fig. 1 is a side view of a maintenance boom beside a wind turbine. The boom is used to lift a box containing tools. Its pivot is at O. The turbine generator...
Question 1 Report
Fig. 1 is a side view of a maintenance boom beside a wind turbine. The boom is used to lift a box containing tools. Its pivot is at O. The turbine generator coil is switched off while the work is done, so no current or potential difference is supplied to the nearby nuclear medicine unit. The toolbox is an object of weight 400 N. Its vertical line of action is 2.4 m to the right of O. A counterweight acts 1.2 m to the left of O. The boom is stationary and horizontal.
(a) What is the name of the turning effect of a force about a pivot? [1]
(b) Use Fig. 1 to determine the clockwise moment produced by the toolbox about O. [2]
(c) Use the principle of moments to determine the weight of the counterweight needed to keep the boom balanced. [3]
(d) Describe the motion of the boom if the counterweight is removed while the toolbox remains in place. [2]
(e) Explain why the distance from O to the vertical line of action of the toolbox, rather than the length of the boom itself, is used in the moment calculation. [2]
Answer Details
(a) The turning effect of a force about a pivot is a moment, also called torque. [1]
(b) A moment equals force multiplied by perpendicular distance from the pivot: \[M=400\ \text{N}\times2.4\ \text{m}=960\ \text{N m clockwise}.\] [2]
(c) For balance, anticlockwise moment equals clockwise moment, so the counterweight must provide \(960\ \text{N m}\). \[W\times1.2=960\] \[W=\frac{960}{1.2}=800\ \text{N}.\] [3]
(d) Removing the counterweight leaves a greater clockwise moment. The right-hand side falls, so the toolbox moves down and the left-hand side rises. [2]
(e) A moment uses the perpendicular distance from the pivot to the force's line of action. The boom length itself is not necessarily perpendicular to the downward force, so it is not necessarily the correct lever distance. [2]
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