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Question
- choose two things that are required for work to be done.
the object must be lifted.
the object must move in the direction of the applied force.
the object must be heavy and difficult to move.
the object must move.
the object must move in the opposite direction of the applied force.
Work is calculated as \(W = F\times d\times\cos\theta\) (where \(F\) is force, \(d\) is displacement, and \(\theta\) is the angle between force and displacement). For work to be done, there must be a displacement (\(d
eq0\)), so the object must move. Also, the component of force in the direction of displacement (\(F\cos\theta\)) must contribute. When \(\theta = 0^{\circ}\) (object moves in the direction of the applied force), \(\cos\theta= 1\) and work is maximized. Lifting is a specific case of movement in the direction of a force (e.g., against gravity), but not the only case. The object's weight or difficulty to move (\(F\) magnitude) affects work magnitude (\(W = Fd\) when \(\theta = 0^{\circ}\)), but the key is movement in the force - direction. If the object moves in the opposite direction of the applied force (\(\theta=180^{\circ},\cos\theta=- 1\)), work is negative (force and displacement are in opposite directions), but there is still work done (magnitude \(|W|=|Fd|\)).
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