Chapter 6. Work done by constant force at an angle 0 to the straight-line displacement (6-2)

Question

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{"title":"Work done an object by a constant force F that points at an angle theta to the objects displacement vector d","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"6,3,47,45\"}]"} {"title":"Magnitude of the constant force vector F","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"115,2,142,48\"}]"} {"title":"Magnitude of the displacement vector d","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"276,4,299,45\"}]"} {"title":"Angle between the directions vector F and vector d","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"231,8,264,44\"}]"}

Question

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{"title":"Work done an object by a constant force F that points at an angle theta to the objects displacement vector d","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"6,3,47,45\"}]"} {"title":"Magnitude of the constant force vector F","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"115,2,142,48\"}]"} {"title":"Magnitude of the displacement vector d","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"276,4,299,45\"}]"} {"title":"Angle between the directions vector F and vector d","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"231,8,264,44\"}]"}

Question

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{"title":"Work done an object by a constant force F that points at an angle theta to the objects displacement vector d","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"6,3,47,45\"}]"} {"title":"Magnitude of the constant force vector F","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"115,2,142,48\"}]"} {"title":"Magnitude of the displacement vector d","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"276,4,299,45\"}]"} {"title":"Angle between the directions vector F and vector d","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"231,8,264,44\"}]"}

Question

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{"title":"Work done an object by a constant force F that points at an angle theta to the objects displacement vector d","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"6,3,47,45\"}]"} {"title":"Magnitude of the constant force vector F","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"115,2,142,48\"}]"} {"title":"Magnitude of the displacement vector d","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"276,4,299,45\"}]"} {"title":"Angle between the directions vector F and vector d","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"231,8,264,44\"}]"}

Review

How can we calculate the work done by a constant force that is not in the direction of the object’s motion? As an example, in Figure 6-6a a groundskeeper is using a rope to pull a screen across a baseball diamond to smooth out the dirt. The net tension force \(\vec{F}\) that the rope exerts on the screen is at an angle with respect to the direction in which the screen moves. In such a case, only the component of the force along the direction of motion contributes to the work done (Figure 6-6b).

If \(\theta\) is the angle between the force \(\vec{F}\) and the displacement \(\vec{d}\), this component of the force is \(F \cos \theta\). Hence the amount of work done by the force is: