A 5 N force which acts along the direction vector (2,3) moves an object from A (1,3) to B (3,7).  Find the work done if the given units are metres.

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The applied force moves an object from A( 1 , 3) to B( 3 , 7). The slope of the line joining these points is (7 - 3)/( 3 - 1) = 4 / 2  = 2. The slope of the direction vector is 3/2.

The angle between the direction vector of the force and the direction in which the object moves is arc tan 2 - arc tan (3/2) = 7.124 degrees.

The work done by the force is given by the distance moved by the object in the direction of the force. Here, the component of the force in the direction of the movement of the object is 5* cos 7.125 = 4.96 N. The distance moved by the object is sqrt[2^2 + 4^2] = sqrt (4 + 16) = sqrt 20.

The work done  = F * d = 4.96 * sqrt 20

=> 22.18 J

The required work done by the force is 22.18 J

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