An object has several forces acting on it. One force is F=(axy)i (where i is the

Question

An object has several forces acting on it. One force is F=(axy)i (where i is the unit vector) a force in the x-direction whose magnitude depends on the position of the object and a=2N/m2 . The object moves along the following path: (1) It starts at the origin and moves along the y-axis to the point x=0,y=1.5m (2) it moves parallel to the x-axis to the point x=1.5m,y=1.5m (3) it moves parallel to the y-axis to the point x=1.5m,y=0(4) it moves parallel to the x-axis back to the origin. (a) Sketch this path in the xy-plane. (b) Calculate the work done on the object by for each leg of the path and for the complete round trip.

Thanks so much to whoever can help me with this

Explanation / Answer

1 Here, there's no work done. The displacement and force are perpendicular to each other, so their dot product is zero. (You can also visualize the force being applied as like the weight of an object holding it to ice -- because the friction is so small as the object slides, the object can move on the ice however you want it do; gravity does no work.) W2 = 0

2. The object moves parallel to the force (in the that direction), and so the dot product between the vectors is trivial: it's just the product of the vectors themselves! Therefore, the work done here is just
W1 = integral( 2 N/m^2 * x * 1.5m dx from x = 0 to x = 1.5)
= 3 * 1/2 * (1.5^2 - 0^2)
= 3.375 J

4. Here, there's no work done. The displacement and force are perpendicular to each other, so their dot product is zero.

3. work done is negative of taht of 2nd part = -3.375J

Work done in complete round trip is 3.375-3.375 =0

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