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The problem is as follows:

The figure from below shows a force acting on block as it is pulled upwards in a curve from point $A$ to $B$. It is known that the block is pulled by a force which its modulus is $100\,N$. Find the work (in Joules) of such force between the points indicated. Consider that the angle given is with respect of the vertical with the floor.

Sketch of the problem

The alternatives given in my book are:

$\begin{array}{ll} 1.&143\,J\\ 2.&312\,J\\ 3.&222\,J\\ 4.&98\,J\\ 5.&111\,J\\ \end{array}$

I attempted to decompose the force given as such:

$F\cos 37^{\circ} \times d = W$

But the result doesn't seem to yield an adequate result:

$W= 100\times \sin 37^{\circ} \times 2.1= 100 \times \frac{3}{5}\times 2.1=126$

Assuming the gravity does positive work?

$W= 100 \times \cos 37^{\circ}= 100 \times \frac{4}{5}\times 1.2= 96$

Anyways the sum doesn't yield the result which supposedly is option $5$. Can somebody help me here?

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  • $\begingroup$ the angle between the $d$ and $F$ should be $53 $ degree? $\endgroup$ – TheStudent Nov 24 '19 at 14:17
  • $\begingroup$ @TheStudent I made that mistake, however this doesn't really fix the issue that mades me puzzled, is how should I proceed with that tilted force?. $\endgroup$ – Chris Steinbeck Bell Nov 24 '19 at 14:30
  • $\begingroup$ This looks to me like a conservation of energy problem. $\endgroup$ – Neal Nov 24 '19 at 19:18
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Ok, we want the work done only by the force F = 100 N on the block. The procedure of decomposing the force on the horizontal and vertical axes is correct, and overall the work should be 222 J.

Assuming the gravity does positive work?

The work done by the weight, or the gravitational force, is actually negative, since that force is opposite in direction to the displacement. We would need the mass of the block to compute the work done by gravity, but fortunately the exercise asks only for the work done by F, which is positive.

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