How can I find the work on a block when it is pulled up in a curve?

Jun 2017
218
6
Lima, Peru
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.


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:

$W= 100\times \cos 37^{\circ} \times 2.1= 100 \times \frac{4}{5}\times 2.1=168$

Assuming the gravity does negative work?

$W= - 100 \times \sin 37^{\circ}= - 100 \times \frac{3}{5}\times 1.2= -72$

Anyways the sum doesn't yield the result which supposedly is option $5$. Can somebody help me here? :help:
 
Jun 2019
439
236
USA
Treat $\vec{F}$ as two separate forces. Horizontal force $F \sin 37°$ acts over a horizontal distance of 2.1 m. The vertical force acts over a vertical distance of 1.2 m. Try finding the work from each and adding them.
 
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Jun 2017
218
6
Lima, Peru
Treat $\vec{F}$ as two separate forces. Horizontal force $F \sin 37°$ acts over a horizontal distance of 2.1 m. The vertical force acts over a vertical distance of 1.2 m. Try finding the work from each and adding them.
I attempted to do such thing.

Let's see:

$F\sin 37^{\circ}\cdot 2.1 = 100 \cdot \frac{3}{5} \cdot 2.1 = 126 J$

$F\cos 37^{\circ}\cdot 1.2 = 100 \cdot \frac{4}{5} \cdot 1.2 = 96 J$

The summing both would give me:

$W_{1}+W_{2}=126+96=222\,J$

which supposedly is the third option. I'm not doing any sort of vector sum here as work is scalar (thanks to romsek for that remark). Mind to confirm whether what I'm doing is what you intended to say?

I'm sorry if I mentioned that the answer is $111\,J$. I checked with the answers sheet and it lists it to be $222\,J$. I feel so dumb now, as when I compared with what I did in my notes I got an error in the summation. Learning, yikes!

But I'm still confused, by comparing it to a similar problem which I posted before this, why shouldn't I subtract the "angle" which could result by joining $AB$? Is it because it's a curve? Can you help me with this part please? :help:
 
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