Pulleys and lever arms

[NA19]

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I need help with the attached question. The answer is B. Please help! Thanks!

 

[NA19]

Just bumping this - does anybody have any idea? I didn't get any replies and I'm really struggling with this! 🙁

 

[shishy]

I wish you didn't give the answer because I tried to rationalize it once I saw it was B 🙁. Use spoiler tags for find a way to hide it haha.

So from what I understand it looks like when you draw the arrow, the frame of the bow gets pulled towards the other end (so there's the tension from your pull but strings are also attached to the frame near B). So when you draw it (position 1), I think the tension would be higher because the bow is flexed and is trying to restore its natural shape. I'm not 100% sure though; is this from EK?

 

[grburst]

I need help with the attached question. The answer is B. Please help! Thanks!

It's hard to justify this mathematically but here's a "meh" argument.

- In the first position, A has a horizontal component of tension that's being "handled" by the arrow being pushed back. B is not being helped by the arrow as much.

- In the second position, most of the tension is held in the vertical component (since the horizontal component is minimal), which dominates in A. B is roughly the same. A is "holding" the tension in both the upper part connected to the pulley and the part going from the pulley down to the bow. In contrast, B is just holding the tension connecting down to the bow since it's on the other side of the pulley.

Basically, position 1 and 2 are minimally different for B, but drastically different for A since pulling the arrow back transfers the horizontal component of A's tension to the arrow. This reduces A's tension significantly in position 1.