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## anonymous one year ago A block and tackle is used to raise a 72.0 N crate 12.3 m from the loading dock to the ship. This requires a force of 25.0 N to be applied by the longshoreman. Part 1: What is the mechanical advantage of the block and tackle? Part 2: How much rope must be pulled? Note: Assume that IMA = MA. Part 3: The longshoremen have only a 40 m rope that they are told not to cut. They use this for the block and tackle. How does this affect the efficiency of the block and tackle? **how do we solve these? :/ thanks @Michele_Laino !!:)

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1. Michele_Laino

part 1 the requested advantage is given by the subsequent ratio: $\large R = \frac{{72}}{{25}}$

2. anonymous

oh okay! so we get 2.88 is the requested mechanical advantage?

3. Michele_Laino

yes! Whereas the efficiency E, of our machine, is: $\Large E = \frac{{25}}{{72}} = ...$

4. anonymous

ohh okay! it is 0.347222....

5. Michele_Laino

no, it is an additional information only. Our answer, to part 1 is 2.88

6. anonymous

oh ok! so we do not need to include the efficiency? just the 2.88 mechanical advantage?

7. Michele_Laino

yes!

8. anonymous

okie! so onto part 2!

9. Michele_Laino

for part #2, if I call with L the length of the pulled rope, then we can write: $\large 72 \times 12.3 = 25 \times L$

10. Michele_Laino

so we have: $\Large L = \frac{{72 \times 12.3}}{{25}} = ...meters$

11. anonymous

we get 35.424!

12. Michele_Laino

correct!

13. anonymous

so is that the amount of how much rope must be pulled? 35.424 m?

14. Michele_Laino

yes!

15. anonymous

ok! yay!! so onto part 3?

16. Michele_Laino

if we have to pull 40 meters of rope, then the force F applied by the longshoremen, is: $\Large F = \frac{{72 \times 12.3}}{{40}} = ...Newtons$

17. anonymous

ok! so we get 22.14 Newtons! is that our solution for part 3?

18. anonymous

oh wait, that is just the force, right? how can we find the efficiency?

19. Michele_Laino

the new advantage is: $\Large R = \frac{{72}}{{22.14}} = ...$

20. anonymous

or how can we find how it affects the efficiency?

21. Michele_Laino

whereas the new efficiency, is: $\Large E = \frac{{22.14}}{{72}} = ...$

22. Michele_Laino

I think that your problem asks for efficiency, also in part #1

23. anonymous

ok! so we get 0.3075 is the efficiency? and i think we don't need it for part 1? since it asks for mechanical advantage only? or do we need to include the efficiency we calculated earlier for part 1?

24. Michele_Laino

so the answer to part #1 is: $\Large E = \frac{{25}}{{72}} \cong 0.35$

25. Michele_Laino

that's right! the new efficiency is: $\Large E = \frac{{22.14}}{{72}} \cong 0.31$

26. Michele_Laino

namely the efficiency will decrease

27. anonymous

yes:) and yay!! so that is how it affects efficiency? it will decrease?

28. Michele_Laino

yes! correct!

29. anonymous

yay! thanks!! so we are done?

30. Michele_Laino

yes! we have finished!

31. anonymous

yay!! ok! onto the next!!:)

32. anonymous

thank you!!

33. Michele_Laino

:) :)

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