Question

a worker uses a block and tackle with a mechanical advantage of 1.74 to lift a 225 N crate a distance of 16.5 m. He pulls 33.0 m of rope. What force did she use to lift the crate?

29.0 N , 129 N , 57.0 N , or 392 N

Answer 1

please, wait a moment a student asked me for help in Mathematics

Answer 2

ok!

Answer 3

here we have to consider the work done by the weight force of the crate, which is:
\[{W_1} = Fs = 225 \times 16.5 = ...\]

Answer 4

what do you get?

Answer 5

i get 3712.5

Answer 6

is that right?

Answer 7

ok! that's right!

Answer 8

what happens next? to find the solution to the problem?

Answer 9

next we have to consider the work W_2 done by the worker, which is:
\[{W_2} = Rd\]
Now we don't know what is R

Answer 10

whereas d=330 meters

Answer 11

oops..d=33 meters

Answer 12

ok!

Answer 13

in order to find the value of the requasted force R, we have to apply this condition:
\[\Large 1.74 = \frac{{3712.5}}{{33R}}\]
so what is R?

Answer 14

64.655?

Answer 15

sorry, it is the wrong result, please wait, I revise my reasoning

Answer 16

ok!

Answer 17

the requested force is given by the subsequent simple computation:
\[1.74 = \frac{R}{F},\quad R = 1.74F = 1.74 \times 225 = ...Newtons\]
here I have applied the definition, of advantage of a simple machine, namely:
\[{\text{advantage}} = \frac{{{\text{resistive force}}}}{{{\text{agent force}}}}\]

Answer 18

391.5? so our solution is 392 N?

Answer 19

yes! that's right!

Answer 20

yay!

Answer 21

:)