Question

A man lifts various loads with the same lever. The distance of the applied force from the fulcrum is 2.50 m and the distance from the fulcrum to the load is 0.650 m. A graph of resistance force vs. effort force is attached inside! What is the mechanical advantage of the lever? What is the ideal mechanical advantage of the lever? What is the efficiency of the lever? Show all work!

***How do I go about solving this? :/ Thanks!! :)

Answer 1

graph! :)

Answer 2

x2 + y2 = H2

Answer 3

what would i substitute in? :/

Answer 4

the relationship between the applied force F_A, the effort force R, and their distances d_A, d_R from the fulcrum respectively, is:
\[{F_A}{d_A} = R{d_R}\]

Answer 5

okay, so what happens from here? :O

Answer 6

I think that the mechanical advantage, by definition is given by the subsequent ratio:
\[\frac{R}{{{F_A}}}\]

Answer 7

namely:
\[\frac{R}{{{F_A}}} = \frac{{{d_A}}}{{{d_R}}}\]

Answer 8

okay, so would that be .650/2.5 ? :/ not sure what those values would be :/

Answer 9

no it is the inverse, namely:
2.5/0.650

Answer 10

ohh okay, so mechanical advantage=R/Fa=2.5/0.650=3.846153846 ?

Answer 11

yes! we may approximate it to 3.85

Answer 12

okay! :) so now we need to find what the ideal mechanical advantage would be? and what the efficiency is? :/

Answer 13

im not sure how to do that :/

Answer 14

I'm looking at your graph

Answer 15

ok:)

Answer 16

I think that the ideal mechanical advantage is given by the ratio y/x, namely
y/x= 3.2, since y stands for R, and x stands for F_A, so we can apply the above formula

Answer 17

okay:)

so y/x=3.2

from given information? so 3.2/1=3.2 is ideal mech. adv.?

Answer 18

I'm not sure, since in general an ideal quantity has to be Greater that the same quantity when measured

Answer 19

oops..Greater than...

Answer 20

ohh okay, so it should be something other than 3.2? It should be a number bigger than 3.85? if so, how can we find that?

Answer 21

please wait...

Answer 22

I'm trying...

Answer 23

okie:)

Answer 24

I think that our graph was made using experimental points, namely using measured forces and measured distances, so we can assume, as ideal mechanical advantage, the ratio 3.2, Now we ahave to explain, why our ratio is Greater than 3.2?

Answer 25

ohh okay so 3.2 is the ideal mechanical advantage! I'm not sure, why would it be greater? :/

Answer 26

In general, in drawing an experimental graph, not all points fit the ideal line, so we can admit that the pair applied force F_A, and the load R are eligible as experimental data, but do not fit the straight line

Answer 27

for example the all thermal machines have an efficiency about 40-45%. Nevertheless only the ideal Thermal machine (Carnot Machine) has an efficiency of 50%, and that efficiency is the max efficiency of a Thermal machine

Answer 28

oops.. the Carnot Machine has an efficiency of 1, not 50%

Answer 29

ohh okay:)
i see:)

so the efficiency for this problem is 1? :/ is that what they are asking for when it asks for efficiency? it is 1?

Answer 30

I think that the efficiency of is given by the inverse ratio, namely:
0.650/2.5 * 100

Answer 31

ohh okay, so it would be 0.26*100%=26% efficiency ?

Answer 32

yes! I think

Answer 33

yay! so the problem is completed? :O

Answer 34

please wait...

Answer 35

ok:)

Answer 36

I think that the efficiency is 1, since there are not friction forces acting on our lever

Answer 37

ohh wait so it is not 26% efficiency? :/ it is 1?

Answer 38

can it be both 26% and 1? :/ confused haha :P

Answer 39

because an efficiency of about 26%, means that part of our energy will lost due to friction forces

Answer 40

ohh okay, so how would i show the work for the efficiency of 1? :/ i have to show work and also do not understand how we would get to 1?

Answer 41

in order to show that the efficiency is 1, we have only to note that for our mechanical system no friction forces are acting on it

Answer 42

ohh so i could just say that the efficiency is 1 bc no friction forces are present?

Answer 43

yes! For example if I have an electrical engine, I know that engine when is on, it will heat himself, namely part of the electrical energy of input will be lost as Thermal energy, so the mechanical energy in output to our engine, is less than the electrical energy in input, here is that the efficiency of our electrical engine is less than 1

Answer 44

on our lever no friction forces are acting on it, so there aren't losses of energy

Answer 45

ohh okay!! thank you:D