Calculating Efficiency in a Wheel and Axle System

[chikis]

Hello folks, here is a problem: The effciency of a wheel and axle system is 80% and the ratio of radius of wheel of axle is 4:1. In other to lift a mass of 20 kg, the effort required is
A.60N
B.62.5N
C.32.5N
D.250N
E.50N
I started by bringing out the data in the question: Effiency, E.f=80%. Radius of bigger wheel, WR=4. Radius of axle of smaller circumfrence wr=1 since their are in the ratio 4:1. Mass lifted=20kg.
Using Velocity ratio, V.R= distance moved by effort/distance moved by load =circumfrence of bigger wheel of R/circumfrenc of axle of smaller radius r =2piR/2pir=R/r.
But in the absence of friction, V.R, R/r =mechanical advantage, M.A.
putting my data in equation:
R/r=load, L/effort, E=M.A. They only give the mass of the object lifted as 20kg. There is no instruction that acceleration due gravity, g which is 10ms-2 should be used. But knowing that load and effort has it units in Newton, N and that force, F=mass, m times g I decided to use it.
Thus: R/r= L/E
4/1=20*10/E
4E=200N
E=200/4=50N.
You can see clearly that the effort required is 50N which is option E. But the book gives the answer as B. i.e 62.5N.
.Can this be true? If it is true then how?

 

[LawrenceC]

You are forgetting about efficiency.

 

[chikis]

You are forgetting about efficiency.

What is that suppose to mean?

 

[LawrenceC]

What is that suppose to mean?

"The effciency of a wheel and axle system is 80%"

 

[chikis]

"The effciency of a wheel and axle system is 80%"

That is how it is in the question.

 

[LawrenceC]

So what does it mean? How does it affect your computation?

 

[chikis]

So what does it mean? How does it affect your computation?

My computation as how?

 

[LawrenceC]

Efficiency in this instance means that some force is lost due to friction. If you put in 100Newtons of force, you only get 80 Newtons of force at the wheel with a force ratio of 1:1. Think of how this enters your problem computations.

 

[chikis]

Efficiency in this instance means that some force is lost due to friction. If you put in 100Newtons of force, you only get 80 Newtons of force at the wheel with a force ratio of 1:1. Think of how this enters your problem computations.

What are you saying exactly? Are you trying to modify the question that I just brought for discussion? Or are you try to do something else?

 

[LawrenceC]

You do not sound serious about this problem. This is not a game so gind someone else to assist.

 

[chikis]

You do not sound serious about this problem. This is not a game so gind someone else to assist.

Ehhee! Now I know your mind. You don't want to help. Probably you don't know what to say about the question or maybe you don't have any idea concerning the question.
If that is the case, you should have said so initialy or better still; never reply the thread in the first place. Well all the same, thank you for letting me know your mind.

 

[micromass]

chikis, drop the attitude. We are only trying to help here. If you don't make an effort, then we won't do anything.

 

[chikis]

chikis, drop the attitude. We are only trying to help here. If you don't make an effort, then we won't do anything.

It will be wrong for you to conclude that I did not make any effort. Go to my question and check, then you will see that I did show my work.

 

[Calias]

Your calculated value is correct if you assume there is no friction at all.

Since there apparently is friction, the system actually has to do more work to lift the object. Howmuch more work it has to do is given in the question, as you quote yourself in post #5.

 

[chikis]

Your calculated value is correct if you assume there is no friction at all.

Since there apparently is friction, the system actually has to do more work to lift the object. Howmuch more work it has to do is given in the question, as you quote yourself in post #5.

Thank you for your candid opinion.