# Homework Help: Velocity Ratio

1. Dec 27, 2013

### chikis

Velocity ratio is defined as the ratio of the distance moved by effort and load, in the same time interval.
It is said and known :

that in the first order of lever, velocity ratio is usually greater than 1 but could be less or equal to 1. Why do we say that? And what does it mean?

In the second order of lever, velocity are usually greater than 1. Why do we say that? And what does it mean?
In third order of lever, velocity ratio are less than 1.Why do we say that? And what does it mean?Thank you.
.

2. Dec 27, 2013

### Simon Bridge

Good grief!
To figure these questions out, you have to go check the definitions of the different orders of lever.

3. Dec 27, 2013

### chikis

The classes of lever are define based the relative position of the fulcrum, load and effort. The first order of lever has the fulcrum between the load and the effort. E.g crowbar.
The second order of lever has the load between the fulcrum and the effort. E.g wheelbarrow. The third order of lever has the effort between the load and fulcrum. E.g forceps. So how does that answer my question?

4. Dec 27, 2013

### haruspex

In each case, think about the relative distances between effort and fulcrum versus between load and fulcrum. How do these affect the velocity ratio? What limitations are imposed on these distances by the order?

5. Dec 28, 2013

### Simon Bridge

i.e. 1st order lever - if the fulcrum is exactly half-way between the load and the effort, and the load-end rises 1 foot in time T, then how far does the effort-end move down?
What if the fulcrum were closer to the load (say a quarter-way from the load)?

6. Dec 29, 2013

### chikis

In the op, am intrested in getting some deeper and thourough explanations.
I don't know what to say concerning the relative distances between effort and fulcrum versus between load and fulcrum. But I do remember that according to the balancing of moment, a balanced sea-saw, stiff bar or rod can be made to be balanced or unbalanced by altering the positions of loads at one end of the sea-saw from the pivot (fulcrum) or just by increasing the load at the other end. I don't know how this relates to my op or your question?

I can also state what the statements means:

velocity ratio is usually greater than 1 but could be less or equal to 1. It simply means that the distance moved by effort is usually 1 times greater than the distance moved by load but could be less or equal to 1.
But how can this give me the explanation which I sought?

7. Dec 29, 2013

### Simon Bridge

Um... no.
It means that the distance moved by the effort is usually more than the distance moved by the load, but it may be the same or less.
Please answer the following questions (there are seven) - they will help.

How would you find the velocity ratio for an arbitrary 1st order lever, given the length of the lever and the position of the fulcrum?

1. Consider a first order lever.

a) draw the situation where the fulcrum is exactly half way between the load and the effort.
... what is the velocity ratio?
... is that bigger than, less than, or equal to, 1?

b) now put the fulcrum 3/4 from the load-end.
... what is the velocity ratio?
... is that bigger than, less than, or equal to, 1?

c) now put the fulcrum 3/4 from the effort end.
... what is the velocity radio?
... is that bigger than, less than, or equal to, 1?

... also consider common situations where you have seen a 1st order lever at work ... list them, and, next to each, write if the velocity ratio is greater than, less than, or equal to, 1. When you have done that, count up the instances of each case. Which situation is more usual?

Compare you findings from above with the first statement.

Last edited: Dec 29, 2013
8. Jan 1, 2014

### chikis

Then why does the statement: the force ratio of a machine is 5 and it velocity ratio is 8 means that the load moved is five times the effort applied and the distance moved by the effort is eight times the distance moved by the load at the same time interval.
Because that is where( my physics textbook) I got my explanation from. What is the difference between your explanation and mine?

9. Jan 1, 2014

### haruspex

I think what Simon wrote is what you intended, but what you actually wrote was a bit garbled:
If you delete the bits in italics it is right.

10. Jan 1, 2014

### chikis

Suppose the the distance from effort E to fulcrum F is a, and the distance from fulcrum F to load L is b. According to the principle of moment, we state
E*a = L*b .... eq 1

from eq 1
L/E = a/b
where a/b is the ratio of the two arms of the lever.

The velocity ratio is equal to 1.

It is less than 1.

It is bigger than I.
The situations where I have seen the first order of lever at work and their velocity ratios:
- a pair of scissors ( V.R greater than 1)

- crowbar (V.R greater than 1)

- claw hammer (V.R greater than 1)

and

- pliers (V.R greater than 1)

The situations where the velocity ratios are greater than 1 are more usual.

How?

Last edited: Jan 1, 2014
11. Jan 1, 2014

### chikis

How do you mean?

12. Jan 1, 2014

### Simon Bridge

... read the first statement, and read what you just wrote, and see if there are any similarities between the two statements.

i.e.
The first statement was:
velocity ratio is usually greater than 1 but could be less or equal to 1.

You wrote:
The situations where the velocity ratios are greater than 1 are more usual.
(you also found situations where the velocity ratio could be less than or equal to 1)

Spot the similarities?
That's what the first part of the question is asking you ... we say that VR>1 is more usual because there are more of them.
The second part of the question "what does it mean?" is asking you how come?
Why should there be more of them?

In order for us to help you, you have to attempt the problems yourself.

It is very difficult to answer the question more clearly without doing your homework for you.

13. Jan 1, 2014

### Simon Bridge

Well, you wrote:
"1 times greater than" is the same as "equal to".
So what you said was that velocity ration greater than 1 means the load moves the same distance as the effort.

14. Jan 1, 2014

### chikis

Exuse me! Let's get something correct here.
Does"1 times greater than", means "equal to" or "more than"?
When we say "1 times the load", that could mean equal to the load rather. How do you look at that?

15. Jan 2, 2014

### Simon Bridge

Well, it is actually ambiguous.

Strictly speaking "one times greater than" is actually 2x.

If $a$ is greater than $b$, then the amount $a$ is greater than $b$ by is $(a-b)$.
This would make $a$ $[(a-b)/b]$times greater than $b$.

If $a$ is $y$ times greater than $b$, then $a=b+by = (y+1)b$

However, it looked like a funny use for the context... what I should have said (sorry) was that the way you constructed the sentence would have lead many English readers in NZ to take your intended meaning for "equal to". If you want to say "greater than or equal to" just say that ... any other way and people will wonder why you didn't, suspect a mistake, and then try to guess what else you may mean. That's how conversational English works.

Last edited: Jan 2, 2014
16. Jan 2, 2014

### haruspex

You wrote:
"1 times greater than " is not a form of words that would normally be used in English. As Simon wrote, the most reasonable interpretation is "greater than, by an amount 1 times the original", that is, twice. Thus 4 is 1 times greater than 2, say. What you actually meant, I assume, is simply "greater than".
"The distance moved by effort ... could be less or equal to 1" leaves the reader asking "1 what?" - one metre? One km? I suggest you meant "... Could be less than or equal to the distance moved by the load".
Sorry, I don't mean to criticise your command of English, but it might help you express yourself more clearly.

17. Jan 6, 2014

### chikis

So do we say this is the most acceptable explanation for now?

Last edited: Jan 6, 2014
18. Jan 6, 2014

### Simon Bridge

That would be what the author hoped you'd get from that statement.
Can you do the rest of the questions now?

19. Jan 6, 2014

### chikis

But I believe that would have the same explanation with the first statement I gave in disguise.

20. Jan 6, 2014