lousymum:

pls help


kumar had 50% more bookmarks than leon.
max had 75% as many bookmarks as kumar.
kumar and leon gave max a number of bookmarks in the ratio 3:1.
as a result, maz had twice as many bookmakrs as before, and leon had 16 bookmarks more than kumar.
how many bookmarks did kumar give to max?

tia

hi lousymum, if i may say, for whatever reasons, i don't think you are lousy as a mum. the fact that you care for your son or daughter shows that you aren't as lousy as you think you are.

let k be kumar bookmarks

le the number of bookmarks leon gave be x

so

kumar = k
leon = (2/3)k
max = 0.75k

so after giving, leon had 16 more than kumar

(2/3 k - x) - (k - 3x) = 16 ---- equation 1

so after giving, max had twice as many as before

0.75k = 4x

solving,

k = (16/3)x

sub into equation 1

32/9 x - x - 16/3 x + 3x = 16

2/9x = 16
x =72
k= 384

so how many bookmarks did kumar give to max? = 3x = 216

well i went to check up what you meant by condition clause III


take a look at this website

http://www.edufind.com/english/grammar/if_conditional9.php

the type III that you are talking about is different. it is used with 'would' .

but in the original question of John not being able to go to school, it is type I. as such, 'unless' here always goes with the present tense.

if you want to use type III then it should be

john would have left the school already, unless he had not sought the principal's approval. this emphasizes that john has already left the school, if not for his pesky principal for e.g

but if you notice, this sentence's meaning is totally different from the original sentence of

john cannot leave the school early, unless he seeks the principal's approval.
this emphasizes whether john has sought or not the approval, i.e if he seeks he can leave early, and not if otherwise

ning_akn:

Hi Elkniwt,


May I know have your DD school teacher gives you an explanation on why the answer found in the answer is right?

I was pondering over this question and could not figure out why the answer was written in this manner.

Zack7 mentioned that Unless is always followed by present tense. I beg to differ. Under Conditional Clause Condition 3, we can write the sentence as :
John could not leave the school early unless he had sought the principal's approval.

I have yet to find a supporting to use \"cannot\"...unless...\"had sought\"..

Aks

hi, your example is not right.

for a sentence structure like yours ,using could not means it is a past action . your sentence structure is talking about John not leaving the school yesterday for example, that means it is cast in stone, it is the past, it has happened. you are not talking about the ability to leave school or not. unless signifies the ability to be able to do it or not in this type of sentences.

essentially, let me provide an analogy for the contrast

john could not run as he was ill yesterday. VS. john cannot run unless he wears his shoes. i.e, you don't use the past tense to signify an ability. you don't say john could not run unless he wore his shoes.

so the right sentence in your example should be

(yesterday) John could not leave the school early as he had not sought the principal's approval.

you don't use unless in this case. it makes your sentence not sound.

or if you want to use unless, then

John cannot leave the school early unless he seeks the principal's approval.

atutor2001:

Zack7:

.....But no, it does not depend on surface area.

The classical modeling of friction involves the assumption that friction force is independent of surface area.

Which means the empirical equation that you use has the above assumption.

In fact from the video, if you notice, when the prof released both of the blocks with different surface areas, both of them dropped at approximately the same angle even though the surface area differed by more than 2times. This tells you that surface area plays a very small part and the assumption of independence is good in this regime.

Of course there are always exceptions, then perhaps there r higher level of theories to describe. But for a primary school syllabus, if we were to follow the standard model of friction, then no, surface area is taken to be independent.

Maybe it is useful to understand why the empirical formula was developed. Empirical formulas are developed when the actual formula is too complex and no physicist is able to come up with the complete basis for actual relationship between frictional force, mass and type of surface yet. Such formula is only an \"approximation\". It is intended mainly as an aid for engineers to make a good-enough estimate on frictional force - something they need for their daily work. However, engineers do know that in reality, frictional force does depend on the size of the surface areas that are in contact. Therefore, probably the Primary school syllabus is geared to teach our young the real situation and thus teaching the students that frictional force does depend on the surface area that is in contact.

ps
This is a link to a table on static and kinetic coefficient
http://blog.mechguru.com/machine-design/typical-coefficient-of-friction-values-for-common-materials/

You can find at the end of the table, the following qualification :

\"....The friction coefficient value changes not only with material but also with the position and orientation of the participation materials.

Hope this can help clear your doubts on whether does frictional force depend on the surface area in contact.

let me clear your misunderstanding

friction force does depend on surface area. that is reality. but in physics, science, we assume independence for the normal day regime

if you are going to say friction force depends on surface area, then can you give an equation that says so? can you give the relationship between surface area vs friciton force?

if you can, then case closed. but i can tell you that is not possible at the current level of knowledge. that is why we can only obtain such 'constants' (coefficients) through experiment.

now why do we assume independence? the fact that surface area plays a very minuscule role in friction gives the green light to assuming independence in the normal day regime.

now let me ask you this question

F= ma

are you going to add in the quantum Schrodinger equation that is the analog to this motion equation?

the obvious answer is no. why? because we assume the quantum effects are minuscule in the classical, or normal day regime.

but hey, reality says it is dependent on quantum effects. this is what you are saying. sure you are right, but is it useful to know that quantum effects affect the classical regime? no. because we know its effects are small... just like in the case of friction, the surface area plays a very small non-linear role. that is why we have assumptions in theories because it works and it simplifies our lives.

and this is why we say classical regimes are mostly independent of quantum effects.

sharon1234:

1. \"(In or Within) half an hour, we have to be off, so don't delay,\" he told us.


2. \"You can think (about/over) what I have said, and when you have made up your mind, inform me of your decision,\" he said.

Thanks for your answers and explanations.

In is a better choice. Conveys a maximum timeframe. Within is also sound, but it conveys a general timeframe. So for not delaying, in would tie in better. But in my opinion both convey different meanings.


Over would be the right choice here. You think over what someone has said before making a decision. That is, to review his points. Thinking about is also acceptable but they convey slightly different meanings.

For example,

I gave some thought about what he had said. After thinking over them, I decided to ...

atutor2001:

Zack7:

take a look at this video by MIT


http://www.youtube.com/watch?v=Oagnr0cMLIU

it shows that sliding friction is independent of mass and surface area.

Just some clarifications.

The video demonstrated that friction coefficient is independent of mass and not that friction is independent of mass. Friction is dependent on mass because :

Frictional Force = friction Coefficient x Normal Force
= friction Coefficient x (mass x g)
= mass x [friction Coefficient x g]



The equation Friction Force = friction coeff x normal force, is an empirical formula. It is not derived from any theory. It is based on the assumption that the \"friction coefficient\" is independent of the \"pressure\" at the surfaces in contact with each other. In reality, the \"friction coefficient\" is not independent of the \"pressure\". When the \"pressure\" is small, the coefficient is usually greater than when the \"pressure\" is smaller.

Therefore, if 2 objects of the same mass and material are resting on the same surface, the object with a bigger surface area in contact will be pressing down with a smaller pressure and the frictional force will be greater. Try this out. Place an aluminium foil flat on a plank. Take another aluminium foil of exactly the same size and fold it as many times as possible to form a small cuboid and place it on the same plank. When the plank is tilted, the first one to move will definitely be the foil that has been folded.

Yes friction force depends on mass.

But no, it does not depend on surface area.

The classical modeling of friction involves the assumption that friction force is independent of surface area.

Which means the empirical equation that you use has the above assumption.

In fact from the video, if you notice, when the prof released both of the blocks with different surface areas, both of them dropped at approximately the same angle even though the surface area differed by more than 2times. This tells you that surface area plays a very small part and the assumption of independence is good in this regime.

Of course there are always exceptions, then perhaps there r higher level of theories to describe. But for a primary school syllabus, if we were to follow the standard model of friction, then no, surface area is taken to be independent.

elkniwt:

tianzhu:

Hi

Good Morning.

I’d go for either of these sentences.

John cannot leave the school early unless he seeks the principal's approval.

John cannot leave the school early unless he has sought the principal’s approval.

Please seek confirmation from your teachers.

Best wishes

Hi Tianzhu,

Your two suggestions sound more right than the answer given in the answer key which is :

John cannot leave the school early unless he had sought the principal’s approval.

Thanks. Will ask dd to check with her teacher.

Regards.

the answer key is wrong

unless is always followed by the present tense, i.e seeks.

but in my opinion, the right way should be

john cannot leave the school UNLESS he seeks the principal's approval
this conveys the need to seek the principal and not the timing

or

john cannot leave the school UNTIL he has sought the principal's approval.
Until conveys the timing along with the 'has/hasn't'

Tresille:

Hi, need your assistance.


John has a total of 20 apples and pears. If he exchanges every pear for 2 apples, she will have 28 apples. How many apples and pears does he have? Can we use model drawing to solve this qn?

let x be pears
let y be apples

x + y = 20
2x + y = 28

20-x = 28 -2x
x = 8 pears
y = 12 apples



it is possible to use models to solve this question
but you have to do it to scale. or have a relative scale
like 1cm to 1 unit. but it is not an efficient way to do this sort of questions.

in fact , i just need to use logic to be able to solve this question. logic is the best approach for simple cases like these.
if 1 pear becomes 2 apples, then that would mean every pear i change to apple will yield me a net of +1

so if i have 28 as a new total, where did the 8 extra came from? it would mean i have a net of +8. then, it would mean i have changed 8 pears.

if i had 38 as a new total, it would mean 38-20 = 18, which means i have changed 18 pears and so on...

take a look at this video by MIT


http://www.youtube.com/watch?v=Oagnr0cMLIU

it shows that sliding friction is independent of mass and surface area.

if we were assuming the simple model of classical friction, then friction does not depend on the contact surface area for 2 materials sliding over each other.


F_friction = u F_normal force

Pressure =Force /Area
PA = F

for a constant Force, i.e the weight of the object, increasing the area means a decrease in pressure.

thus, F does not change, and hence the normal force does not change.

if the normal force does not change, and ‘u’ is the coefficient of friction which is determined empirically, then F_friction does not depend on the area.


however, this is merely a model, simplified per say. in reality, surface areas do play a part in more complicated models. for example, surface areas play a significant role in the nano-scale regions.

but for the sake of a primary school physics question, i believe that friction being independent of surface area would suffice.