# Hardest Mechanics Question Ever - Can you solve?

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Hi, so I (and 10 others) have been stuck on a Mechanics Question shown below - part cii, in particular. I was wondering whether anyone on TSR could solve it. Thank you to everyone in advance - I have spent hours on it to no avail! :/

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#3

Assuming you've done the other parts correctly? What do you get for the basic forces equation with theta < alpha? You're really just bounding the terms in b)

Last edited by mqb2766; 1 month ago

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(Original post by

is this Y2 maths or uni?

**Timo werner**)is this Y2 maths or uni?

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(Original post by

Assuming you've done the other parts correctly? What do you get for the basic forces equation with theta < alpha? You're really just bounding the terms in b)

**mqb2766**)Assuming you've done the other parts correctly? What do you get for the basic forces equation with theta < alpha? You're really just bounding the terms in b)

What do you mean by 'bounding the terms in b)'?

I got:

Mbg - T = MbA (A = acceleration)

T - (mu*Magcos(theta) + Magsin(theta)) = MaA

?

EDIT: Left out mu accidentally.

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#6

(Original post by

The other parts were pretty easy.

What do you mean by 'bounding the terms in b)'?

I got:

Mbg - T = MbA (A = acceleration)

T - (mu*Magcos(theta) + Magsin(theta)) = MaA

?

EDIT: Left out mu accidentally.

**TheWilkerWay**)The other parts were pretty easy.

What do you mean by 'bounding the terms in b)'?

I got:

Mbg - T = MbA (A = acceleration)

T - (mu*Magcos(theta) + Magsin(theta)) = MaA

?

EDIT: Left out mu accidentally.

Last edited by mqb2766; 1 month ago

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(Original post by

So eliminate T and get A = ...

**mqb2766**)So eliminate T and get A = ...

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#8

(Original post by

I got A = (Mbg - (mu*Ma*g*cos(theta)) - (Ma*g*sin(theta)) / (Ma + Mb)

**TheWilkerWay**)I got A = (Mbg - (mu*Ma*g*cos(theta)) - (Ma*g*sin(theta)) / (Ma + Mb)

then factor out g and look at the desired expression, what bounding can you do?

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(Original post by

put the expression for mu and that's the first part done.

then factor out g and look at the desired expression, what bounding can you do?

**mqb2766**)put the expression for mu and that's the first part done.

then factor out g and look at the desired expression, what bounding can you do?

I have attached an image of what I have so far - am I correct?

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#10

For the 2nd term in the numerator

* Its negative

* Cos (theta) > cos(alpha)

You want to make the expression simple and a lower bound for the actual acceleration, so what could you replace it by?

Is the tan term positive?

* Its negative

* Cos (theta) > cos(alpha)

You want to make the expression simple and a lower bound for the actual acceleration, so what could you replace it by?

Is the tan term positive?

Last edited by mqb2766; 1 month ago

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(Original post by

For the 2nd term in the numerator

* Its negative

* Cos (theta) > cos(alpha)

You want to make the expression simple and a lower bound for the actual acceleration, so what could you replace it by?

Is the tan term positive?

**mqb2766**)For the 2nd term in the numerator

* Its negative

* Cos (theta) > cos(alpha)

You want to make the expression simple and a lower bound for the actual acceleration, so what could you replace it by?

Is the tan term positive?

I am still so confused, sorry.

The only thing that I can think of is that all the negative terms will always be less than zero?

Last edited by TheWilkerWay; 1 month ago

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#12

Tan term is pos as it's double negative?

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(Original post by

Cos is decreasing on 0..90 (first part of question. Sin is increasing.

Tan term is pos as it's double negative?

**mqb2766**)Cos is decreasing on 0..90 (first part of question. Sin is increasing.

Tan term is pos as it's double negative?

I am still not sure how to solve it via bounding. The only thing I can think of is somehow comparing the two terms with Mb with each other and to do the same for the two terms with Ma.

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#14

(Original post by

Yeah I was stupid on both. I forgot the double negative.

I am still not sure how to solve it via bounding. The only thing I can think of is somehow comparing the two terms with Mb with each other and to do the same for the two terms with Ma.

**TheWilkerWay**)Yeah I was stupid on both. I forgot the double negative.

I am still not sure how to solve it via bounding. The only thing I can think of is somehow comparing the two terms with Mb with each other and to do the same for the two terms with Ma.

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(Original post by

Take the tan(alpha) term. What is the minimum it can be?

**mqb2766**)Take the tan(alpha) term. What is the minimum it can be?

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#16

(Original post by

Well tan alpha would tend to zero if alpha and theta both tend to zero?

**TheWilkerWay**)Well tan alpha would tend to zero if alpha and theta both tend to zero?

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(Original post by

The game is to fix alpha (the answer includes it) but remove theta and masses from the expression by boundin g. Can you upload the expression you're working withnow?

**mqb2766**)The game is to fix alpha (the answer includes it) but remove theta and masses from the expression by boundin g. Can you upload the expression you're working withnow?

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#18

(Original post by

I might just be stupid as my expression is the same as before. I don't really understand how to eliminate parts of the expression by using limits or inequalities.

**TheWilkerWay**)I might just be stupid as my expression is the same as before. I don't really understand how to eliminate parts of the expression by using limits or inequalities.

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#19

You want to bound things. Have a go at getting (bounding) the numerator as something like

mA(1 - tan(alpha)) + mB(1 - tan(alpha))

The rest then follows. So group the two mA terms together and the two MB terms.

mA(1 - tan(alpha)) + mB(1 - tan(alpha))

The rest then follows. So group the two mA terms together and the two MB terms.

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#20

That is an old version of the question which I had corrected a few days after posting it.

The corrected version of the question is here: https://www.thestudentroom.co.uk/sho...&postcount=225

The game remains the same though, you bound variables and expressions in some way to obtain the lower bound for .

The corrected version of the question is here: https://www.thestudentroom.co.uk/sho...&postcount=225

The game remains the same though, you bound variables and expressions in some way to obtain the lower bound for .

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