C3 Iteration formula and Logarithms/Exponentials help

creativebuzz

2

I managed to do part (a) but I'm stuck on how to do the rest...

(b): Stationary point means that dy/dx = 0. I presume you'll have found it in part (a).
Afterwards, you should make it so that you get the equation above. I'd say the natural log function is a big giveaway.

Reply 2

Ocean3

1

Anyone help me with putting x=cos2t and y=cosect into cartesian form? Thanks

Reply 3

creativebuzz

OP

2

Original post by simonli2575

(b): Stationary point means that dy/dx = 0. I presume you'll have found it in part (a).
Afterwards, you should make it so that you get the equation above. I'd say the natural log function is a big giveaway.

I managed to get this far..

But where have I gone wrong? :/

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Reply 4

tiny hobbit

15

Original post by creativebuzz

I managed to get this far..

But where have I gone wrong? :/

You'll find it easier if you get e^(1-4x) on its own before you take logs.

Reply 5

creativebuzz

OP

2

Original post by tiny hobbit

You'll find it easier if you get e^(1-4x) on its own before you take logs.

Ah okay, I'll give it another shot.

By the way, how can I tell (in this case) whether the force is acting clockwise or anticlockwise?

I looked online and it mentioned that a force is acting clockwise if it's on the downward force then it's moving clockwise. The answer sheet said that 7N and 4N are acting anticlockwise, but how can that be true if 7N is acting downwards and 4N is acting upwards?

Original post by creativebuzz

Ah okay, I'll give it another shot.

By the way, how can I tell (in this case) whether the force is acting clockwise or anticlockwise?

I looked online and it mentioned that a force is acting clockwise if it's on the downward force then it's moving clockwise. The answer sheet said that 7N and 4N are acting anticlockwise, but how can that be true if 7N is acting downwards and 4N is acting upwards?

That depends on where the pivot point is.

Put your pencil firmly on the point P so that the page will rotate about P (easier on a piece of paper than a book!). Push your finger along the line of the force in the direction of its arrow and the paper will start to rotate. That will give you your answer.

Reply 7

creativebuzz

OP

2

Original post by tiny hobbit

That depends on where the pivot point is.

Put your pencil firmly on the point P so that the page will rotate about P (easier on a piece of paper than a book!). Push your finger along the line of the force in the direction of its arrow and the paper will start to rotate. That will give you your answer.

But the force is acting upwards, so are you saying to push the piece of paper upwards or?

Reply 8

tiny hobbit

15

Original post by Ocean3

Anyone help me with putting x=cos2t and y=cosect into cartesian form? Thanks

Try to find an identity connecting cos 2t and cosec t and substitute into it.

cosec t = 1/sin t so y = 1/sin t and sin t = 1/y

Can you write cos 2t in terms of sin t? If so you can substitute 1/y wherever there is a sin t to get rid of t.

Reply 9

tiny hobbit

15

Original post by creativebuzz

But the force is acting upwards, so are you saying to push the piece of paper upwards or?

For the 4 N force, yes. The paper will start to rotate anticlockwise.

For the 3 N force, push upwards and the paper will start to rotate clockwise.

For the 7 N force, push downwards and the paper will rotate anticlockwise.

This is so much easier to demonstrate than it is to describe!

(edited 9 years ago)

Reply 10

davros

16

Original post by creativebuzz

Ah okay, I'll give it another shot.

By the way, how can I tell (in this case) whether the force is acting clockwise or anticlockwise?

I looked online and it mentioned that a force is acting clockwise if it's on the downward force then it's moving clockwise. The answer sheet said that 7N and 4N are acting anticlockwise, but how can that be true if 7N is acting downwards and 4N is acting upwards?

You should be wary of trying to apply general rules like downward = clockwise - this won't be true in every situation!

In this case, if your arrangement was pivoted at P you can see that the 7N force is trying to pull downwards causing the rod (or whatever it is) to rotate anticlockwise. Similarly, the 4N force is pulling upwards, tending to cause an anticlockwise rotation about P.

Reply 11

Dalek1099

21

Original post by creativebuzz

Ah okay, I'll give it another shot.

By the way, how can I tell (in this case) whether the force is acting clockwise or anticlockwise?

I looked online and it mentioned that a force is acting clockwise if it's on the downward force then it's moving clockwise. The answer sheet said that 7N and 4N are acting anticlockwise, but how can that be true if 7N is acting downwards and 4N is acting upwards?

You need to imagine that the rod is the diameter of the circle the arrow of the force indicates which way the radius it is on will move due to that force only and that should tell you whether it is clockwise or anticlockwise.

Reply 12

Hasufel

16

Original post by Ocean3

Anyone help me with putting x=cos2t and y=cosect into cartesian form? Thanks

Use the identity (it`s in a different form):

\cos(2t) \equiv 1-2 \sin^{2}(t)

and the fact that

\displaystyle \sin^{2}(t) = \frac{1}{y}

(what`s the t range? - it may be important)

(edited 9 years ago)

Reply 13

simonli2575

5

Original post by Hasufel

and the fact that

\displaystyle \sin^{2}(t) = \frac{1}{y}

Wait, y=cosec(t), so sin(t)=1/y.

Reply 14

Hasufel

16

Original post by simonli2575

Wait, y=cosec(t), so sin(t)=1/y.

yup

Reply 15

creativebuzz

OP

2

Original post by tiny hobbit

You'll find it easier if you get e^(1-4x) on its own before you take logs.

Ah I've got it now, thanks! By the way (just because I really want to understand this completely) but what made you think to get e^(1-4x)/why is it easier to do that?

Reply 16

tiny hobbit

15

Original post by creativebuzz

Ah I've got it now, thanks! By the way (just because I really want to understand this completely) but what made you think to get e^(1-4x)/why is it easier to do that?

Getting the e term on its own before taking logs means that you don't have to be so imaginative in dealing with the logs.

Reply 17

creativebuzz

OP

2

Original post by tiny hobbit

Getting the e term on its own before taking logs means that you don't have to be so imaginative in dealing with the logs.

I had a go at that same question again to test that I really understood it and I got stuck again! I looked at the mark scheme and I don't understand what they did here (the part I put a box around):