We resolve forces in Classical Mechanics to simplify our problems. For instance, let us say we have a block on a table. We would pick our x-axis to be along the table, and our y-axis to be perpendicular to the table (so at right angles). Then, if the block is pulled by a piece of string at some angle to the table, say 45 degrees, the block will have part of the tension (T) in the x-direction (Tcos45) and part of the tension in the y direction(Tsin45). So what we have done is resolved the force into two forces; one acting along the table and one acting perpendicular to the table. These two forces act independently of each other, as the motion of the block in the x-direction is independent of the motion of the block in the y direction, so our problem has been simplified. 



As with all mechanics problems, this is much easier seen with a diagram!
Hope this helped. 

Physics

I'm learning physics at a GCSE grade level, and I wanted to ask, what exactly is resolving forces and why do we use it? (New spec 9-1)

Unsure of the question, but assuming you're asking what the terms of the sequence are, and assuming we take n to be running through the natural numbers, then the sequence generated is {5,8,11,14,17,...}.


Maths

3n+2 sequence

A constant is held constant (as the name suggests), where as a variable is a number that is aloud to change. For instance, if we let y=5+x, here, 5 is constant because it does not change, where as x is aloud to vary. For instance, we could consider x over a certain range, say x=1, x=2, x=3 and get a different y for respective x. Hope this helps.

What is the difference between a variable and a constant?

This is easiest explained with an diagrams, but as I cannot, I’ll try make this as clear as possible.

We have some triangle, with angles A, B and C and side lengths a, b and c, where the length a is OPPOSITE the angle A, b is OPPOSITE B etc. Now, the sine rule states a/sin(A) = b/sin(B) = c/sin(C).

What is this actually telling us? Well, we say we know two lengths a and b and the angle A, then we can write B=arcsin(bsin(A)/a), thus we have found the angle B. 

Basically, if we know two lengths and one angle, then we can work out an angle.

If we know two angles and one length, we can find another length.

Hope this helps. 

How do you use the sine rule?

Cuts the x-axis at x ={-3, 5+sqrt(19), 5-sqrt(19)}

Turning points occur at x={-4/3, 6} 
Found by setting f’(x)=0 (taking the first derivative and setting =0 gives turning points)

F (x)=x^3-7x^2-24x+18 Sketch the graph of the gradient function y=f'(x). Use algebraic methods to determine any points where the graph cuts the coordinate axes and mark these on the graph. Use calculus,  find the coordinates of any turning points on the graph.

I don't know how to answer this question. Please help!

John Parry

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