Math Is Fun Forum

hello

I have a question

a hollow steel shaft with a diameter ratio of 0.75 and a length of 4m is required to transmit 1Mw at 120rpm. the maximum shear stress is not to exceed 7 Mpa and the overall angle of twist is not to exceed 1.75degree. assume the modulus of rigidity for steel is 80Gpa.

a) determine the necessary outside diameter of the shaft so that both of the above limitations are satisfied

b) determine the actual maximum shear stress and the actual angle of twist.

first I tried finding the torque(T) using P(power) = Tw(w being 2piN( N is rotational speed in rps)) I think w is omega

I rearranged the formula to get T = P/w

so, 1000,000 / 2pi 2                   the second 2 is from 120(rpm) / 60(rps) to get seconds

= 79577.47

then, as I have degrees and would require radians I converted that

1.75 * pi / 180 = 0.0305 radians

so using a formula to find J ( the symbol for second moment of area)

the formula is J = T * L / G (theta sign), so

79577.47 * 4 / 80x10^9 * 0.0305 = 130454.87x10^-9 = J

which im not sure about. I have to find the outside diameter using D^4-d^4,  D is outside diameter and d is inside diameter.

J = pi * (D^4 - d^4) / 32, this is the formula using diameter to find J, I have J and so would try to rearrange

I tried this,

D^4 - d^4 = pi * J / 32

any help would be great, I only know that diameter ratio is 0.75, the inside diameter is three quarters

If I did, d^4 = pi * J / 32, then d^4 answer would be three quarters of the D^4 answer. so if I took that and cut it into thirds that is what I would add to d^4 to get D^4???

any help would be great

thanks
simon
:):)

hello

I have to find height of a box, I have length and width but I don't know height. unfortunately im not gifted with these things. my brain stops ticking. anyone got any tips or hints
thanks
simon

I have to do second and third order derivatives

(2x-3)^4

for the first one I got

8(2x-3)^3

for the second I got

48(2x-3)

the way I was shown is this,

2x-3=U      du/dx = 2

y= u^4     dy/du = 4u^3
dy/du * du/dx = 4u^3 * 2 = 8u^3

since u = 2x-3

8(2x-3)^3

then I got lost
here I got stuck and not sure where I went wrong, any help

thanks
simon

hello
I have this question and given my answer for second and third derivatives. not sure if its right though

hello
I have a question im stuck with

y = (7x-4) 3/2         (3/2 is supposed to be 3 over 2, I don't know how to do that on here)

I got this,

u = 7x-4

du/dx = 7

y = u 3/2

dy/du = 3/2u -3/2  (the -3/2 is power, supposed to be above right of u)

du/dx * dy/du = 3/2u-3/2 * 7 = 21/2 u -3/2

since u = 7x-4,      21/2 (7x-4) -3/2

im thinking most of it is correct except for the -3/2, the fraction part has me concerned.

thanks

simon:)

hello

I have a problem that involves a scalene triangle. I have one angle and two sides.

I know that all the angles should add to 180. so I thought with two angles I could use: 180-50-14.79= 115.21 which is the wrong answer

I have these values

A 64.783?
a 35.44

B 14.79
b 10

C 50
c 30

I know that the angle and side I have to find are correct (B and a)
though I tried the 180 thing, I got this wrong and my lecturer told me why. unfortunately I didn't write it down and cant remember what I did.

does anyone know about the 180 thing?
I have to show how I got the answers and I think the 180 thing is what I have to use but im doing it wrong.

thanks
simon:)