could someone please let me know if this is correct as I have been told that I have done this wrong though I didn't inform the person of how I did it. this is using division of conjugate complex numbers.
I have followed the method my tutor showed me and I think this is correct.
any help or a push in the write direction would be great!!!
I have a circuit with values
v1 = 20 + j0
r1 = 15 +j0
l1 = 0 +j10
c1 = 0 - j5
I have to use superposition and division of complex conjugate numbers.
the resistor, inductor and voltage source are in series. the capacitor is in parallel with the voltage source
I added the resistor and inductor, (15 + jo) + (0 + j10) = 15 + j10, find the conjugate of this 15 - j10
so then product over sum for the components that are in parallel. the inductor/resistor || capacitor
(0 - j5)*(15 - j10)
(15 + j10)*(15 - j10)
for the numerator I got
0 x 15 = 0
0 x -j10 = 0
-j5 x 15 = -j75
-j5 x -j10 = (j^2)50 = -50 minus 50 because of (j^2) = -1
so the result is -50 -j75, which im not sure about
then the second line
15 x 15 = 225
15 x -j10 =-j150
j10 x 15 = j150
j10 x -j10 = -(j^2)100, (j^2) = -1 x -100 = 100
225 -j150 +j150 +100, the middle terms cancel leaving 225 + 100 = 325
so I have, -50 -j75/325
then I divide each of the numerator by the denominator so,
-50/325 = -0.153846
-75/325 = -0.230769
I think I can use this to find polar notation r and theta(the zero with a line through)
im not sure if any of this is right though, any help would be great thanks
I have these two questions
c) Plot a graph of the kinetic energy of the mass against time. Explain your calculations and state formulae used.
d) Plot a graph of the kinetic energy of the mass against distance. Explain your calculations and state formulae used.
I have used this formula for the first one,
Ek = ½ mv2 = ½ ma2t2
Ek is proportional to t2.
this for the second
Ek = ½ mv2 , but we can substitute, giving
Ek = mgy
in not too sure how to show the graphs, but is the above formula along the right lines?
also I have to explain the use of the formula. I think this is just explain why I used it and any transposing required. if anyone knows a better answer for this one please give some advice.
taken from here, http://colourpoint.co.uk/sample_files/physics_as.pdf
this is the first part of the question,
A horizontal force of 80 N acts on a mass of 6 kg resting on a horizontal surface. The mass is initially at rest and covers a distance of 5 m in 0.92 s under the action of the force. Assuming there are no energy losses due to air resistance and therefore that the acceleration is constant:
a) Calculate the total energy expended in the acceleration, I got 11.81 acceleration
b) Calculate the coefficient of kinetic friction between the mass and the surface. Suggest materials from which the block and table might be made in order to give such results. I got 0.155
I have a question
the lengths of pins produced by a machine follow a normal distribution with mean 2.54cm and standard deviation 0.04cm. a pin is rejected if the length is less than 2.44cm or more than 2.60cm
A/ find the percentage of pins that are accepted.
B/ if it is decided that 2.5% of the pins are to be rejected because they are too long and 2.5% because they are too short, determine the new range of acceptable lengths.
for the first part I have the formula, z = x-MU / sigma, I rearranged this
sigma is 0.04cm
MU is 2.54cm
so I used this z * sigma + MU = x, z * 2.58 = ? so here I thought I would take a value from a table and divide by 2.58 until I got an accurate z value. then use that z for the rest.
if anyone could confirm this method as im not to sure? the rest I think I can get.
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
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
s = integration sign (top number, bottom number)
i have this :
s (1, 0) (2xe^3x dx)
u = 2x
du/dx = x/2
dv/dx = e^3x
v = s 1/3 ^e3x
i really have no clue what im doing.
if someone could tell me what i do any of this it would really help
i have 2x so to integrate it, i increase the power by 1 and divide by this figure. so 2x = 2x^1, add 1 = 2x^2/2 (correct?)
is 2xe^3x treated as one number, like 2*xe^3x. one answer the lecturer wrote was 2e^3x/3, = 2/3 s e^3x dx
i am looking on the internet at the moment for any answers and coming up with nothing.
does anyone know any good sites that explain with good, easy to follow examples.
NEVERMIND, I GOT THE ANSWER THANKS ANYWAY ALL THE BEST!!!:D:D
I have this question
a rectangular sheet of metal measuring 120mm by 80mm has equal squares of size x cut from each of the corners. the remaining flaps are then folded upwards to form an open tray. draw a neat sketch of the net and prove that the volume of the tray is given by:
v = 4x^3 - 400x^2 + 9600x
a) find the value of x such that the volume is a maximum, making sure you show how you prove your value is a maximum not a minimum. work out the maximum volume of the tray.
b) verify your result for question 6a using a second method. present your alternative method in writing, ensuring you compare both ease of use and accuracy of results of the two methods.
the second bit is whats getting me. I can use the results of length and width which are 88.612mm and 48.612mm respectively. I cant include height and have to find volume.
im guessing its something to do with the cut outs.
I have maximum volume of box when x = 15.594
length = 120 -2 * 15.694 = 88.612
width = 80 -2 * 15.694 = 48.612
so I have the starting width and length, the finishing width and length and two lots of something to be taken away.
I found something close, I have 15.69499126 = x, this came from the general quadratic equation
I did this,
120 - 2 * 15.69499126 = 88.61001748
88.61001748 + 2 = 90.61001748
120 - 90.61001748 = 29.38998252
divide this by 2 to get = 14.69499126
this last number is supposed to be x but it is a whole 1 out. 14 instead of 15. I think this is correct but there is a 1 missing somewhere.
I think if I put all this together I should be able to get the correct answer giving me a final volume and height.
unless I have done something really daft here and got a knot in my brain.....again!:D
NEVERMIND, I GOT THE ANSWER THANKS ANYWAY ALL THE BEST!!!
anyway, if anyone could point me in the right direction. I would really appreciate it
I have a question im stuck on.
a beam must withstand a bending moment of 285kNm. if the maximum stress must not exceed 200Mpa, determine the elastic modulus z and select an appropriate I section from the given table. (the table is in the book that I have)
im not sure what the math formula im supposed to use.
the elastic modulus is z = I / y
I don't know what I is or Y
I have M, the maximum bending moment Nm
and, sigma which is stress in pa
so I thought M/sigma = z. 285*10^3 * 200 = 1425
im not sure if the M in Mpa is mega(1000 000) or milli or what. when I use mega the answer is really small.
a push in the right direction please
how do you do the third with that, also I checked an online derivative calculator and it says that is wrong?
it gave the same answer with the power of 2, 48(2x-3)^2
I looked at the steps on this calculator and didn't understand them.
Im not sure how to go onto the third derivative.
would I use (2x-3) as U or 48(2x-3) as U?
I have to do second and third order derivatives
for the first one I got
for the second I got
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
then I got lost
here I got stuck and not sure where I went wrong, any help
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.