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1. Question about the Triple Product

Homework Statement [/B] Homework Equations a⋅(b x a) = 0 The Attempt at a Solution Is my working below correct? In particular, can you apply the rCB to both the first part of the bracket (0.2j) and the second part (w x rCB) individually like that? My second question relates to: Is...
2. Question about the inertia matrix of a bar

Homework Statement Homework Equations ml2/12 The Attempt at a Solution So according to my databook: The axis x'-x' in the question corresponds to axis ZZ in the databook image above. That means in terms of radius, the moment of inertia about axis x'-x' is mr2/2. So in light of this...
3. Vector Multiplication

Homework Statement Homework Equations RAO = b(Sinβj+Cosβk) The Attempt at a Solution [/B] The box in red is ω. However I am unsure of where they got the box in blue from? As mentioned above, RAO = b(Sinβj+Cosβk) so not sure where they got the box in blue from? I know of the vector triple...
4. Determining the rank of a matrix

Homework Statement Homework Equations N/A The Attempt at a Solution I know that they got a rank of 2 since there are 2 linearly independent columns but what if we decided to count rows? In that case we would have 4 linearly independent rows which would suggest the rank is 4? How do we...
5. Inverse Laplace transform of 1/s

Homework Statement Homework Equations N/A The Attempt at a Solution The left hand side (red box) is the data sheet provided to us in the exam. The right hand side (blue box) is Wolfram Alpha. The data sheet says that the inverse Laplace transform of 1/s is equal to u(t) (i.e. the unit step)...
6. Transfer function of a second order system

Homework Statement Homework Equations The Attempt at a Solution I have done question 1.18 and I understand it completely. However, for question 2.5, I do not understand how they got G(s)? Why isn't the G(s) in question 2.5 the same as G(s) at the bottom of question 1.18? I asked my lecturer...
7. Response of a 2nd order system

Homework Statement Homework Equations N/A The Attempt at a Solution I understand how they got the answer and the calculations they did but I have 3 questions about this screenshot. 1) Why the box in red is the transfer function? Is there a way to tell this from the Y(s) = ... expression? 2)...
8. Inertia matrix of a homogeneous cylinder

Homework Statement [/B] Homework Equations N/A The Attempt at a Solution What I am confused about is where they got the (1/4)mR^2 + (1/12)ml^2 and (1/2)mR^2 from? I am guessing that these came from the integral of y'^2 + z'^2 and x'^2 +y'^2 but I don't understand how this happened exactly...
9. Dynamic Analysis of a 5 DoF robot

Homework Statement Homework Equations N/A The Attempt at a Solution I am confused as to where the ω3sin(θ)k term disappeared to? It is not included in the very last line? I asked my lecturer and he said it's ''constant'' but he kind of shrugged off the question. I understand everything...
10. Kinematics of a four bar linkage system

Homework Statement Homework Equations N/A The Attempt at a Solution I have 2 (basic) questions about this system: 1) The question says that ωAB = ωABk, I understand that bold indicates vectors whilst the plain text indicates a magnitude so ωAB (magnitude) multiplied by k (direction vector)...
11. Application of circularity of hybrid product

Homework Statement http://photouploads.com/images/8ba21e.png {moderator's not: Inserted image so it's visible without having to follow a link} 2. Homework Equations a·(b x c) = b·(c x a) The Attempt at a Solution How did they get from the (b) to (c)? In particular, I am referring to the...
12. Calculating the maximum shear stress in a shaft

Homework Statement Homework Equations Torque = Force x Distance Shear stress = Force/Area 3. The Attempt at a Solution I know how to do this question as I've seen the mark scheme. However, initially I did it wrong. What I did was as follows: Torque = Force x Distance therefore...
13. Question about where a thermodynamics formula comes from

Homework Statement How do we obtain: w = q - Δh Homework Equations The Attempt at a Solution If you neglect the second half of the SFEE and simplify we get: What is the next step from the last line in the above image to w = q - Δh I mean dw/dt = dq/dt - Δh so if we multiply by dt we...
14. Gas turbine TS cycle question

Homework Statement Homework Equations N/A The Attempt at a Solution I am confused what 5-5b and 5b-6 represent in the above TS diagram. I know that 1-2 is compression, 2-3 is cooling, 3-4 is compression and 4-5 is regeneration (since these are indicated in the block diagram) but as for 5-5b...
15. Difference between the various COP formulae

Homework Statement Homework Equations N/A The Attempt at a Solution My question is a simple one: how is the above equation for COPref different to the COPref equations I've already encountered (such as COPref = Qc/Win = (h1-h4)/(h2-h1). Is the above just a different form of these? Or is the...
16. Confused on a question about vapour refrigeration cycle

Homework Statement http://photouploads.com/images/ae1d2f.png Homework Equations N/A The Attempt at a Solution In the image linked above, I have copied and pasted 4 different slides. In the last slide, I am confused how they got the expression for T2 (the working out). I know that they did...
17. Ph diagram for a vapour compression cycle

Homework Statement Homework Equations N/A The Attempt at a Solution I am trying to understand the above ph diagram (for a vapour compression cycle), In some examples, point 1 is situated as above in the image (i.e. to the right of the saturated vapour line) and at other times it's situated...
18. Interpreting enthalpy on a ph diagram

Homework Statement 2. Homework Equations q = w+Δh The Attempt at a Solution I fail to understand how they obtained the 3 equations at the bottom. For the first one I understand that q = Δh since w = 0 but why is it h1-h4 rather than the other way around? Also, why does this h1-h4 equal...
19. Basic implicit differentiation question

So it has been quite a few years since I learnt about implicit differentiation so the content is a bit rusty in my mind. x=rcos(θ) How do you find dx/dt? I know the answer but I am trying to figure out why. I mean dx/dt can be written as (dx/dθ)*(dθ/dt) so why is the answer not just...
20. How to create a matrix with variables?

Hello, I am kind of new to Matlab so the questions I will ask probably sound a bit basic. Anyways, here goes: I want to create the matrix below which has both constants and variables. How can I do this? I know how to create a normal matrix (e.g. B = [1 0 2; 3 4 5; 0 2 3]) but I don't know how...
21. Beam deflection integration

Can someone explain why the slope dy/dx = 0 at x = L/2? L/2 is the midpoint and there would be a deflection here so surely the slope of the deflection curve shouldn't be 0? I'm finding it hard to visualise this. EDIT: I think I understand the above. The slope of the deflection curve at x = L/2...
22. Area of a ring element

The circumference of the shaded ring is 2πρ however I am struggling to understand how the area, dA, of the ring is equal to (2πρ)dρ? I mean the circumference varies depending on the value of ρ so surely we can't multiply by dρ to yield the entire area of the shaded ring? If we decided to go by...

Homework Statement Homework Equations M = 3(L – 1) – 2J L= number of links, J = number of joints The Attempt at a Solution As far as I can see, using the above L and J values for each linkage yields the correct M value. However, the L and J values lead me to think I'm missing something...
24. The ''apparent'' velocity in an axis fixed to the body

The above states that the velocity of point Q relative to P is represented by dr/dt. However, it also states that ∂r/∂t is the apparent velocity of Q in Pxyz. How does that make sense? I mean P is the origin of axes Pxyz so surely the velocity of point Q relative to P should be the same as the...
25. Question on streamlines around a Rankine Half Body

I have several questions that I am seeking clarification on. The first 2 are rather simple: 1) The formula for r describes the blue streamline (the stagnation streamline) right? (Just confirming) 2) I assume that the stagnation streamline is called so because it passes through the stagnation...
26. Simple differentiation mistake?

The working out states that v = (m/r)sin(theta) but surely this should be (-m/r)sin(theta) ? I mean there is a negative in front of the ∂Ψ/dx ? Also, if v=0 then 0 = (m/r)sin(theta), therefore sin(theta) = 0? And from this we know cos(theta) = 1 or -1 which would mean u = Uinfinity + (m/r) or...
27. Fluid circulation around a closed curve

I know that the circulation is defined as the counter clock wise integral around the closed curve of the flow velocity component along the curve but what is its meaning in real life? I mean what does circulation actually refer to in real life? Also could someone explain the above image? What is...
28. Integration of the Stream Function & Velocity Potential

How did they go from ∂Ψ/dθ = m to Ψ = mθ + f1(r) ? I mean I understand how they got mθ but can someone explain the f1(r) term? Similarly, how did they go from -∂Ψ/dr = 0 to Ψ = c1 + g1(θ) ? I understand how they got c1 but why the additional term? I can't provide further working out as...
29. Resolving in the vertical direction and along the direction of the normal force

Ok I know this is simple resolving but I'm a bit confused. If we resolve forces in the vertical y direction (as in the attached image), we obtain Rcos(theta)-W=0 and hence Rcos(theta) = W meaning R = W/cos(theta) [where theta = 18 degrees] However, if we resolve forces along the direction of...
30. Tangential force acting on a skier has been set to zero?

Can anyone explain why sum of Ft has been set to be = 0? The slope is smooth so no frictional forces act but by setting it to 0 they are neglecting the component of the weight along the slope? Having said that, this is a curved slope and not a straight one so does the component of the weight...