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Please give the formula you use here, rather than the final number. | 1 |
Give latex2 and latex3 in terms of latex8 and latex9 . | 1 |
(This calculation will allow us to find how fast the door swings open when the latch is released). | 0 |
Hence, show that this gives the correct time dilation equation. | 1 |
Assume that, in general, there are always people walking at a constant speed on the travelator; and walking at a constant speed beyond the end of the travelator, i.e on the floor; and standing stationary next to the travelator. | 0 |
It has an latex6 of latex20 at this wavelength. | 0 |
When the latex1 of a buffer equals the latex20 of the buffering agent, the buffer is most resistant to changes in latex1 and latex0 takes its maximum value. | 1 |
Find where latex5 Sketch latex1 | 1 |
What is the current that the source has to provide in the below circuit? | 1 |
Include all three world lines, as well as the paths the light pulses travel to Rick and Lucy. | 1 |
The gun from *Question 5* now fires its shells up a hill that rises at an angle latex0 radians to the horizontal. | 0 |
What effect on the required file size has: I. | 1 |
A liquid bath assumed to be Newtonian with constant and uniform density latex4 separates both walls. | 0 |
**(L3)** A father pulls a child on a sled with a rope that has a constant tension of latex0 and makes an angle of latex1 to the horizontal. | 0 |
Find the pressure field in terms of latex4 and latex3 . | 1 |
Again, find the relative velocity between latex1 and latex2 where latex2 is the frame in which the two events are either simultaneous or at the same position (give your answer in terms of latex5 ). | 1 |
Comment on how you expect the analytical approximation to differ from the solution to the governing equations of this problem. | 1 |
What is the minimum plate thickness, latex6 , required to ensure plane strain conditions at the crack tip? | 1 |
This problem investigates wall-temperature effects on the friction force. | 0 |
latex3 , latex4 , latex5 , latex6 . | 0 |
The figure shows a photo taken in an airport showing Person (1) walking at a constant speed on the travelator, and Person (2) standing stationary on the floor. | 0 |
Explain briefly what each group means. | 1 |
Assuming the lamina to be of uniform density, find the position of the centre of mass of the part that lies in the first quadrant ( latex1 . | 1 |
Find the minimum length of the rope, latex8 , if the tension in it is not to exceed latex9 . | 1 |
For the following figures write down (**for the surfaces marked**) * the normal direction * the tangential component of the fluid velocity * the normal derivative of the tangential velocity Figure 1: Figure 2: Figure 3: | 0 |
Look up the density of the materials used online. | 1 |
Leave your answer in fractional form, or as a number to 1 decimal place. | 1 |
Using them, we find: latex2 (by the Divergence Theorem) latex3 (by Stokes' Theorem) Since latex4 , latex5 is conservative, or there is a parent function latex6 such that: latex7 . | 0 |
A Zener diode voltage regulator is required to supply a constant latex0 from a maximum voltage supply of latex1 DC. | 0 |
Did accounting for changes in atmospheric pressure make much difference? | 1 |
A volume of gas in a sealed tank is heated externally. | 0 |
Assume that latex19 m latex20 s latex21 . | 0 |
The bob of mass latex2 at the other end of the string rotates around the vertical axis at constant angular velocity latex3 . | 0 |
This is the diffraction pattern of a single slit. | 0 |
(Based on P4.35, White) Neglecting gravity, the continuity and Navier--Stokes equations for incompressible flow with velocity latex0 in cylindrical polar coordinates latex1 are latex2 latex3 latex4 latex5 respectively. | 0 |
A small absorbance value means the solution does not absorb that wavelength of light much; a high value means it absorbs that wavelength strongly. | 0 |
What is the greatest speed, latex6 , with which a train of mass latex7 can hit the buffer stop if, at the end of its latex1 travel it is not to exceed latex9 ? | 1 |
Find the components of the electric field at point latex5 By considering the components of latex6 due to the elements at ±y, are the forces from +y and -y equal and opposite? | 1 |
( latex2 ) latex0 has two electrons to pass on, and latex2 can only take up one. | 0 |
The angular speed, latex10 , of the rotating assembly depends on the other quantities as follows, latex11 What is the minimum number of dimensionless groups necessary to describe the function latex12 ? | 1 |
Calculate the resistor nominal value and upper and lower limits for each of the following parameters: The resistor parameters are given in the table below: [table] | 1 |
(Assume latex2 at latex3 , and consider air a perfect gas with latex4 =1.4 and latex5 =287 J/(kg K)). | 0 |
Obtain an expression for the density ratio latex5 at the throat. | 1 |
What types of controls should we prioritise when managing risk? | 1 |
In this question you will derive the flow profile of an incompressible Newtonian fluid that is flowing with volume flux latex0 in a channel of width latex1 created by the gap between two plates, each of length latex2 and width latex3 , at latex4 and latex5 . | 1 |
Pinion latex8 meshes with gearwheel latex12 which has a pitch circle radius latex13 and a mass moment of inertia latex14 about its axis of rotation. | 0 |
Why does the inverse latex14 exist? | 1 |
His 'friend' Banxy has told him that he will surely need an infinite amount of paint - and he senses that this might be expensive... His partner Andromeda observes that the volume inside the funnel is finite so all he has to do is to pour in the correct volume of paint and pour away any surplus. | 0 |
This form for the drag force is appropriate for fluid flow around the object which is laminar (don't worry, you don't need to know the details of the physics of this for this course). | 0 |
Which intensity pattern will be recorded in the limit latex14 ? | 1 |
At latex8 , it is at latex9 . | 0 |
The rate at which latex3 decays, latex14 , is proportional to the number of radioactive latex3 nuclei, latex16 , that are present in the sample. | 0 |
Same as (b) but the foundation has a vertical stiffness of latex8 | 0 |
Give the corresponding boundary conditions. | 1 |
A stagnation tube is placed in the jet as shown, and the water reaches a height of 80 cm. | 0 |
Write down the expression for the Fourier transform, latex7 , of the initial temperature distribution. | 1 |
Find the trigonometric Fourier series for the functions below, defined on the interval latex0 . | 1 |
As the mRNA is degraded, the amount of labelled mRNA decreases exponentially with time (we will assume no radioactive uracil is recycled): latex1 latex2 * latex3 Mass of labelled mRNA [embedded] * latex4 Mass of labelled mRNA at beginning of experiment [embedded] * latex5 Half-life of the mRNA (time it takes for half the mRNA to degrade) [embedded] * latex6 Decay constant Rearrange the left-hand equation for latex6 Calculate the half-lives of histone H3 and fructose-*bis*-phosphatase mRNAs from the data below. | 1 |
Explain in one sentence what is meant by the exergy of a fluid in a given state. | 1 |
You should ***not*** have got the correct Lorentz contraction formula. | 0 |
With these values, sketch the time evolution of concentration at the coastline directly in the path of contaminant. | 1 |
For latex0 where latex1 is the distance from the origin: Show that latex2 . | 1 |
To understand what is going on, look at the transformation of the line latex9 constant to the latex10 plane, for constant latex11 , and this should explain what happens to the line latex12 . | 0 |
Hence, the total period is latex5 Inertial frame M observes the entire apparatus moving to the right with speed latex6 in the latex1 direction. | 0 |
It would seem that from the recorded pattern of intensities of the scattered light, we would be able to find the shape of the slits through an inverse Fourier transform. | 0 |
If a weak acid, latex0 , is dissolved in water to an total initial molarity of latex1 , a very small amount of the acid will dissociate into protons, latex2 , at a concentration we will call latex3 . | 0 |
latex4 latex5 latex6 latex7 | 0 |
Two masses, latex0 kg and latex1 kg, are moving in the latex2 - latex3 plane. | 0 |
Glacier flow (effective viscosity of ice is latex4 Pa s and speed of glacier is around 50 m/year). | 0 |
Write the order of magnitude of each term and show that the approximate equation near the wall is latex23 To complete this equation you will need a relation latex24 You can assume that latex25 , because higher values do not maintain the second order term, and lower values lead to results that can't inflect so can't match the outer solution. | 1 |
Making use of the equation for degree of reaction and of the relationship between specific work and flow angles (via the Euler turbomachine equation), calculate the required flow angles relative to the blades, assuming that an identical stage follows this one. | 1 |
Same as (b) but the roller is raised by latex6 . | 0 |
For which latex11 does it actually start to look a bit like the imaginary part of latex12 ? | 1 |
Sketch one example of each type. | 1 |
Show that the solution indeed satisfies this boundary condition. | 1 |
Entropy change, in general, is defined by the two relationships latex0 and latex1 Does the entropy of a system remain constant during reversible and irreversible adiabatic processes? | 1 |
A mixture of latex0 and latex1 in a sealed, rigid container is at a pressure of latex2 bar and a temperature of latex3 . | 0 |
For relatively large particles in large water depths, sediment suspension occurs in a small layer close to the bed. | 0 |
Which condition would feel colder? | 1 |
Fill in the blanks for the diagram below and identify which is most suitable for for a solid and which is more suitable for a fluid. | 1 |
Gear wheels latex0 and latex1 are mounted on a right-angled carrier latex2 . | 0 |
Note: error is defined as latex0 | 0 |
*(Take rotation in the anti-clockwise direction to be positive)* | 0 |
*Sketch of trapezoidal irrigation channel. | 0 |
One "trick,'' e.g , to evaluate latex1 is to write latex2 where latex3 differentiates latex4 but gives zero when operating on latex5 - i.e , it treats latex5 as constant - and vice versa for latex7 . | 0 |
What is the most general form of latex4 for which continuity is satisfied and latex5 at latex6 ? | 1 |
A blow-down wind tunnel is designed for a Mach number of latex0 . | 0 |
In service, there is an end load which causes the shaft to extend latex4 in length and to contract latex5 in diameter. | 0 |
Consider the function latex0 on the interval latex1 . | 0 |
The Imperial Racing Green car below is initially horizontal, has a mass of latex0 and its centre of mass is latex1 above and latex2 forward of the point where the rear wheel touches the ground. | 0 |
The Lineweaver-Burk equation is the reciprocal transformation of the Michaelis-Menten equation, which allows us to linearise this equation and easily estimate values for latex3 and latex5 . | 0 |
Pick the two most suitable Reynolds' Numbers for C. Keeping the Reynolds' numbers the same but reversing the flow direction, state which of the streamlines of the three resulting flows could be found by reversing the arrows on the streamlines shown above. | 1 |
For the functions in part (a), identify latex4 . | 1 |
(i) Evaluate the specific work input for the feed water pump using the result from part (a). | 1 |
Steady flow in 3 dimensions, negligible diffusion. | 0 |
Hence estimate the upstream pressure latex4 needed to produce this jet. | 0 |
See below for an animation of how the gear wheels move. | 0 |
Use this rotation matrix to calculate the positions of all of the vertices of the parallelogram, latex6 after application of this rotation. | 1 |
*Note: this question uses notation latex2 and latex3 , as defined below. | 0 |
The line from the central source to P has length latex6 and makes an angle latex7 to the horizontal. | 0 |
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