0 stringlengths 10 969 | label int64 0 1 |
|---|---|
The potential energy of a system of discrete point charges is given by latex0 where the sum is taken over all distinct pairs of charges. | 0 |
Calculate the maximum concentration latex6 at latex15 , at the coastline directly in the path of the contaminant. | 1 |
Calculate the (scalar) area of the parallelogram formed by latex2 and latex3 . | 1 |
Steam exits as saturated vapour at latex3 with a velocity of latex4 . | 0 |
First, you must determine the range of acceptable transmission ratios to meet the performance targets. | 1 |
What explains the difference? | 1 |
In order to estimate the distance from lightning, it is common to estimate the time delay in seconds between the lightning and the sound of thunder, multiply the result by 3 and then divide by 10. | 0 |
What is the probability of a randomly synthesised 6 nucleotide-long piece of DNA beginning with any base except adenine? | 1 |
The compressor has an isentropic efficiency of latex2 . | 0 |
Given that the regulations for Formula Miniature stipulate that your car is allowed to travel no faster than 3 m/s, you are going to have to limit the speed of the motor. | 0 |
latex18 latex19 Using your knowledge of how logs work, give an equation for the latex4 in terms of latex14 and the ratio of **base to acid**, latex22 . | 1 |
This is the basis of radiocarbon dating. | 0 |
What would we expect the x-component of the pressure to equal? | 1 |
**(L4,6)**: Write as a determinant and hence alculate the volume of the parallelepiped (in latex0 ) with three sides given by the position vectors, latex1 , latex2 , and latex3 . | 1 |
Calculate the area of the parallelogram spanned by the two vectors latex2 and latex13 . | 1 |
latex2 * latex3 Difference in energy between ground and excited states ( latex4 ) * latex5 Avogadro constant ( latex6 ) * latex7 Planck constant ( latex8 ) * latex9 Speed of light ( latex10 ) * latex11 Wavelength of light ( latex12 ) Chloroplasts possess a second photosystem (PS-II) absorbing at a different wavelength. | 0 |
Given that the pipe has an inner diameter of latex5 and wall thickness latex6 . | 0 |
const: latex2 Motor constant: latex3 Viscous friction: latex4 Calculate the motor time constant and the final speed with latex5 D.C. applied. | 1 |
Assume the shaft rotates at 3,000 rpm, and the runner mean radius is latex0 , with pads latex1 long (radially). | 0 |
Note that latex3 Find the function latex4 such that: latex5 Evaluate **explicitly** latex6 where latex2 is the straight line from latex8 to latex9 . | 1 |
Find an expression for latex10 with latex11 slits on each side of latex12 , each separated by latex8 (a diffraction grating). | 1 |
The position latex0 of the centre of mass of latex1 objects with masses latex2 at positions latex3 is given by: latex4 Show that the vector sum of the momenta of all of the masses is zero in the centre-of-mass frame. | 1 |
What is the operating voltage? | 1 |
Most of the spectrophotometers we use in lab can also measure the near ultraviolet absorbance of solutions that appear colourless to our eyes. | 0 |
What is the overall size of your domain? | 1 |
The absorbance is essentially a measure of the depth of colour of a solution at a particular wavelength. | 0 |
Due to the potential contamination by the sediment disposal, the company is interested in knowing whether the material will be transported in suspension with the river or whether it will settle on the bed. | 0 |
For simplicity, assume that steam is an ideal gas. | 0 |
Write the momentum integral equation (see lecture notes, or the previous problem) and solve for latex4 . | 1 |
For a 70 kg human the internal diameter of the inferior vena cava is 0.6 - 1.5 cm and the average velocity of the blood flow is 21 cm/s. | 0 |
We consider two cases: * the flow passes through a single normal shock wave * the flow first goes through an oblique shock wave with latex0 , followed by a normal shock. | 0 |
Answer the questions below by drawing the relevant lines and events in the spacetime diagram.What is the order in which the lamps turn on in the ground rest frame? | 1 |
Describe what happens near the origin and why this flow could never be realised there. | 1 |
Calculate the products and excess air requirements for latex3 of the fuel. | 1 |
Find the angle between latex3 and latex4 . | 1 |
Most students did OK, but the sketches of orbits in part (a) were often incorrect. | 0 |
Estimate the velocity of the water in the jet. | 1 |
How does the relative humidity change? | 1 |
Flywheel latex0 has mass latex1 , radius latex2 , and radius of gyration latex3 . | 0 |
Let us consider still air in standard atmospheric conditions at ground level: latex0 , latex1 . | 0 |
An alloy sphere of mass latex0 radius latex1 has its centre of mass at a point a distance d from its centre. | 0 |
On a latex107 -bit machine, this is likely to happen after the latex108 -nd bit (this is the size of the significand for a double-precision real number): $ \begin{array}{l} 0.0001,1001,1001,1001,1001,1001,1001,1001,1001,1001,1001,1001,1001,[table] % +/- significand exponent % 1 64-11-1=52 11 <-- number of allocated bits % % for more information, go to: http://en.wikipedia.org/wiki/Floating_point % ......................................................................... % ................. create two very similar initial values for the tent map x1 = round(rand(nsignificand,1));% generate nsignificand bits x2 = x1;% take the same set and negate the state of the last bit if x1(end) == 1 x2(end) = 0; else x2(end) = 1; end % convert from the binary system back to the decimal system X1 = 0; X2 = 0; for i = 1:length(x1) X1 = X1 + x1(i)*(2^(-i)); X2 = X2 + x2(i)*(2^(-i)); end% X1 & X2 are two very similar decimal numbers! | 1 |
Show, by substitution, that for light damping the solution is latex2 where latex3 . | 0 |
The rotor exit gas relative velocity. | 0 |
What is then the change in volume of the block from its free condition? | 1 |
Draw these light pulses in your spacetime diagram. | 1 |
Calculate the molar percentage of water vapour in the flue gases and hence their dew point for a total pressure of latex6 atm. | 1 |
Show from first principles that the critical buckling load for a slender strut built-in at both ends is: latex0 | 1 |
What is the reduced mass of the system? | 1 |
A car battery has an internal resistance of latex0 and a nominal voltage of latex1 . | 0 |
[embedded] * latex5 Time The population latex2 is a function of time ( latex5 ) whilst latex3 and latex4 are fixed for a particular population. | 0 |
If the maximum bending stress is not to exceed latex3 . | 0 |
latex0 * latex1 Velocity of enzyme-catalysed reaction ( latex2 ) * latex3 Maximum rate of the reaction ( latex2 ) * latex5 Michaelis constant ( latex6 ) * latex7 Concentration of substrate ( latex6 ) Sketch the graph of this equation: latex1 is the latex10 -variable, latex7 is the latex12 -variable. | 1 |
Calculate the end thrust on the shaft. | 1 |
In order to protect the sensor, a resistor is placed in series with it. | 0 |
The op-amp stage used here is responsible for ensuring that the compressor is driven if the pressure sensor voltage drops below latex2 by some tolerance. | 0 |
Its radial velocity latex1 is latex2 m latex3 s latex4 and its angular velocity is latex5 rad latex3 s latex4 . | 0 |
The assembly is released from rest with the centre of latex0 vertically above latex4 . | 0 |
The normal stress on the perpendicular plane is zero. | 0 |
He wakes up and discovers that his dream is true... | 0 |
For the diesel engine, the compression ratio, latex0 has been estimated to be 18. | 0 |
The corresponding rate of heat rejection from the condenser to the environment. | 0 |
At time latex2 , the mass is at position latex3 m and is moving with velocity latex4 m latex5 s latex6 . | 0 |
By considering a Cartesian frame of reference attached to the ground, with origin in the centre of the tank and with latex2 -axis aligned with latex0 , determine: An expression for the velocity field The deformation tensor The spin tensor The vorticity field | 1 |
If the turbine total-to-total isentropic efficiency is latex3 , what is the specific work output? | 1 |
What is the change in concentration ( latex21 ) of NADH if an enzyme reduces the absorbance of a solution of NADH from latex22 to latex23 ? | 1 |
In essence, the protein complex is performing the process below: latex13 For every two latex0 molecules we oxidise, we get one latex0 back! | 0 |
Calculate the stagnation pressure behind the shock in the first case (a single normal shock wave). | 1 |
The Avogadro number is latex4 , and the universal gas constant is latex5 .Calculate the number of molecules latex6 per unit volume. | 0 |
* Steady flow * Fully developed flow (the velocity does not depend on latex7 ). | 0 |
Use latex11 as the constant of integration for latex5 and latex13 as the constant of integration for latex6 . | 1 |
Using complex impedances develop the gain and phase shift relationships between the input and output voltages of the passive high-pass filter below and draw a Bode diagram of the filter. | 1 |
Estimate the fracture toughness of the material. | 1 |
The principal reason that it is colder at the Earth’s poles than at its equator is because the light from the sun hits the Earth’s surface more or less perpendicularly at the equator, but much more obliquely at the poles. | 0 |
Prove that the maximum bending stress will equal the maximum shear stress when the relationship between the length and depth is latex0 . | 1 |
The wall of an industrial furnace is constructed from a latex0 thick fireclay brick having a thermal conductivity of latex1 . | 0 |
A helicopter drive shaft is latex0 diameter, with a wall thickness of latex1 . | 0 |
What is the pressure coefficient at a point on the aerofoil where the local Mach number is equal to 1? | 1 |
Find the position at which the particle strikes the wall. | 1 |
Compute the turbulence kinetic energy, latex7 , of the flow at that location Estimate the velocity scale of the large eddies, latex8 . | 1 |
The specific heat ratio, latex5 , of air is latex6 and its gas constant, latex7 , is latex8 . | 0 |
If useful, you can use the transforms covered in lectures, combined with the transformation rules. | 0 |
Applying the elementary matrices to another matrix causes operations similar to Gaussian elimination. | 0 |
This figure is rotated through one complete revolution about the line latex3 . | 0 |
How does the concentration at latex14 depend on latex9 ? | 1 |
Normalise this result. | 1 |
Finally when plotting this equation we need to consider the units for each axis. | 0 |
What is the size of the smallest scales in the turbulent flow? | 1 |
What is the *overall* height of the tree to the closest metre? | 1 |
\[*Riley 11.26*] A vector field latex0 is defined in cylindrical polar coordinates latex1 by latex2 Calculate, as a surface integral, the outward flux of latex0 through the portion of the cylinder latex4 between the planes latex5 and latex6 . | 1 |
We will make the following assumptions: * Two-dimensional flow (no dependence on latex6 and no flow in the third direction). | 0 |
The turbulent diffusivity is related to the mean velocity as latex2 . | 0 |
The rotor exit absolute gas velocity and flow angle. | 0 |
Consider a 1D instantaneous point release at latex0 , in a medium with latex1 , and where the total mass of contaminant is latex2 . | 0 |
You may use the result from lectures that the amplitude latex0 of a diffraction pattern is given by: latex1 where latex2 with latex3 the scattering angle, latex4 the wavelength of the light, and latex5 is the Fourier Transform of the aperture function latex6 (where latex7 is the displacement along the aperture). | 0 |
Compute the bed shear stress, latex5 . | 1 |
Consider the two waves latex0 and latex1 . | 0 |
Determine the shock wave angle latex5 . | 1 |
In lectures, you saw how to use Newton’s second law for two particles, latex0 to show that the rate of change of the total momentum, latex1 , is equal to the total external force, latex2 . | 0 |
Find this constant and write down an expression for latex43 that has no unknown constants in it. | 1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.