0 stringlengths 10 969 | label int64 0 1 |
|---|---|
Water is poured into a spout of diameter latex2 cm at a rate of latex3 ml/s. | 0 |
Depending on the strength of the throw, the rock may follow three different types of trajectory. | 0 |
Hence calculate the surface area of the torus. | 1 |
The sediment size has a medium sediment size of latex2 . | 0 |
What is the optimum $pH latex13 K_{a}= 0.0002\, \mathrm{M} latex14 K_{b}= 0.00032 \, \mathrm{M} latex15 pH latex16 pH=-\log_{10}{[H^{+}]} $ | 1 |
Use the formula from part (a) to show that the area of the curved surface latex7 between the planes latex8 and latex9 is: latex10 *** **Hint:** Here latex11 is an azimuthal angle with latex12 and latex13 should just be considered a parameter. | 1 |
Do you now get the right expression for the Lorentz contraction? | 1 |
You are part of an engineering team whose role is to design a drone that can fly in the atmosphere of Mars. | 0 |
Calculate the temperature in the tank. | 1 |
Use a coordinate system in which her vertical position latex4 is measured upward from the point latex1 metres below the platform. | 1 |
Now draw a separate spacetime diagram for a moving frame, in which Rick, Lucy, and Matt are moving at latex5 . | 1 |
State the value of latex30 in the rest frame and hence use the Lorentz transformation equations to find latex31 and latex32 . | 1 |
For the following systems evaluate the transfer functions latex0 and latex1 : | 1 |
* A \`solution' script is also provided but you are advised not to look! | 0 |
Simplify the expression for velocity, latex3 , on latex4 . | 1 |
Plot the speed at all locations along latex17 and latex18 , at latex19 , i.e plot: i. the latex5 component of latex21 ii. | 1 |
The approximation in the limit latex18 (from part (f)) was latex19 Solve this equation for latex1 and estimate the error, compared to the exact solution in part (d) for latex21 Compare the errors to part (e) where you calculated errors for the approximation using latex22 Plot the following: * The full equation, latex23 * The approximation for latex6 , from part (c): latex25 * The approximation for latex16 , from part (f): latex27 * The roots of the equation, i.e the following two points: latex28 To plot the approximations, you will need to choose a value of latex2 , for example latex30 . | 1 |
Find the ratio of the maximum possible bending moment to the bending moment that will cause the onset of yielding for the beam cross-sections described below. | 1 |
*** You may quote the result from lecture that the area element latex5 of a spherical surface of radius latex1 is latex7 . | 0 |
A researcher needs a latex0 of a latex1 solution citric acid ( latex2 ) solution for applying to a single leaf in an experiment. | 0 |
Ignore any movement of the Earth relative to the centre of the Milky Way. | 0 |
What would a filter for the DA card need to achieve? | 1 |
* thinner than this value. | 0 |
You can write the trigonometric functions latex11 and latex12 as 'sin(x)' and 'cos(x)', *etc*. | 1 |
From these you will work out latex6 , latex10 and latex11 before converting to the centre-of-mass frame to find latex22 , latex8 and latex24 . | 1 |
Think particularly about the use of only 1 gear stage. | 0 |
In Newtonian fluids the viscosity depends on the deformation rate. | 0 |
Use this formula to estimate the equilibrium separation latex3 of two water molecules and the amount of energy required to completely separate them from equilibrium. | 1 |
This requires 'numerical integration', for example in MATLAB use `trapz` or in Python \`numpy.trapz. | 0 |
A carriage is lifted from the ground at A to the top of the hill at B using a chain system, then released from B at a very low initial speed. | 0 |
Explain, with the help of some sketches, how the interference pattern changes as latex1 gets larger (but latex25 is fixed). | 1 |
The axial component of steam velocity is constant and equal to latex4 times the blade velocity, and the stator blade exit steam angle is latex5 . | 0 |
If the probe surface has an emissivity of latex2 and the probe does not receive radiation from other surfaces, as, for example, from the sun, what is its surface temperature? | 1 |
What is the safety factor according to the shear-strain energy criterion, if fatigue considerations are ignored? | 1 |
The container undergoes a rotation around its vertical axis ( latex0 ) at a constant angular velocity latex1 . | 0 |
The blood passes through tubing of length latex3 , with a rectangular cross section latex4 latex5 . | 0 |
A cup anemometer comprises latex0 cups, each of diameter, latex1 , held on struts at a distance, latex2 , from a shaft. | 0 |
Find the transfer function for the systems described by the following differential equations, assuming latex0 and latex1 to be the input and the output signals respectively. | 1 |
In this 'tutorial' question we will guide you through the approximation of this equation in two limits, matching them in the overlapping zone, and comparing to the general solution. | 0 |
A turbine is operating steadily with negligible heat transfer to the surroundings. | 0 |
Assume that latex4 and ignore all forces other than gravity. | 0 |
Are the following functions even, odd, or neither? | 1 |
The molar mass and gas constant of the mixture. | 0 |
You need to check that the engine will have a suitable cylinder capacity to generate the required 3kW of power at its minimum operating speed. | 1 |
latex4 is the kinematic viscosity. | 0 |
14.7), show that for high Reynolds numbers and zero streamwise pressure gradient ( latex1 ) the equation reduces to latex2 where latex3 is a constant. | 1 |
In the manometer shown below, Fluid 1 is water with a density of latex0 kg/m latex1 and Fluid 2 has a density of latex2 kg/m latex3 . | 0 |
Choosing latex5 , use a computer to plot latex2 and the quadratic approximation to latex2 over the following values of latex8 , zooming in by a factor of latex9 every time: 1. latex10 2. latex11 3. latex12 4. latex13 What can you conclude? | 1 |
In this question you may neglect gravitational and viscous effects. | 0 |
Hint: the integral of latex10 from latex11 to latex12 to is equal to latex13 . | 0 |
*** In the answer box below, input the form of the intensity diffraction pattern that you have derived. | 1 |
What is the temperature of the air at the stagnation point on the nose of the aircraft? | 1 |
The circuit illustrated below applies a near constant armature voltage to the motor M. The armature resistance of the motor is latex0 , so that if it were stalled whilst switched on, this is the minimum resistance which the transistor would need to drive. | 0 |
Is the student's claim true or false? | 1 |
The flow rates of hot water into the tower and cooled water from the tower are equal. | 0 |
There is no power input to the system. | 0 |
Where is the car relative to the street lights when the light from street lamp D reaches it? | 1 |
Is momentum conserved in the collision? | 1 |
Solve the equation and apply the boundary conditions at latex1 and at latex2 to show that latex58 Use a similar method to find an expression for latex10 . | 1 |
The rock orbits the asteroid and returns to its starting point, hitting Biff on the back of the head. | 0 |
We're working on a solution.] | 0 |
Frame M measures the separation to be latex8 , which we want to determine in terms of latex2 and latex6 .View the situation from within frame M. Let the time for the light to travel from the emitter to the mirror in this frame be latex11 . | 0 |
This greatly speeds up the counting process. | 0 |
For a driven oscillator, the power supplied by the drive to the oscillator, averaged over one cycle, is latex0 . | 0 |
\[i.e , in the corner of the first octant of the cartesian system]. | 0 |
Consider an infinitely long line of charge with linear charge density latex0 cm latex1 , lying along the latex2 axis, as shown in the Figure. | 0 |
Which sketch best represents the streamlines? | 1 |
**Tent map in binary** Owing to the way we have constructed (3), we know that all latex55 values will be any real number between latex14 and latex3 . | 0 |
Find its mass if its density \[mass per unit area] at each point latex1 is proportional to the square of the distance from the origin to latex1 . | 1 |
The measurements are shown below. | 0 |
What is the safe working pressure if the ultimate compressive strength is three times the ultimate tensile strength? | 1 |
A cylindrical pressure vessel is latex0 diameter, with hemispherical ends, and is made of steel with a yield strength of latex1 , latex2 thick. | 0 |
Note: waves labeled (a), (b), (c) and (d). | 0 |
Obtain an expression for the pressure ratio latex4 at the throat. | 1 |
The figure below is a crude representation of the potential energy of two deuterons (a deuteron consists of a proton bound to a neutron) as a function of the distance latex0 between them. | 0 |
Using the formulae for latex0 , calculate the indefinite integral latex1 | 1 |
Remember also to show that the latex0 and latex1 terms are orthogonal and not just the latex0 and latex1 terms with themselves. | 1 |
latex0 For the closed-loop system shown above, apply a PI controller to achieve a damping of latex1 and a natural frequency of latex2 . | 1 |
You may wish to use . | 0 |
The reservoir pressure is latex1 . | 0 |
Pendulum clocks tick every half period of the pendulum’s swing. | 0 |
Sketch the graphs of the following: latex0 latex1 latex2 latex3 latex4 where latex5 and latex6 are polar coordinates and latex7 is a positive constant. | 1 |
Use this equation, plus momentum conservation, to derive the following expressions for the final velocities of the two bodies (of masses latex6 and latex7 ) in the case when the second body is initially at rest ( latex8 ): latex9 | 1 |
The specific volume of saturated steam at latex1 . | 0 |
What do you conclude about using the cross product to find angles? | 1 |
Explain what the covariances latex0 and latex1 represent physically. | 1 |
Is the function: | 0 |
Express latex10 in terms of latex2 . | 1 |
This corresponds to an intensity of 0.13 W m latex10 . | 0 |
Try using the following brochure and pp.18. | 1 |
(Give 2 decimal places) | 1 |
At steady-state the turbine performs work equal to latex4 of steam flowing through the turbine. | 0 |
Using the same state numbering as in the notes, derive an expression for the specific net work of an ideal Joule cycle in terms of latex0 and latex1 (which can be regarded as a constant) and the two parameters latex2 and latex3 , respectively defined as latex4 latex5 This should provide one of the reasons why gas turbine designers are constantly striving to increase the maximum gas temperature. | 1 |
Select reasonable pressures for the evaporator and condenser, explaining your choices. | 1 |
In addition, think about why is it more sensible to use base-10 logarithm than natural logarithm, for this particular experiment. | 1 |
These polycistronic mRNAs have Shine-Dalgarno sequences (SDS) *c.* 5 nucleotides upstream of the AUG start codon. | 0 |
Sketch graphs of latex2 and latex3 . | 0 |
Determine the magnitude and direction of the couple which a person holding the sander must apply in order to rotate the sander about: The fixed x-axis at latex3 in the direction shown. | 1 |
The Michaelis-Menten model for enzyme kinetics can be expressed as: latex0 where: * latex1 is the velocity of the reaction * latex2 is the Michaelis constant * latex3 is the maximum velocity of the reaction * latex4 is the substrate concentration Differentiate the formula above with respect to latex4 using the quotient rule, and from that determine latex6 when latex7 \[If you are used to calling the numerator and denominator of the quotient rule latex8 and latex1 , be extremely careful not to muddle up latex1 (denominator) and latex11 (velocity)!] | 1 |
If this turbine were designed for driving an AC generator, would it be intended for a European ( latex8 power system) or North American ( latex9 ) market? | 1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.