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  1. AN630078

    Graphs of s, v and a for a mass with a piece of paper attached

    I understand that velocity is defined as the rate of change of position or the rate of displacement; and that acceleration is defined as the rate of change of velocity (it is the derivative of velocity). Morever, I believe I know that for SHM these graphs vary sinusoidally (I have attached a...
  2. AN630078

    Thermodynamics: Internal Energy, Heat and Work Problem

    Well, internal energy is the sum of the kinetic and potential energies of all the molecules within a given mass of a substance; this energy is associated with the random, disordered motion of the molecules. An example of internal energy is compressed gases; since gases occupy the total volume...
  3. AN630078

    Can heat flow into a body without increasing the mean kinetic energy?

    Yes, heat can flow into a body without increasing the mean kinetic energy of its molecules. Transferring heat energy to an object will raise its internal energy, this will not necessarily cause an increase in temperture. Specific latent heat is the energy required to change the state of one...
  4. AN630078

    Why do we not need to convert from degrees Celsius to Kelvin?

    I understand that the Kelvin scale begins at absolute zero and that the Kelvin scale may even be referred to as the absolute scale. As the units begin from a definite zero and increase with equal amounts of energy being added to the particles of the substance being measured (at equal intervals...
  5. AN630078

    Alpha, Beta and Gamma Energies

    Well, gamma photons are pure energy, so surely a gamma photon would have the most energy since gamma-ray photons generally have energies greater than 100 keV. An alpha particle has the highest ionising power of the three on account of its mass, it roughly has a kinetic energy of 5 MeV, whereas...
  6. AN630078

    Background radiation sources question

    Several sources of background radiation include; Radon gas from soil, rocks and building minerals; since radon is produced by the decay of uranium ore present in certain rocks e.g. granite. On Earth, approximately 42-51% of background radiation is the result of naturally radioactive gases like...
  7. AN630078

    Transformer; make primary voltage x10 of the secondary voltage

    I understand that transformers function using electromagnetic induction and Faraday's Law. This implies; Vs=-Ns (dΦ)/(dt) Meaning the secondary voltage is proportional to the number of turns on the secondary coil. Vs∝Ns Using the relationship; Vp/Vs=Np/Ns If we want Vs=10Vp that would imply...
  8. AN630078

    Root-mean squared values and a.c. emf

    1. We are given the root-mean squared value for the voltage at 230V. Therefore by rearranging the equation Vrms=V0/√2 one can find the value of the peak voltage; ie. V0= Vrms *√2 V0=230*√2 V0=325.269... ~ 325 V (which is the peak voltage of mains electricity in the UK). To find ω use the formula...
  9. AN630078

    Graphical Transformation of y=ln (x)

    a. I believe that y=ln(2x) is a horizontal stretch of y=ln(x) of scale factor 1/2. In the transformation y=ln(2x), each x-value is multiplied by 2 before the corresponding y-value is calculated. b. I think that y=ln(4-x) is a reflection in the y-axis followed by a translation by the vector...
  10. AN630078

    Rates of change: surface area and volume of a sphere

    The surface area of the sphere is 4πr^2. dr/dt is given as 3cm^-1. dS/dt=dS/dr*dr/dt Differentiating 4πr^2 is dS/dr= 8πr dS/dt=8πr*3 dS/dt=24πr Given that r=5 dS/dt=24π*5=120 π The volume of the sphere is 4/3πr^3, differentiating which is dV/dr=4πr^2 dV/dt=dV/dr*dr/dt dV/dt= 4πr^2*3...
  11. AN630078

    Coefficients in the expansion of (1+x)n in A.P, find n

    https://www.toppr.com/ask/question/if-in-the-expansion-of-1-xn-the-coefficient-of-14th-15th-and-16th/ https://www.sarthaks.com/402983/if-in-the-expansion-of-1-x-n-the-coefficients-of-14-th-15-th-and-16-th-terms-are-in-a-p-find-n Specifically regarding my problem the coefficients of x^8, x^9 and...
  12. AN630078

    Capacitor Questions Charging and Discharging

    Question 1: a. I am aware that the general equation for capacitance is C=Q/V thus Q=CV. 22 μF = 0.000022 or 2.2*10^-5 F Would the charge stored by equal to Q=2.2*10^-5*12 Thus, Q=2.64*10^-4 C b. The energy stored by a capacitor is given by E=1/2QV=1/2CV^2=1/2Q^2/C I think with the information...
  13. AN630078

    Van der Graaf Generator: Charge, Potential and Redesign Questions

    1. i. I think that the potential on the surface will be the same as that of a point charge at the centre of the Van der Graaf sphere, which will be 30cm away (since this is the radius of the top sphere). Convert 30cm to m which is equal to 0.3 m. Therefore, to find the charge it can hold one can...
  14. AN630078

    Drawing Radial Field Equipotentials and Field Lines

    I have just attached a standard depiction of a radial field as one may similarly choose to draw it. So I understand that the gravitational field strength in a field is defined as the force per unit mass at that point. The field lines in a radial field move further apart further away from the...
  15. AN630078

    Finding the Coefficients of a Binomial Expansion in an Arithmetic Progression

    Well, I am having a little difficulty knowing how to approach finding a solution to this problem. I am aware that in an arithmetic progression the first term is a and there is a constant common difference defined as d=un+1-un Expanding the binomial given...
  16. AN630078

    Thought experiment: How would ocean levels change?

    I am not too sure how to approach this, initially I thought it may be more of a calculus and related rates of change problem, i.e. finding an expression how the volume and height of water change with respect fo time. I do not know whether this is the right idea or how to progress any further...
  17. AN630078

    Iterative root finding for the cube root of 17

    Firstly, the cube root of 17 is 2.571281591 which is 2.57 to 3.s.f. Initially, I thought about just approaching this problem using the Newton-Raphson Method when x0=2. In which case; x^3=17 x^3-17=0 Using the Newton-Raphson iterative formula xn+1=xr-f(xn)/f’(xn) f(x)=x^3-17 f’(x)=3x^2...
  18. AN630078

    Modulus Inequalities — Help Needed Please

    1. I think the question is asking where is the graph of |3x-2| below the graph of 1/x. To sketch the graph of y= |3x-2| draw the line of y=3x-2 and reflect the section with negative y-values in the x-axis. Alternatively, I could set 3x-2 ≥0, meaning |3x-2|=3x-2 so draw the line of y=3x-2. Then...
  19. AN630078

    Solving Reciprocal Trigonometric Equation cot^2θ+5cosecθ=4

    cot^2θ+5cosecθ=4 cot^2θ+5cosecθ-4=0 cosec^2θ+5cosec-4-1=0 cosec^2θ+5cosec-5=0 Let u=cosecθ u^2+5u-5=0 Solve using the quadratic formula; u=(-5± 3√5)/2 u=(-5+ 3√5)/2=0.8541... Substitute cosecθ=u Therefore, cosecθ=0.8541 1/sinθ=0.8541 sinθ=1/0.8541=1.170... which is not true since sin x cannot be...
  20. AN630078

    Composite and Inverse Functions Problem

    1. a. fg(x)=2(1/2(x-1))+1 fg(x)=2(x/2-1/2)+1 fg(x)=x-1+1 fg(x)=x gf(x)=1/2((2x+1)-1) gf(x)=1/2(2x+1-1) gf(x)=x+1/2-1/2 gf(x)=x The functions functions f(x) and g(x) are inverses of each other. This can be demonstarted by f(x)=2x+1 y=2x+1 x=2y+1 x-1=2y (x-1)/2=y Thus, y=1/2(x-1) = g(x) And...
  21. AN630078

    Graphical Transformations and Finding the Equation of a Curve

    a. y=x^2 undergoes transformation 1 to become y=(x+2)^2 y=x^2+2 undergoes transformation 2 to become y=3(x+2)^2 y=3(x+2)^2 undergoes transformation 3 to become y=3(x+2)^2+4 So would the equation of the resulting curve be y=3(x+2)^2+4? I am very uncertain when it comes to performing...
  22. AN630078

    Geometric Sequence to solve an Interest Problem

    To find how much would be in the account after ten years, let the balance in the account at the start of year n be bn. Then b1=2000 I believe that this a compound interest problem. Common ratio r = 1.06 bn =2000*1.06^n−1 Thus, b10 =2000×1.06^9 = £3378.95791 The balance of the account at the...
  23. AN630078

    Geometric Sequence and the Limiting Value

    1. When n=1, u1+1=3-1/3(u1) u2=3-1/3(3) u2=2 When n=2 u2+1=3-1/3(u2) u3=3-1/3(2) u3=7/3 When n=3 u3+1=3-1/3(u3) u4=3-1/3(7/3) u4=20/9 The common ratio is defiend by r=un+1/un, but this is different between the terms, i.e. u2/u1=2/3 whereas u3/u2=(7/3)/2=7/6 Have I made a mistake? 2. A...
  24. AN630078

    Factor Theorem and Trigonometric Equations Help

    1. The factor theorem states that (x-a) is a factor of f(x) if f(a)=0 Therefore, suppose (x+1) is a factor: f(-1)=3(-1)^3-4(-1)^2-5(-1)+2 f(-1)=0 So, (x+1) is a factor. 3x^3-4x^2-5x+2=(x+1)(3x^2+...) Expand the RHS = 3x^3+3x^2 Leaving a remainder of -7x^2-5x+2 3x^3-4x^2-5x+2=(x+1)(3x^2-7x+...)...
  25. AN630078

    Biology Water Potential and Osmosis Potatoes Investigation

    a) Evaporation will remove water from the test tubes as it turns into water vapour, meaning that the solution will have a greater solute concentration and thus an increased osmotic potential which results in a more negative osmotic potential. Consequently this lowers the solution's water...
  26. AN630078

    Hydrogen Emission Spectrum and Electron Energy Levels

    1. The 4th line from the left, being the aqua blue line, corresponds to a wavelength of 486 nm, as blue light has a wavelength in the range 450-495 nm. 2. This is where I am having the most difficulty, I have tried to answer the question comprehensively but I am not satisfied with my answer. In...
  27. AN630078

    Photoelectric Effect Graph and Work Function Questions

    1. a)I have plotted the graph on desmos and attached an image here. b i. The threshold frequency is equal to the x-intercept ~ 5.6*10^14 Hz ii. The work function is equal to the y-intercept ~ -3.75*10^19 J (would it be correct to state that this value is negative?) c. Convert to eV; 3.75*10^19...
  28. AN630078

    Gravitational Field Multiple Choice Help

    1. I believe that the gravitational field strength would decrease because it is inversely proportional to the square of the distance from the centre of the Earth, g∝1/r^2. Gravitational potential energy at large distances is directly proportional to the masses and inversely proportional to the...
  29. AN630078

    Gravitational Field Strength at the equator and poles

    1. The centripetal force is equal to F= mv^2/r. The velocity of the earth can be found by: V=2πr/T T=1 day = 24 hr*60min*60sec=86400 s v=2π*6.4 x 10^6/86400 s v=465.4211 ... ~465 ms^-1 to 3.s.f Therefore, F=1*465/6.4 x 10^6 F=98/1280000=7.265626 *10^-5 ~7.3 *10^-5 N Would this be correct since...
  30. AN630078

    Potential Energy and raising a satellite from Earth into a Circular Orbit

    a. V=-GM/r V=-6.67*10^-11*6.0 x 10^24/6.4 x 10^6 V grav = -62531250 ~ -62.5M Jkg^-1 b. To find the gravitational potential 200 km above the surface of the Earth; r=6.4 x 10^6 +2*10^5 m=6.6*10^6 V grav=-6.67*10^-11*6.0 x 10^24/6.6*10^6 V grav= -60636363 ~ -60.6 M Jkg^-1 Can I check that it is...
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