Questions asked by Tom M.

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• Springs: what is the height bounced by a spring, mass *m*, initial length #l_0# compressed length #l_1#, spring constant *k*?
  
• 1.00 g of alkali metal carbonate, #M_2CO_3#, is dissolved in water and made up to #250 cm^3# in a volumetric flask. #25.00 cm^3# portions of this solution are titrated against 0.113M hydrochloric acid. The average titre is #12.80cm^3#. What element is M?
  
• A pop-up toy consists of a mass m stuck to the top of a light spring of natural length #l_0#and spring constant k. The spring is compressed to length #l_1# when the pop-up is stuck to the ground. To what height above the ground does it reach?
  
• A shelf of uniform density is supported by two brackets at a distance of #1/8# and #1/4# of the total length, #L#, from each end respectively. Find the ratio of the reaction forces from the brackets on the shelf?
  
• Say I'm moving parallel to someone else and we are both accelerating in the same direction at the same rate. Would he seem stationary to me? Could we tell we were accelerating?
  
• Why is the boiling point of water higher than would be expected from the trend of Group 6 hydrides? Why is the boiling point of #H_2Te# higher than #H_2Se#?
  
• Why is the derivative of #e^x=e^x#? Just out of curiosity.
  
• In the binomial expansion of #(1+ax)^n#, where #a# and #n# are constants, the coefficient of #x# is 15. The coefficient of #x^2# and of #x^3# are equal. What is the value of #a# and of #n#?
  
• Solve #12sin^2x+7cosx-13=0# for the range #360^o<=x<=540^o#?
  
• Constant acceleration: Two particles P and Q have masses 0.5kg and 0.4kg respectively. The particles are attached to the ends of a light inextensible spring. [cont]...?
  
• Solubility - Explain why propanone is soluble in water? Explain why magnesium chloride is soluble in cyclohexane?
  
• A circle C has equation #x^2+y^2-6x+8y-75=0#, and a second circle has a centre at #(15,12)# and radius 10. What are the coordinates of the point where they touch?
  
• What is the value of x for which #ln(2x-5)-lnx=1/4#?
  
• Which of the following is a redox reaction?
  
• What should you do if you know part of an answer, but not the whole thing? Should you leave a comment?
  
• When sodium chlorate (I), NaClO is heated, sodium chlorate (V) and sodium chloride are formed. What is the ionic equation for this reaction? What type of reaction is this?
  
• What is the reducing agent in the reaction #2HCl(aq)+H_2O_2(aq)->Cl_2(g)+2H_2O(l)?#
  
• Why is the boiling point of #H_2Te# higher than the boiling point of #H_2S#?
  
• Draw the shape of the #ClF_2^+# ion, including any lone pairs, and name the shape made by the atoms? Predict the bond angle in the ion?
  
• What is the systematic name of the compound #CH_3CH(OH)CH_2CHO#?
  
• The graph #y=ab^x# passes through #(2, 400)# and #(5,50)#. Find values for #a# and #b#, and, given that #ab^x>k# for some constant #k>0#, show that #x>log(1600/k)/log2# where log means log to any base?
  
• #log_11(2x-1)=1-log_11(x+4)# What is #x#?
  
• Prove that #sum_(r=1)^nr^5=1/12n^2(n+1)^2(2n^2+2n-1)# using binomial theorem?
  
• Why, in terms of structure and bonding, does but-2-ene exist as two geometric isomers whereas but-1-ene does not?
  
• How could you find the density of an irregular object which floats in water?
  
• One of the most commonly used compounds in the chlorination of swimming pools is sodium hypochlorite, #NaClO.# Once dissolved, an equilibrium is established between #ClO^-# and its conjugate acid. What is the equation of this reaction?
  
• Prove by induction that #f(n)=2^(2n-1)+3^(2n-1)# is divisible by 5 for #n in ZZ^+#?
  
• Given the following information, calculate the density of sand?
  
• #Abs(z-4+2i)=Abs(z+8-6i)#. In the form #asqrt13, ainQQ#, what is the least value of #absz#?
  
• A regular tetrahedron has vertices #A, B, C# and #D# with co-ordinates #(0,0,0,), (0,1,1), (1,1,0), "and" (1,0,1)# respectively. Show the angle between any two faces of the tetrahedron is #arccos(1/3)#?
  
• Challenge I came up with: what is the maximum area of the rectangle inscribed between the line #y=sintheta#, #x=theta# and #x=pi-theta#?
  
• Proof of the shortest distance from a point to a plane formula?
  
• Find a Cartesian Equation of the plane with contains the line #(x-2)/3=(y+4)/2=(z-1)/2# and passes through the point #(1,1,1)#?
  
• Sketch the velocity-time graph for two particles colliding in vertical motion?
  
• Venus is an inner planet which orbits the Sun in almost the same plane as the Earth. Its average radius of orbit is 0.72 AU. Viewed from the Earth’s equator, estimate maximum number of hours before sunrise for which Venus can be observed in the night sky?
  
• A uniform rectangular trapdoor of mass #m=4.0kg# is hinged at one end. It is held open, making an angle #theta=60^@# to the horizontal, with a force magnitude #F# at the open end acting perpendicular to the trapdoor. Find the force on the trapdoor?
  
• Complete the half equation?: #MnO_4^-" + X -> Mn^2+Y# What are X and Y?
  
• If #e=(1+klamda)/(k(1-lambda))#, #0<lamda<1/2# and e is the coefficient of restitution, deduce that #k>1#?