Physic Labs

International Physics Olympiad · Year 2011

Problems

  1. Problem 1An ideal source of emf V=12 VV=12\,\mathrm V is connected in series with resistors R1=2.0 ΩR_1=2.0\,\Omega and R2=4.0 ΩR_2=4.0\,\Omega. The circuit remains closed for t=60 st=60\,\mathrm s; neglect internal resistance and treat all values as constant. The resistors are ohmic and connected in series by ideal wires of negligible resistance. The source maintains a constant voltage for the entire time the circuit is closed. Take conventional current from the positive terminal through both resistors to the negative terminal; electrical energy dissipated is converted to heat. (a) Find the equivalent resistance and circuit current. (b) Determine the voltage across each resistor and check the loop rule. (c) Calculate the total power dissipated and the energy supplied in 60 s60\,\mathrm s.Solutions: 1
  2. Problem 2In an insulated vessel, mh=0.20 kgm_h=0.20\,\mathrm{kg} of water at 80∘C80^\circ\mathrm C is mixed with mc=0.30 kgm_c=0.30\,\mathrm{kg} of water at 20∘C20^\circ\mathrm C. Water has specific heat c=4200 J kg−1K−1c=4200\,\mathrm{J\,kg^{-1}K^{-1}}; neglect the vessel heat capacity and heat loss. After mixing, the water reaches one uniform final temperature, with no evaporation or phase change. Heat is exchanged only between the two portions of water; the insulated vessel takes up no energy. Define heat as positive when the portion considered gains energy and negative when it loses energy. (a) Find the equilibrium temperature TfT_f. (b) Calculate the signed heat transferred by the hot water. (c) Find the heat received by the cold water and check energy conservation. (d) State the ordering of Tc,Tf,ThT_c,T_f,T_h.Solutions: 1
  3. Problem 3Two masses m1=3.0 kgm_1=3.0\,\mathrm{kg} and m2=5.0 kgm_2=5.0\,\mathrm{kg} hang from a light inextensible string over a massless frictionless pulley; the system starts from rest. Take g=10 m s−2g=10\,\mathrm{m\,s^{-2}}. The string stays taut and does not slip on the pulley; its free rotation makes the tensions in the two segments equal. The masses move only vertically, so the lighter mass rises by the same distance and at the same speed that the heavier mass descends. Consider the motion after release. (a) Find the acceleration of each mass and the string tension. (b) Determine their speeds after 3.0 s3.0\,\mathrm s. (c) How far has each mass moved by then?Solutions: 1