Physic Labs

International Physics Olympiad · Year 2014

Problems

  1. Problem 1A block of mass m=4.0 kgm=4.0\,\mathrm{kg} starts from rest and slides s=6.0 ms=6.0\,\mathrm m down a 30∘30^\circ incline. The kinetic-friction coefficient is μ=0.10\mu=0.10; take g=10 m s−2g=10\,\mathrm{m\,s^{-2}}. The plane is fixed and the block remains in contact with it throughout the slide. The coefficient μ\mu is constant along the path, and kinetic friction opposes the motion. The block moves in a straight line down the plane with constant acceleration from its starting point to the stated endpoint. (a) Find the normal force and the acceleration along the plane. (b) Determine the speed at the end of the descent. (c) Calculate the time for the slide, assuming constant acceleration.Solutions: 1
  2. Problem 2An ideal source of emf V=10 VV=10\,\mathrm V is connected in series with resistors R1=2.0 ΩR_1=2.0\,\Omega and R2=3.0 ΩR_2=3.0\,\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
  3. Problem 3In an insulated vessel, mh=0.40 kgm_h=0.40\,\mathrm{kg} of water at 60∘C60^\circ\mathrm C is mixed with mc=0.20 kgm_c=0.20\,\mathrm{kg} of water at 30∘C30^\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