Physic Labs

International Physics Olympiad · Year 2012

Problems

  1. Problem 1A ball is launched horizontally from a cliff of height h=45 mh=45\,\mathrm m with initial speed u=10 m s−1u=10\,\mathrm{m\,s^{-1}}. Neglect air resistance and take g=10 m s−2g=10\,\mathrm{m\,s^{-2}}. Choose the launch point as the origin, with the horizontal axis forward and the vertical axis upward. The ground is a vertical distance hh below the launch point; treat the ball as a point particle that hits no other object before landing. Measure time from the instant it leaves the cliff. (a) Find the time to reach the ground and the horizontal range. (b) Determine the velocity components just before impact. (c) Find the impact speed and its angle below the horizontal.Solutions: 1
  2. Problem 2A block of mass m=2.0 kgm=2.0\,\mathrm{kg} starts from rest and slides s=5.0 ms=5.0\,\mathrm m down a 45∘45^\circ incline. The kinetic-friction coefficient is μ=0.20\mu=0.20; 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
  3. Problem 3An ideal source of emf V=18 VV=18\,\mathrm V is connected in series with resistors R1=3.0 ΩR_1=3.0\,\Omega and R2=6.0 ΩR_2=6.0\,\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