Physic Labs

International Physics Olympiad · Year 2010

Problems

  1. Problem 1Two masses m1=2.0 kgm_1=2.0\,\mathrm{kg} and m2=3.0 kgm_2=3.0\,\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
  2. Problem 2A ball is launched horizontally from a cliff of height h=20 mh=20\,\mathrm m with initial speed u=15 m s−1u=15\,\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
  3. Problem 3A block of mass m=2.0 kgm=2.0\,\mathrm{kg} starts from rest and slides s=4.0 ms=4.0\,\mathrm m down a 30∘30^\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