International Physics Olympiad · Year 1977

Problems

Problem 1A small block of mass $m=2.0\,\mathrm{kg}$ is released from rest at the top of a straight, smooth plane inclined at $\alpha=30^\circ$ to the horizontal. It travels a distance $s=10.0\,\mathrm{m}$ measured along the plane. Take $g=9.80\,\mathrm{m\,s^{-2}}$ , neglect air resistance, and choose downhill as positive. (a) Find the block’s acceleration and the normal force exerted by the plane. (b) Find the travel time and its speed at the bottom. (c) Find the work done by gravity and its average power during the descent.Solutions: 1
Problem 2An ideal constant source of emf $E=12.0\,\mathrm V$ is connected at $t=0$ in series with a resistor $R=200,Omega$ and capacitor $C=50.0,\mu\mathrm F$ . The capacitor is initially uncharged, and the wires and switch are ideal. Let $q(t)$ be the charge on the plate connected toward the positive source terminal, and let $i(t)=dq/dt$ be the charging current, for $tge0$ . (a) Find the time constant and functions $q(t)$ and $i(t)$ . (b) Find when the capacitor voltage reaches $90%$ of its final value and the current then. (c) Find the stored energy at that instant and the limiting charge and current as $t\toinfty$ .Solutions: 1
Problem 3On an optical bench, a thin converging lens of focal length $f=10.0\,\mathrm{cm}$ is used with an object of height $h_o=2.00\,\mathrm{cm}$ placed on the principal axis, initially at distance $u=30.0\,\mathrm{cm}$ . Work in air and in the paraxial approximation. For a real object take $u>0$ ; a real image has $v>0$ . Define transverse magnification by $M=h_i/h_o=-v/u$ . (a) Find the image distance and magnification, and state whether the image is real or virtual and upright or inverted. (b) Find the image height. (c) Move the object to $u=15.0\,\mathrm{cm}$ and repeat the position, magnification, and image-character determination, then compare the two placements.Solutions: 1