Asian Physics Olympiad · Year 2004

Problems

Problem 1An ideal Atwood machine has masses $2m$ and $m$ hanging on opposite sides of a light inextensible string over a frictionless, massless pulley; take $g$ as the gravitational acceleration and assume the system is released from rest. The heavier mass moves downward, with both masses having the same acceleration magnitude because the string length is fixed. (a) Find the acceleration. (b) Find the string tension. (c) Find the speed after the heavier mass has descended a distance $h$ .Solutions: 1
Problem 2An ideal source of emf $\mathcal E$ and internal resistance $r>0$ is connected to a variable resistive load $R>0$ . In steady state the circuit current is $I=\mathcal E/(R+r)$ , and the load power is the electrical energy delivered to $R$ per unit time. Ignore temperature changes and any other circuit elements. (a) Express the load power in terms of $R$ . (b) Determine the load resistance that maximizes that power. (c) Find the maximum power and compare it with the source emf and internal resistance.Solutions: 1
Problem 3A thin converging lens in air has focal length $f=20\,\mathrm{cm}$ , and a real upright object of height $H=2.0\,\mathrm{cm}$ is placed $u=30\,\mathrm{cm}$ in front of it. Use the Cartesian convention in which a real object has positive $u$ and a real image has positive $v$ , so $1/f=1/u+1/v$ ; neglect lens thickness. (a) Find the image distance $v$ . (b) Determine whether the image is real or virtual and upright or inverted. (c) Find its signed magnification and height.Solutions: 1