Asian Physics Olympiad · Year 2012

Problems

Problem 1Two masses $m_1$ and $m_2$ ( $m_2>m_1$ ) are joined by a light inextensible string over an ideal pulley; $m_1$ is on an incline of angle $\alpha$ with kinetic friction coefficient $\mu$ , and $m_2$ hangs vertically. With constant $g$ , find the acceleration and string tension as $m_2$ descends. Assume the string, pulley, electrical source, or optical apparatus is ideal as stated, and neglect any effect not specified. State a clear sign convention, identify the physical Keep one model and sign convention throughout. Reuse each intermediate result with the same convention, then check that the answer has the required physical dimensions. (a) Set up the physical relation. (b) Find an intermediate quantity. (c) Obtain the answer and check its conditions and units.Solutions: 1
Problem 2An ideal source of voltage $V$ is in series with a resistor $R_0$ . Two identical resistors $R$ are connected in parallel across this source. Find the total current and the power dissipated in each resistor $R. Assume the string, pulley, electrical source, or optical apparatus is ideal as stated, and neglect any effect not specified. State a clear sign convention, identify the physical Keep one model and sign convention throughout. Reuse each intermediate result with the same convention, then check that the answer has the required physical dimensions. (a) Set up the physical relation. (b) Find an intermediate quantity. (c) Obtain the answer and check its conditions and units.Solutions: 1
Problem 3An object is placed a distance $u>f$ from a converging thin lens of focal length $f>0$ . Use the thin-lens convention $1/f=1/u+1/v$ , with a real image having $v>0$ . Find the image position and signed lateral magnification $M$ for object height $h. Assume the string, pulley, electrical source, or optical apparatus is ideal as stated, and neglect any effect not specified. State a clear sign convention, identify the physical Keep one model and sign convention throughout. Reuse each intermediate result with the same convention, then check that the answer has the required physical dimensions. (a) Set up the physical relation. (b) Find an intermediate quantity. (c) Obtain the answer and check its conditions and units.Solutions: 1