International Physics Olympiad · Year 1969

Problems

Problem 1A ball is projected horizontally from a table of height $h$ with initial speed $u$ ; the ground is horizontal below. Neglect air resistance, take constant gravity $g$ , and choose $x$ horizontal along launch and $y$ vertically upward. (a) Find flight time. (b) Find range. (c) Find velocity components and speed just before impact, and state the direction. Keep the sign convention consistent and use appropriate SI units throughout. Each part builds on intermediate results from the preceding part; apply a physical relation only where the stated model assumptions hold. Finally compare the answers with the initial conditions, expected trends, and an independent check when available.Solutions: 1
Problem 2Two masses of water $m_1,m_2$ initially at temperatures $T_1>T_2$ are mixed in an insulated vessel. Neglect vessel heat capacity, heat loss, and evaporation; water’s specific heat $c$ is constant and no phase change occurs. (a) Write the heat balance and find final temperature $T_f$ . (b) Find heat gained by the colder water. (c) For $m_1=2m_2$ , locate $T_f$ between the initial temperatures. Keep the sign convention consistent and use appropriate SI units throughout. Each part builds on intermediate results from the preceding part; apply a physical relation only where the stated model assumptions hold. Finally compare the answers with the initial conditions, expected trends, and an independent check when available.Solutions: 1
Problem 3A uniform wire of resistivity $\rho$ , length $L$ , and cross-sectional area $A$ is kept at constant temperature. It is slowly drawn into a wire of the same material and volume, length $2L$ , with uniform new area and unchanged resistivity. (a) Find initial resistance. (b) Find new area and resistance. (c) Compare the resistances and explain why the area must change. Keep the sign convention consistent and use appropriate SI units throughout. Each part builds on intermediate results from the preceding part; apply a physical relation only where the stated model assumptions hold. Finally compare the answers with the initial conditions, expected trends, and an independent check when available.Solutions: 1