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II Duluth Physics Olympiad

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April 19th, 2015

University of Minnesota, Duluth

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**Part I: Theoretical**

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**Problem 1: **

Alice and Bob left their houses at sunrise and started moving towards each other with constant speeds. At noon they met and continued their motions. At 3:00 pm Alice reached the house of Bob, and at 9:00 pm Bob reached the house of Alice. At what time was the sunrise?

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**Problem 2:**

A small ball is suspended on a thin weightless string of length *l* = 10 cm as shown in the figure below. What is the smallest speed one must give the ball (at point *B*) in the horizontal direction so that it hits the point *A*.

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**Problem 3:**

A thermally insulated cylinder holds one mole of monoatomic ideal gas, as shown in the figure below. The weightless piston can move without friction and is held in place by two identical weights. The pressure outside the cylinder is zero (vacuum). The initial temperature of the gas is *T*_{0}. A physics student removes one of the weights and after some time puts it back on the piston. What is the final temperature of the gas?

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**Problem 4:**

Three identical small metal balls are placed (in vacuum) at the corners of an equilateral triange, such that the distance between every pair of balls is the same. One after another, each ball is connected to a wire that is held at a constant electric potential, and then disconnected. As a result, the first ball accumulates charge *Q*_{1} and the second ball accumulates charge *Q*_{2}. What is the charge on the third ball?

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**Problem 5:**

The force of air resistance *F* experienced by a paper cone is proportional to the square of its velocity *v*, i.e.
*F* = *f*(*R*)*v*^{2}.

where*f* is a function of the radius *R* of the cone’s base. Determine experimentally what kind of function is *f*(*R*). Propose a mathematical expression for *f*(*R*).

*Equipment: 8-10 templates of cones, scissors, graph paper, measuring stick, glue stick. *