Olympiad problems

2011 F = Ma, 1

Tags: 2011 , Problem 1

A cyclist travels at a constant speed of $\text{22.0 km/hr}$ except for a $20$ minute stop. The cyclist’s average speed was $\text{17.5 km/hr}$. How far did the cyclist travel? (A) $\text{28.5 km}$ (B) $\text{30.3 km}$ (C) $\text{31.2 km}$ (D) $\text{36.5 km}$ (E) $\text{38.9 km}$

2011 F = Ma, 17

Tags: 2011 , problem 17

Jonathan applies a normal force that is just enough to keep the rope from slipping. Becky makes a small jump, barely leaving contact with the floor of the box. Upon landing on the box, the force of the impact causes the rope to start slipping from Jonathan’s hand. At what speed does the box smash into the ground? Assume Jonathan’s normal force does not change. (A) $\sqrt{2gH}(\mu_k/\mu_s)$ (B) $\sqrt{2gH}(1-\mu_k/\mu_s)$ (C) $\sqrt{2gH}\sqrt{\mu_k/\mu_s}$ (D) $\sqrt{2gH}\sqrt{1-(\mu_k/\mu_s)}$ (E) $\sqrt{2gH}(\mu_s-\mu_k)$

2011 F = Ma, 21

Tags: 2011 , problem 21

An engineer is given a fixed volume $V_m$ of metal with which to construct a spherical pressure vessel. Interestingly, assuming the vessel has thin walls and is always pressurized to near its bursting point, the amount of gas the vessel can contain, $n$ (measured in moles), does not depend on the radius $r$ of the vessel; instead it depends only on $V_m$ (measured in $\text{m}^3$), the temperature $T$ (measured in $\text{K}$), the ideal gas constant $R$ (measured in $\text{J/(K} \cdot \text{mol})$), and the tensile strength of the metal $\sigma$ (measured in $\text{N/m}^2$). Which of the following gives $n$ in terms of these parameters? (A) $n=\frac{2}{3}\frac{V_m\sigma}{RT}$ (B) $n=\frac{2}{3}\frac{\sqrt[3]{V_m\sigma}}{RT}$ (C) $n=\frac{2}{3}\frac{\sqrt[3]{V_m\sigma^2}}{RT}$ (D) $n=\frac{2}{3}\frac{\sqrt[3]{V_m^2\sigma}}{RT}$ (E) $n=\frac{2}{3}\sqrt[3]{\frac{V_m\sigma^2}{RT}}$

2011 F = Ma, 18

Tags: 2011 , Problem 18

A block of mass $\text{m = 3.0 kg}$ slides down one ramp, and then up a second ramp. The coefficient of kinetic friction between the block and each ramp is $\mu_\text{k} = \text{0.40}$. The block begins at a height $\text{h}_\text{1} = \text{1.0 m}$ above the horizontal. Both ramps are at a $\text{30}^{\circ}$ incline above the horizontal. To what height above the horizontal does the block rise on the second ramp? (A) $\text{0.18 m}$ (B) $\text{0.52 m}$ (C) $\text{0.59 m}$ (D) $\text{0.69 m}$ (E) $\text{0.71 m}$