Olympiad problems

2010 F = Ma, 8

Tags: 2010 , Problem 8

A car attempts to accelerate up a hill at an angle $\theta$ to the horizontal. The coefficient of static friction between the tires and the hill is $\mu > \tan \theta$. What is the maximum acceleration the car can achieve (in the direction upwards along the hill)? Neglect the rotational inertia of the wheels. (A) $g \tan \theta$ (B) $g(\mu \cos \theta - \sin \theta)$ (C) $g(\mu - \sin \theta)$ (D) $g \mu \cos \theta$ (E) $g(\mu \sin \theta - \cos \theta)$

2009 F = Ma, 8

Tags: 2009 , Problem 8

Determine the angular acceleration of the disk when $t=\text{2.0 s}$. (A) $\text{-12 rad/s}^2$. (B) $\text{-8 rad/s}^2$. (C) $\text{-4 rad/s}^2$. (D) $\text{-2 rad/s}^2$. (E) $\text{0 rad/s}^2$.

2011 F = Ma, 8

Tags: 2011 , Problem 8

When a block of wood with a weight of $\text{30 N}$ is completely submerged under water the buoyant force on the block of wood from the water is $\text{50 N}$. When the block is released it floats at the surface. What fraction of the block will then be visible above the surface of the water when the block is floating? (A) $1/15$ (B) $1/5$ (C) $1/3$ (D) $2/5$ (E) $3/5$

2008 F = Ma, 8

Tags: 2008 , Problem 8

Riders in a carnival ride stand with their backs against the wall of a circular room of diameter $\text{8.0 m}$. The room is spinning horizontally about an axis through its center at a rate of $\text{45 rev/min}$ when the floor drops so that it no longer provides any support for the riders. What is the minimum coefficient of static friction between the wall and the rider required so that the rider does not slide down the wall? (a) $\text{0.0012}$ (b) $\text{0.056}$ (c) $\text{0.11}$ (d) $\text{0.53}$ (e) $\text{8.9}$