This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 4

2011 F = Ma, 10

Tags: 2011 , problem 10
Which of the following changes will result in an [i]increase[/i] in the period of a simple pendulum? (A) Decrease the length of the pendulum (B) Increase the mass of the pendulum (C) Increase the amplitude of the pendulum swing (D) Operate the pendulum in an elevator that is accelerating upward (E) Operate the pendulum in an elevator that is moving downward at constant speed.

2010 F = Ma, 10

Tags: 2010 , problem 10
A block of mass $m_\text{1}$ is on top of a block of mass $m_\text{2}$. The lower block is on a horizontal surface, and a rope can pull horizontally on the lower block. The coefficient of kinetic friction for all surfaces is $\mu$. What is the resulting acceleration of the lower block if a force $F$ is applied to the rope? Assume that $F$ is sufficiently large so that the top block slips on the lower block. [asy] size(200); import roundedpath; draw((0,0)--(30,0),linewidth(3)); path A=(7,0.5)--(17,0.5)--(17,5.5)--(7,5.5)--cycle; filldraw(roundedpath(A,1),lightgray); path B=(10,6)--(15,6)--(15,9)--(10,9)--cycle; filldraw(roundedpath(B,1),lightgray); label("1",(12.5,6),1.5*N); label("2",(12,0.5),3*N); draw((17,3)--(27,3),EndArrow(size=13)); label(scale(1.2)*"$F$",(22,3),2*N); [/asy] (A) $a_\text{2}=(F-\mu g(2m_\text{1}+m_\text{2}))/m_\text{2}$ (B) $a_\text{2}=(F-\mu g(m_\text{1}+m_\text{2}))/m_\text{2}$ (C) $a_\text{2}=(F-\mu g(m_\text{1}+2m_\text{2}))/m_\text{2}$ (D) $a_\text{2}=(F+\mu g(m_\text{1}+m_\text{2}))/m_\text{2}$ (E) $a_\text{2}=(F-\mu g(m_\text{2}-m_\text{1}))/m_\text{2}$

2008 F = Ma, 10

Tags: 2008 , problem 10
Which is the best value for the mass of the block? (a) $\text{3 kg}$ (b) $\text{5 kg}$ (c) $\text{10 kg}$ (d) $\text{20 kg}$ (e) $\text{30 kg}$

2009 F = Ma, 10

Tags: 2009 , problem 10
A person standing on the edge of a fire escape simultaneously launches two apples, one straight up with a speed of $\text{7 m/s}$ and the other straight down at the same speed. How far apart are the two apples $2$ seconds after they were thrown, assuming that neither has hit the ground? (A) $\text{14 m}$ (B) $\text{20 m}$ (C) $\text{28 m}$ (D) $\text{34 m}$ (E) $\text{56 m}$