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

2009 F = Ma, 15

Tags: 2009 , Problem 15
A $\text{22.0 kg}$ suitcase is dragged in a straight line at a constant speed of $\text{1.10 m/s}$ across a level airport floor by a student on the way to the 40th IPhO in Merida, Mexico. The individual pulls with a $\text{1.00} \times \text{10}^2 \text{N}$ force along a handle with makes an upward angle of $\text{30.0}$ degrees with respect to the horizontal. What is the coefficient of kinetic friction between the suitcase and the floor? (A) $\mu_\text{k} = \text{0.013}$ (B) $\mu_\text{k} = \text{0.394}$ (C) $\mu_\text{k} = \text{0.509}$ (D) $\mu_\text{k} = \text{0.866}$ (E) $\mu_\text{k} = \text{1.055}$

2011 F = Ma, 15

Tags: 2011 , Problem 15
A vertical mass-spring oscillator is displaced $\text{2.0 cm}$ from equilibrium. The $\text{100 g}$ mass passes through the equilibrium point with a speed of $\text{0.75 m/s}$. What is the spring constant of the spring? (A) $\text{90 N/m}$ (B) $\text{100 N/m}$ (C) $\text{110 N/m}$ (D) $\text{140 N/m}$ (E) $\text{160 N/m}$

2010 F = Ma, 15

Tags: 2010 , Problem 15
A small block moving with initial speed $v_\text{0}$ moves smoothly onto a sloped big block of mass $M$. After the small block reaches the height $h$ on the slope, it slides down. Find the height $h$. (A) $h=\frac{v_\text{0}^2}{2g}$ (B) $h=\frac{1}{g}\frac{Mv_\text{0}^2}{m+M}$ (C) $h=\frac{1}{2g}\frac{Mv_\text{0}^2}{m+M}$ (D) $h=\frac{1}{2g}\frac{mv_\text{0}^2}{m+M}$ (e) $h=\frac{v_\text{0}^2}{g}$

2008 F = Ma, 15

Tags: 2008 , Problem 15
A uniform round tabletop of diameter $\text{4.0 m}$ and mass $\text{50.0 kg}$ rests on massless, evenly spaced legs of length $\text{1.0 m}$ and spacing $\text{3.0 m}$. A carpenter sits on the edge of the table. What is the maximum mass of the carpenter such that the table remains upright? Assume that the force exerted by the carpenter on the table is vertical and at the edge of the table. [asy] size(10cm); import graph; xaxis(-3.6,3.6); //The legs draw((-1.4,1.4)--(-1.4,0)); draw((-1.6,1.4)--(-1.6,0)); draw((1.4,1.4)--(1.4,0)); draw((1.6,1.4)--(1.6,0)); //The tabletop draw((-2.5,1.6)--(-2.5,1.4)--(2.5,1.4)--(2.5,1.6)--cycle); path a = ((-3.2,0.1)--(-3.2,1.5)); draw(a,Arrows); label("1.0m",a,E); draw((-2.6,1.6)--(-3.6,1.6),dashed+linewidth(0.4)); path c = (-1.4,-0.5)--(1.4,-0.5); draw(c,Arrows); label("3.0m",c,2*S); draw((-1.5,-0.1)--(-1.5,-0.8),dashed+linewidth(0.4)); draw((1.5,-0.1)--(1.5,-0.8),dashed+linewidth(0.4)); draw((-2.5,-0.1)--(-2.5,-1.8),dashed+linewidth(0.4)); draw((2.5,-0.1)--(2.5,-1.8),dashed+linewidth(0.4)); path d = (-2.4,-1.5)--(2.4,-1.5); draw(d,Arrows); label("4.0m",d,2*S); //The Man pair A = (2.4,1.7); draw(circle((2.5,3.7),0.5),linewidth(1.6)); draw((2.4,1.7)--(2.5,3.2),linewidth(1.6)); draw((2.15,2.8)--(2.85,2.8),linewidth(1.6)); draw(A--A+(0.6,0)--A+(0.4,-0.8)--A+(0.6,-1.2),linewidth(1.6)); draw(A--(A+(0.64,-0.12)--A+(0.73,-0.9)--A+(1,-0.9)),linewidth(1.6)); draw((2.15,2.8)--(2.15,2.4)--(2.9,2),linewidth(1.6)); draw((2.85,2.8)--(3,2.3)--(3.5,2.1),linewidth(1.6)); [/asy] (a) $\text{67 kg}$ (b) $\text{75 kg}$ (c) $\text{81 kg}$ (d) $\text{150 kg}$ (e) $\text{350 kg}$