Found problems: 4
2009 F = Ma, 11
A $\text{2.25 kg}$ mass undergoes an acceleration as shown below. How much work is done on the mass?
[asy]
// Code by riben
size(350);
// Axes
draw((0,0)--(12,0),lightgray);
draw((0,-3)--(0,5));
// Tick Marks
draw((2,0)--(2,-0.2));
label("2",(2,-0.2),S*2);
draw((4,0)--(4,-0.2));
label("4",(4,-0.2),S*2);
draw((6,0)--(6,-0.2));
label("6",(6,-0.2),S*2);
draw((8,0)--(8,-0.2));
label("8",(8,-0.2),S*2);
draw((10,0)--(10,-0.2));
label("10",(10,-0.2),S*2);
draw((12,0)--(12,-0.2));
label("12",(12,-0.2),S*2);
draw((0,-2)--(-0.2,-2));
label("-2",(-0.2,-2),W);
draw((0,0)--(-0.2,0),lightgray);
label("0",(-0.2,0),W);
draw((0,2)--(-0.2,2),lightgray);
label("2",(-0.2,2),W);
draw((0,4)--(-0.2,4));
label("4",(-0.2,4),W);
// Dashed Lines
draw((0,-2)--(12,-2),dashed);
draw((0,2)--(12,2),dashed+lightgray);
draw((0,4)--(12,4),dashed);
draw((2,5)--(2,0.2),dashed);
draw((4,5)--(4,0.2),dashed);
draw((6,5)--(6,0.2),dashed);
draw((8,5)--(8,0.2),dashed);
draw((10,5)--(10,0.2),dashed);
draw((12,5)--(12,0.2),dashed);
draw((2,-1)--(2,-3),dashed);
draw((4,-1)--(4,-3),dashed);
draw((6,-1)--(6,-3),dashed);
draw((8,-1)--(8,-3),dashed);
draw((10,-1)--(10,-3),dashed);
draw((12,-1)--(12,-3),dashed);
// Path
path A=(0,0)--(2,4)--(4,4)--(6,2)--(8,0)--(10,-2)--(12,0);
draw(A,linewidth(1.5));
// Labels
label(scale(0.85)*rotate(90)*"Acceleration (m/s/s)",(0,1),W*7);
label(scale(0.75)*"Position (m)",(11,0),N);
[/asy]
(A) $\text{36 J}$
(B) $\text{22 J}$
(C) $\text{5 J}$
(D)$\text{-17 J}$
(E) $\text{-36 J}$
2010 F = Ma, 11
The three masses shown in the accompanying diagram are equal. The pulleys are small, the string is lightweight, and friction is negligible. Assuming the system is in equilibrium, what is the ratio $a/b$? The figure is not drawn to scale!
[asy]
size(250);
dotfactor=10;
dot((0,0));
dot((15,0));
draw((-3,0)--(25,0),dashed);
draw((0,0)--(0,3),dashed);
draw((15,0)--(15,3),dashed);
draw((0,0)--(0,-15));
draw((15,0)--(15,-10));
filldraw(circle((0,-16),1),lightgray);
filldraw(circle((15,-11),1),lightgray);
draw((0,0)--(4,-4));
filldraw(circle((4.707,-4.707),1),lightgray);
draw((15,0)--(5.62,-4.29));
draw((0.5,3)--(14.5,3),Arrows(size=5));
label(scale(1.2)*"$a$",(7.5,3),1.5*N);
draw((2.707,-4.707)--(25,-4.707),dashed);
draw((25,-0.5)--(25,-4.2),Arrows(size=5));
label(scale(1.2)*"$b$",(25,-2.35),1.5*E);
[/asy]
(A) $1/2$
(B) $1$
(C) $\sqrt{3}$
(D) $2$
(E) $2\sqrt{3}$
2008 F = Ma, 11
Which is the best value for the coefficient of friction between the block and the surface?
(a) $\text{0.05}$
(b) $\text{0.07}$
(c) $\text{0.09}$
(d) $\text{0.5}$
(e) $\text{0.6}$
2011 F = Ma, 11
A large metal cylindrical cup floats in a rectangular tub half-filled with water. The tap is placed over the cup and turned on, releasing water at a constant rate. Eventually the cup sinks to the bottom and is completely submerged. Which of the following five graphs could represent the water level in the sink as a function of time?
[asy]
size(450);
picture pic;
draw(pic,(0,0)--(10,0)--(10,7)--(0,7)--cycle);
for (int i=1;i<10;++i) {
draw(pic,(i,0)--(i,7),dashed+linewidth(0.4));
}
for (int j=1;j<7;++j) {
draw(pic,(0,j)--(10,j),dashed+linewidth(0.4));
}
label(pic,scale(1.2)*"time",(5.5,-0.5),S);
label(pic,rotate(90)*scale(1.2)*"water level",(-0.5,2.5),W);
add(pic);
path A=(0,1)--(10,6);
draw(A,linewidth(2));
label("(A)",(4.5,-1.5),1.5*S);
picture pic2=shift(13*right)*pic;
add(pic2);
path B=(0,1)--(4,4)--(10,6);
draw(shift(13*right)*B,linewidth(2));
label("(B)",(17.5,-1.5),1.5*S);
picture pic3=shift(26*right)*pic;
add(pic3);
path C=(0,1)--(4,3)--(4,2)--(10,5);
draw(shift(26*right)*C,linewidth(2));
label("(C)",(30.5,-1.5),1.5*S);
picture pic4=shift(13*down)*pic;
add(pic4);
path D=(0,1)--(4,3)--(4,4)--(10,7);
draw(shift(13*down)*D,linewidth(2));
label("(D)",(4.5,-14.5),1.5*S);
picture pic5=shift(13*down)*shift(13*right)*pic;
add(pic5);
path E=(0,1)--(4,3)--(4,2)--(10,4);
draw(shift(13*down)*shift(13*right)*E,linewidth(2));
label("(E)",(17.5,-14.5),1.5*S);
[/asy]