Found problems: 4
2009 F = Ma, 12
Batman, who has a mass of $\text{M = 100 kg}$, climbs to the roof of a $\text{30 m}$ building and then lowers one end of a massless rope to his sidekick Robin. Batman then pulls Robin, who has a mass of $\text{m = 75 kg}$, up the roof of the building. Approximately how much total work has Batman done after Robin is on the roof?
(A) $\text{60 J}$
(B) $\text{7} \times \text{10}^3 \text{J}$
(C) $\text{5} \times \text{10}^4 \text{J}$
(D) $\text{600 J}$
(E) $\text{3} \times \text{10}^4 \text{J}$
2011 F = Ma, 12
You are given a large collection of identical heavy balls and lightweight rods. When two balls are placed at the ends of one rod and interact through their mutual gravitational attraction (as is shown on the left), the compressive force in the rod is $F$. Next, three balls and three rods are placed at the vertexes and edges of an equilateral triangle (as is shown on the right). What is the compressive force in each rod in the latter case?
[asy]
size(300);
real x=-25;
draw((x,-8)--(x,8),linewidth(6));
filldraw(Circle((x,8),2.5),grey);
filldraw(Circle((x,-8),2.5),grey);
draw((0,-8)--(0,8)--(8*sqrt(3),0)--cycle,linewidth(6));
filldraw(Circle((0,8),2.5),grey);
filldraw(Circle((0,-8),2.5),grey);
filldraw(Circle((8*sqrt(3),0),2.5),grey);
[/asy]
(A) $\frac{1}{\sqrt{3}}F$
(B) $\frac{\sqrt{3}}{2}F$
(C) $F$
(D) $\sqrt{3}F$
(E) $2F$
2008 F = Ma, 12
A uniform disk rotates at a fixed angular velocity on an axis through its center normal to the plane of the disk, and has kinetic energy $E$. If the same disk rotates at the same angular velocity about an axis on the edge of the disk (still normal to the plane of the disk), what is its kinetic energy?
(a) $\frac{1}{2}E$
(b) $\frac{3}{2}E$
(c) $2E$
(d) $3E$
(e) $4E$
2010 F = Ma, 12
A ball with mass $m$ projected horizontally off the end of a table with an initial kinetic energy $K$. At a time $t$ after
it leaves the end of the table it has kinetic energy $3K$. What is $t$? Neglect air resistance.
(A) $(3/g)\sqrt{K/m}$
(B) $(2/g)\sqrt{K/m}$
(C) $(1/g)\sqrt{8K/m}$
(D) $(K/g)\sqrt{6/m}$
(E) $(2K/g)\sqrt{1/m}$