Found problems: 4
2011 F = Ma, 14
You have $\text{5}$ different strings with weights tied at various point, all hanging from the ceiling, and reaching down to the floor. The string is released at the top, allowing the weights to fall. Which one will create a regular, uniform beating sound as the weights hit the floor?
[asy]
size(300);
// (A) bar
picture bar;
draw(bar,(0,0)--(0,42));
for (int i=0;i<43;i+=2) {
draw(bar,(-2,i)--(-3,i));
}
add(bar);
picture ball;
filldraw(ball,circle((0,0),0.5),gray);
add(ball);
add(shift(12*up)*ball);
add(shift(22*up)*ball);
add(shift(30*up)*ball);
add(shift(36*up)*ball);
add(shift(40*up)*ball);
add(shift(42*up)*ball);
label(scale(0.75)*"(A)",(-1,0),2*S);
// (B) bar
add(shift(15*right)*bar);
add(shift(15*right)*ball);
add(shift(6*up)*shift(15*right)*ball);
add(shift(12*up)*shift(15*right)*ball);
add(shift(18*up)*shift(15*right)*ball);
add(shift(24*up)*shift(15*right)*ball);
add(shift(30*up)*shift(15*right)*ball);
add(shift(36*up)*shift(15*right)*ball);
add(shift(42*up)*shift(15*right)*ball);
label(scale(0.75)*"(B)",(14,0),2*S);
// (C) bar
add(shift(30*right)*bar);
add(shift(30*right)*ball);
add(shift(2*up)*shift(30*right)*ball);
add(shift(6*up)*shift(30*right)*ball);
add(shift(12*up)*shift(30*right)*ball);
add(shift(20*up)*shift(30*right)*ball);
add(shift(30*up)*shift(30*right)*ball);
add(shift(42*up)*shift(30*right)*ball);
label(scale(0.75)*"(C)",(29,0),2*S);
// (D) bar
add(shift(45*right)*bar);
add(shift(45*right)*ball);
add(shift(2*up)*shift(45*right)*ball);
add(shift(8*up)*shift(45*right)*ball);
add(shift(18*up)*shift(45*right)*ball);
add(shift(32*up)*shift(45*right)*ball);
label(scale(0.75)*"(D)",(44,0),2*S);
// (E) bar
add(shift(60*right)*bar);
add(shift(60*right)*ball);
add(shift(2*up)*shift(60*right)*ball);
add(shift(10*up)*shift(60*right)*ball);
add(shift(28*up)*shift(60*right)*ball);
label(scale(0.75)*"(E)",(59,0),2*S);
[/asy]
2008 F = Ma, 14
A spaceborne energy storage device consists of two equal masses connected by a tether and rotating about their center of mass. Additional energy is stored by reeling in the tether; no external forces are applied. Initially the device has kinetic energy $E$ and rotates at angular velocity $\omega$. Energy is added until the device rotates at angular velocity $2\omega$. What is the new kinetic energy of the device?
(a) $\sqrt{2}E$
(b) $2E$
(c) $2\sqrt{2}E$
(d) $4E$
(e) $8E$
2009 F = Ma, 14
A wooden block (mass $M$) is hung from a peg by a massless rope. A speeding bullet (with mass $m$ and initial speed $v_\text{0}$) collides with the block at time $t = \text{0}$ and embeds in it. Let $S$ be the system consisting of the block and bullet. Which quantities are conserved between $t = -\text{10 s}$ and $ t = \text{+10 s}$?
[asy]
// Code by riben
draw(circle((0,0),0.3),linewidth(2));
filldraw(circle((0,0),0.3),gray);
draw((0,-0.8)--(0,-15.5),linewidth(2));
draw((5,-15.5)--(-5,-15.5)--(-5,-20.5)--(5,-20.5)--cycle,linewidth(2));
filldraw((5,-15.5)--(-5,-15.5)--(-5,-20.5)--(5,-20.5)--cycle,gray);
draw((-15,-18)--(-16,-17)--(-18,-17)--(-18,-19)--(-16,-19)--cycle,linewidth(2));
filldraw((-15,-18)--(-16,-17)--(-18,-17)--(-18,-19)--(-16,-19)--cycle,gray);
[/asy]
(A) The total linear momentum of $S$.
(B) The horizontal component of the linear momentum of $S$.
(C) The mechanical energy of $S$.
(D) The angular momentum of $S$ as measured about a perpendicular axis through the peg.
(E) None of the above are conserved.
2010 F = Ma, 14
A $\text{5.0 kg}$ block with a speed of $\text{8.0 m/s}$ travels $\text{2.0 m}$ along a horizontal surface where it makes a head-on, perfectly elastic collision with a $\text{15.0 kg}$ block which is at rest. The coefficient of kinetic friction between both blocks and the surface is $0.35$. How far does the $\text{15.0 kg}$ block travel before coming to rest?
(A) $\text{0.76 m}$
(B) $\text{1.79 m}$
(C) $\text{2.29 m}$
(D) $\text{3.04 m}$
(E) $\text{9.14 m}$