Found problems: 4
2011 F = Ma, 9
A spring has an equilibrium length of $2.0$ meters and a spring constant of $10$ newtons/meter. Alice is pulling on one end of the spring with a force of $3.0$ newtons. Bob is pulling on the opposite end of the spring with a force of $3.0$ newtons, in the opposite direction. What is the resulting length of the spring?
(A) $\text{1.7 m}$
(B) $\text{2.0 m}$
(C) $\text{2.3 m}$
(D) $\text{2.6 m}$
(E) $\text{8.0 m}$
2010 F = Ma, 9
A point object of mass $M$ hangs from the ceiling of a car from a massless string of length $L$. It is observed to make an angle $\theta$ from the vertical as the car accelerates uniformly from rest. Find the acceleration of the car in terms of $\theta$, $M$, $L$, and $g$.
[asy]
size(250);
import graph;
// Left
draw((-3,0)--(-23,0),linewidth(1.5));
draw((-13,0)--(-13,-14));
filldraw(circle((-13,-15),2),gray);
draw((-13,-15)--(-21,-15),dashed);
draw((-21,-14)--(-21,-1),EndArrow(size=5));
draw((-21,-1)--(-21,-14),EndArrow(size=5));
label(scale(1.5)*"$L$",(-21,-7.5),2*E);
// Right
draw((3,0)--(23,0),linewidth(1.5));
draw((13,0)--(13,-19),dashed);
draw((13,0)--(5,-12));
filldraw(circle((3.89,-13.66),2),gray);
label(scale(1.5)*"$\theta$",(12,-9),1.5*W);
real f(real x){ return 5x^2/12-95x/12+25; }
draw(graph(f,12,7),Arrows);
[/asy]
(A) $Mg \sin \theta$
(B) $MgL \tan \theta$
(C) $g \tan \theta$
(D) $g \cot \theta$
(E) $Mg \tan \theta$
2008 F = Ma, 9
A ball of mass $m_\text{1}$ travels along the x-axis in the positive direction with an initial speed of $v_{\text{0}}$. It collides with a ball of mass $m_\text{2}$ that is originally at rest. After the collision, the ball of mass $m_\text{1}$ has velocity $v_{\text{1x}}\hat{x}+v_{\text{1y}}\hat{y}$ and the ball of mass $m_\text{2}$ has velocity $v_{\text{2x}}\hat{x}+v_{\text{2y}}\hat{y}$.
Consider the following five statements:
$\text{I)} \ \ \ \ \ \ 0=m_{\text{1}}v_{\text{1x}}+m_{\text{1}}v_{\text{2x}}$
$\text{II)} \ \ \ \ \ m_{\text{1}}v_{\text{0}}=m_{\text{1}}v_{\text{1y}}+m_{\text{2}}v_{\text{2y}}$
$\text{III)} \ \ \ \ 0=m_{\text{1}}v_{\text{1y}}+m_{\text{2}}v_{\text{2y}}$
$\text{IV)} \ \ \ \ m_{\text{1}}v_{\text{0}}=m_{\text{1}}v_{\text{1x}}+m_{\text{1}}v_{\text{1y}}$
$\text{V)} \ \ \ \ \ m_{\text{1}}v_{\text{0}}=m_{\text{1}}v_{\text{1x}}+m_{\text{2}}v_{\text{2x}}$
Of these five statements, the system must satisfy
(a) $\text{I and II}$
(b) $\text{III and V}$
(c) $\text{II and V}$
(d) $\text{III and IV}$
(e) $\text{I and III}$
2009 F = Ma, 9
Through what net angle does the disk turn during the $3$ seconds?
(A) $\text{9 rad}$.
(B) $\text{8 rad}$.
(C) $\text{6 rad}$.
(D) $\text{4 rad}$.
(E) $\text{3 rad}$.