Found problems: 8
2017 F = ma, 16
A rod moves freely between the horizontal floor and the slanted wall. When the end in contact with
the floor is moving at v, what is the speed of the end in contact with the wall?
$\textbf{(A)} v\frac{\sin{\theta}}{\cos(\alpha-\theta)}$
$\textbf{(B)}v\frac{\sin(\alpha - \theta)}{\cos(\alpha + \theta)} $
$\textbf{(C)}v\frac{\cos(\alpha - \theta)}{\sin(\alpha + \theta)}$
$\textbf{(D)}v\frac{\cos(\theta)}{\cos(\alpha - \theta)}$
$\textbf{(E)}v\frac{\sin(\theta)}{\cos(\alpha + \theta)}$
2017 F = ma, 3
A ball of radius R and mass m is magically put inside a thin shell of the same mass and radius 2R. The system is at rest on a horizontal frictionless surface initially. When the ball is, again magically, released inside the shell, it sloshes around in the shell and eventually stops at the bottom of the shell. How far does the shell move from its initial contact point with the surface?
$\textbf{(A)}R\qquad
\textbf{(B)}\frac{R}{2}\qquad
\textbf{(C)}\frac{R}{4}\qquad
\textbf{(D)}\frac{3R}{8}\qquad
\textbf{(E)}\frac{R}{8}$
2017 F = ma, 4
Several identical cars are standing at a red light on a one-lane road, one behind the other, with negligible (and equal) distance between adjacent cars. When the green light comes up, the first car takes off to the right with constant acceleration. The driver in the second car reacts and does the same 0.2 s later. The third driver starts moving 0.2 s after the second one and so on. All cars accelerate until they reach the speed limit of 45 km/hr, after which they move to the right at a constant speed. Consider the following patterns of cars.
Just before the first car starts accelerating to the right, the car pattern will qualitatively look like the pattern in I. After that, the pattern will qualitatively evolve according to which of the following?
$\textbf{(A)}\text{first I, then II, and then III}$
$\textbf{(B)}\text{first I, then II, and then IV}$
$\textbf{(C)}\text{first I, and then IV, with neither II nor III as an intermediate stage}$
$\textbf{(D)}\text{first I, and then II}$
$\textbf{(E)}\text{first I, and then III}$
2017 F = ma, 12
A small hard solid sphere of mass m and negligible radius is connected to a thin rod of length L and mass 2m. A second small hard solid sphere, of mass M and negligible radius, is fired perpendicularly at the rod at a distance h above the sphere attached to the rod, and sticks to it.
In order for the rod not to rotate after the collision, the second sphere should have a mass M given by which of the following?
$\textbf{(A)} M = m\qquad
\textbf{(B)} M = 1.5m\qquad
\textbf{(C)} M = 2m\qquad
\textbf{(D)} M = 3m\qquad
\textbf{(E)}\text{Any mass M will work}$
2017 F = ma, 15
An object starting from rest can roll without slipping down an incline.
Which of the following four objects, each a uniform solid sphere released from rest, would have the largest speed after the center of mass has moved through a vertical distance h?
$\textbf{(A)}\text{a sphere of mass M and radius R}$
$\textbf{(B)}\text{a sphere of mass 2M and radius} \frac{R}{2}$
$\textbf{(C)}\text{a sphere of mass }\frac{M}{2} \text{ and radius 2R}$
$\textbf{(D)}\text{a sphere of mass 3M and radius 3R}$
$\textbf{(E)}\text{All objects would have the same speed}$
2017 F = ma, 11
A small hard solid sphere of mass m and negligible radius is connected to a thin rod of length L and
mass 2m. A second small hard solid sphere, of mass M and negligible radius, is fired perpendicularly
at the rod at a distance h above the sphere attached to the rod, and sticks to it.
A: h = 0
B: h = L/3
C: h = L/2
D: h = L
E: Any L will work
2017 F = ma, 18
A uniform disk is being pulled by a force F through a string attached to its center of mass. Assume
that the disk is rolling smoothly without slipping. At a certain instant of time, in which region of the
disk (if any) is there a point moving with zero total acceleration?
A Region I
B Region II
C Region III
D Region IV
E All points on the disk have a nonzero acceleration
2017 F = ma, 1
A motorcycle rides on the vertical walls around the perimeter of a large circular room. The friction coefficient between the motorcycle tires and the walls is $\mu$. How does the minimum $\mu$ needed to prevent the motorcycle from slipping downwards change with the motorcycle's speed, $s$?
$\textbf{(A)}\mu \propto s^{0} \qquad
\textbf{(B)}\mu \propto s^{-\frac{1}{2}}\qquad
\textbf{(C)}\mu \propto s^{-1}\qquad
\textbf{(D)}\mu \propto s^{-2}\qquad
\textbf{(E)}\text{none of these}$