Styrofoam pellets. We will assume that when an object enters the pit its acceleration is
given by
2
a
g
cs
=
−
, where
g
is the acceleration of gravity,
c
is a constant and
s
is the
distance below the surface of the particles in the pit.
If the velocity of a mass is
v
0
at the surface of the particles, find
a) the distance it will need to stop, that is, the minimum depth of the loose particles
so that the mass does not hit the bottom of the pit
b) the time it will take to stop. Hint: You may assume that you know the velocity as a
function of
s
in the particles,
v
(
s
)
.
For both parts a) and b) it is sufficient to leave your solution in the form of a definite
integral with proper limits of integration.

Name: ________________________________
Problem 2.
The cam is designed so that the center of the
roller
A
which follows the contour moves on a limaçon
defined by
cos
r
b
c
θ
=
−
, where
b
>
c
.
If the cam does not
rotate, determine the magnitude of the total acceleration of
A
in terms of
b
,
c
, and
θ
if the slotted arm revolves with a
constant counterclockwise angular rate
!
θ
=
ω
.

Name: ________________________________
Problem 3.
An excursion train traveling 30 mph
from left to right in the picture encounters a rain
shower.
Point A lies 7 ft. directly beneath the lip
of the overhang on the observation car.
The
raindrops are falling straight down at a constant
speed of 25mph.
a. What is the velocity of a raindrop with respect
to an observer in the train?
b. How far onto the observation platform will the
raindrops land?
v
train
Observation platform

Name: ________________________________
Problem 4.
In a 5-meter-high
tunnel, a projectile is launched at
an angle of
θ
= 35° from the floor,
as shown.
Determine the correct
launch velocity to maximize the
horizontal range of the projectile
without hitting the top of the tunnel.
Do not calculate the range.

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- Spring '08
- josephmansour