EM311M - Dynamics
Exam 1
Monday, Sep 20, 2004
1. -4particle is moving in a straight line with a constant acceleration a. .it some time to > 0,
the corresponding position and velocity are xo and vol respectively. Derive the formulas for
position x ( t ) and velocity v ( t ) a t any time t (5 points)
2. The large and small hands of a clock meet a t noon. What time will they meet next again?
Give the answer in terms of a fraction (no decimal round off. please ...) i 5 points)
-
3. Can a particle moving on a curvilinear path have a zero acceleration (vector)? Explain.
(5 points)
- dv
- Y
at L, -
0-r
:/
=
~
L
bet
a,
L-
A&4
;
t
*:
.
j = CI
at- 0
P
--
Cc,
=
&%d
6 -
4
9
d y
4
f
-12
.
r4,(d
2
--3m
-
&-Jd
&.<,
C~
d
. ,,<rL<
,,
,
A
,-..&,-it
.-?PC(&
i
at
c'
-A
1
A
2
k-2
.
7:m L,".&~$
4.
Lb&4+
.&Ad
.
dd4z
4. Derive the formula for acceleration vector components a, and as in the polar system of
coordinates (5 points)
e, ,,(
o,
e, -- (-LC,
--r
-
v c
L
r e,r
c
e,@i?
r,
s,
-, - I ;.f ( r + r dx
=?
-
J~:;P~-E
1
r
.
-
A
..
r $,
+
(r
- c.;'ie.
'-uL/'
A,-
+
,
r -
.do
'
e < t ~ e $ ~
(
.
-e,8
J@;-
cic
+
z ; , j ,& jp,
w
.
,
+
6.6
5. .A particle moves along a parabola y = x2 with a constant speed v. Determine the
carteslan components of the velocitv vector as a function of coordinate x. (5 points)
u' -
-,%,/
x*
6. Water leaves the nozzle at 20" above the horizontal and strikes the wall at the point
indicated. What is the velocity of the water as it leaves the nozzle? Hint: Determine the
motion of the water by treating each particle of \rater as a projectile. (25 points)
7 . A car is tested on the track shown. Suppose that the tangential component of acceleration
of the car is given in terms of the car's position by at = 0.4 - 0.001s m/s2, where s is the
distance, the car travels along the track from point A. What are the car's velocity and
acceleration in terms of normal and tangential components a t point B ?
(25 points)
Vt/t
'-
7r* V
7
at;!
G,,: ?,
8. In the cam-follower mechanism, the slotted bar rotates with constant angular velocity
w = 12 rad/s, and the radial position of the follower A is determined by the profile of the
stationary cam. The slotted bar is pinned a distance h = 0.2m to the left of the center of
the circular cam. The folloer moves in a circular path .4 m in radius. Determine the velocity
of the follower when 0 = 40°,
(a) in terms of polar coordinates, and
=
/3 &
r
h,=. Z +
5
(b) in terms of cartesian coordinates.
(25 points)
r
'.
4-
"'7
&-01L(5.=q00