This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: C15 MEEN 221 Summer 2009  Worksheet 15 Dr. A. Palaggolo
(1) HWSlS Ch 13 (105, 108, 111, 112) (— ‘D we Tues. 3‘2, {8
(2) Attendance Mandatory for 10:00 am — 12:39pm, unless excused by instructor. Multiple Quizzes may be given anytime during this period.
(3) Today’s Material: Kinematics Curvilinear Motion Section 13.5 FINAL EXAM WILL BE HELD ONT” ESOAV, «11 AUGUST
10:30 am—12z30 pm ZACH 104B (I) Plane 'Curvilinear Motion Consider a particle P' that travels along the path P in the xy "lane as shown
in Figure 1. Y) may :1“ “oP ‘ y  RECmu in km
. QOQO\HAT€S Rectangular: Since x(t) and y(t) locate particle P the rectangular
coordinate motion quantities are: POSITION: R = x(t)z° '+ y(t)}' (1)
VELOCITY: I7 =' Vj + Vyj' = xi + y} ‘ (2)
ACCELERATION: ii = aj + ay} = fo + 17,} = + (3)
Polar: The polar coordinate unit vectors vary in direction with time as they follow the particle, although their magnitudes remain equal to one, as
shown in Figure. 2 I Figure 2. Polar Coordinate Unit Vec‘lbrs Note. that Aé, = (1A 60!?a (4) A so ‘ é, = EEAA‘géa = 9 ég (5)
Similarly a, = —9' (E, ' (6)
So that if ‘ Rp(t)=ré, (7) _. d
V t=" + — é 2V ér + V9 éa ' V
5P =§;(I7P)=a'rér +a9 ée +fér + féﬁﬂ +réé9 + :> ar=i"—r92 (10)
as ﬂawa (11) Normal  Tangential
The tangential and normal unit vectors vary in direction with time as ' they follow the path of particle P, although their magnitudes remain equal to
one, as shown in Fig. 3. .. a; 42.97111.. 1_+__6_3}ae:2_;;: ‘ “a . a7.
, : V 0 = L
Then smce 0&— a 14
. 17P=Vé, /  JO ( )
.  V2 (15)
(16) 59/3 1723'1‘3'”: 5 Particle is f°11°wing a .Spiral path given by r(t) agate 9(t) is in radians and r is in millimeters. Given that 6 = ID/t 'Ead/s and that e = 0 When t = 1 S,.determine the velocity and acceleration l . r . o
16f the particle when 6 = 240 o 13,110* A collar that slides around a circular wine hasa pin that isﬁ sconstrained to move in the slot of arm AB. The arm rotates oounter— 'élockwise at a constant angular speed I of w = 2 rad/s. When_the arn; is 30° ,L :above the horizontal, :a. Determine the radial distanoe r '
' from the pivot A to the pin 3. Sb. Determine the velocity compdnents VI and v9 o§,the‘tollar. io. Determine theaGCeleration ‘ components a? and as of the collar. “d. Verify that the velocity vettor
' V is directed along the wire. 13—118 Arm AC of the‘cam follower mechanism shown is rotating at a
constant angular speed of 0 s 150 _ r
rev/min. A spring holds the pin
3 against the cam lobes. If the
equation that describes the shape
of the cam lobes is . R = 125 f 50 cos 39
phere R is in millimeters, a. Calculate and plot the
'magnitude of the velocity VB and the acceleration a8 ( bf the pin 8 as functions
0 '0 of 9 forO < 9 < 180 . r .
b. Will the shape of the
' curves change if the
angular speed 0 is doubled? % Note Sheet 0: ENGR 221 _ . Instructor Dr. Alan Palazzolo clear
.=linspace(0,0.l,500); thetadot=31.4;
theta_radians=thetadot*t; R=125+50*cos(3*theta_radians);
Rdot=—150*thetadot*sin(3.*theta_radians);
Rdotdot=450*thetadot“2*cos(3*theta_radians);
magnitude_VB=sqrt(Rdot.*Rdot+thetadot“2*R.*R); magnitude_aB=sqrt( (Rdotdot—thetadot“2*R).*(Rdotdot—thetadot“2*R) + 4*thetadot“2*Rdot.*Rdot); % convert theta to degrees, V to m/s and a to m/s“2 , then plot subplot(2,l,l)
plot(theta_radians*57,magnitude_VB/lOOO,'k—'); title('Magnitudes of Velocity and Acceleration for thetadot =3l.4 rad/sec')
xlabel('theta in degrees'); ylabel(‘Velocity in m/s'); grid on subplot(2,l,2)
plot(theta_radians*57,magnitude_aB/lOOO,'k—');
xlabel('theta in degrees');
ylabel('Acceleration in m/SAZ'); grid on Velocity in m/s Acceleration in m/s2 3.5 160 150 140 _.
03
O Magnitudes of Velocity and Acceleration for thetadot =15.71 rad/sec
l l l . . . 4 . . _ . _ I _ _ _ _ _ a _ . . _ _ I . . _ _ _ _ 60 80 100 120 140 1 60 180 theta in degrees 20 40 _ _ _ _ . _ . . _ _ _ h . _ . _ . _ i _ _ _ _ _ _ . _ _ _ . _ _ 4 _ _ _ . _ _ . _ _ _ _ _ . a _ . . . _ _ . _ _ _ _ _ _ _ _ _ _ _ r . _ _ _ _ _ h . . . . . . I . _ . . . _ _ _ _ _ _ . A
100 120 140 160 180 a
theta in degrees Magnitudes of Velocity and Acceleration for thetadot =31.4 rad/sec P
m .b Velocity in m/s .03
m 0 20 40 60 80 100 120 140 160 180
theta in degrees 650 600 A U1 ()1
01 O 01
O O O A
O
O Acceleration in m/s2 350 300 250
0 20 40 60 80 1 00 120 140 160 180 theta in degrees ...
View
Full
Document
This note was uploaded on 07/16/2009 for the course MEEN 221 taught by Professor Mcvay during the Spring '08 term at Texas A&M.
 Spring '08
 McVay

Click to edit the document details