tutorial 13 planar dynamics of rigid body
Post on 30-Dec-2015
65 Views
Preview:
DESCRIPTION
TRANSCRIPT
Rotation about a fixed axis for a mass point
dt
dmm
vrarFr
vrv
rvr
mdt
d
dt
dm
dt
md
)(
MH
Fr dt
dAngular momentum:
Calculation of moment of inertia dmrrmI
m
ii 22
Circle:
Rectangle:
A bar:2
12
1mlIO
A BO
L
2
3
1mlII BA
x
y
O
2
12
1mhI x 2
12
1mbI y
)(12
1 22 bhmIO
O x
y
b
h
R2
4
1mRIO
2
8
1mRII yx
Example 1 A horizontal force F = 30 lb is applied to the 230-lb refrigerator as
shown. Friction is negligible. (a) What is the magnitude of the refrigerator’s acceleration? (b) What normal forces are exerted on the refrigerator by the floor at
A and B?
Solution: Assume the box doesnot tip over, then the box
has only horizontal velocity and acceleration.
NA NB
F
G28in
60in
28in
Vx, axxx
maF F
0 BAyNNGF
0141432 BAONNFM
Force equilibrium:
What’s the condition of F for tipping?
O
2ft/s2.4xa
lb7.80AN lb3.149BN
Example 2 Bar AB rotates with a constant angular velocity of 10 rad/s in the co
unterclockwise direction. The masses of the slender bars BC and CDE are 2 kg and 3.6 kg, respectively. The y axis points upward.
Determine the components of the forces exerted on bar BC by the pins at B and C at the instant shown.
Bx
By
Cy
Cx
B
C
C
D
ECx
Cy
1. Dynamics analysis:
xBCxx amCB G
yBCyy amCB
Moment equlibrium equations
BCBCyxyx ICCBB )35.02.0()35.02.0(
CDDCEy IC 40.0
Bx
By
Cy
Cx
2 Kinematics analysis
B
C
C
D
E
VBVC
At this instant, point A is the instantaneous center of BC.
ABABAB
BCABBCB
R
Rv
400
400
CDCDCE
BCACBCC
R
Rv
400
700
Cx
Cy
rad/s 10 ABBC
rad/s 5.174
7 BCCD
)(m/s jjja 2B 404.0100)( 2 ABAB R
BCBCBC2
BC RαR)(aa BCFrom AB-BC:
From CD: jijiaC CDCDCDCDCD α.RαR 405.122)( 2
top related