Transcript Notes for Dynamic Equilibrium - University of Dayton : Homepages

Section 6
Newton’s 2nd Law:
A body with unbalanced forces will
accelerate proportional to the unbalanced
force and in the direction of the force.
SF = ma
10 lb.
100 lb.
Inertial Force
 Define inertial force:
Fi = - ma
opposite to the acceleration
direction
 Then
SF + Fi = 0
Free Body Diagram
FBD
Fwind
W
Fi
a
v
Ff
FB
Problem 6-2:
An electric hoist is being used to raise crate A as
shown. The crate weighs 200 lbs. When the motor is
initially powered, it accelerates to 1800 rpm in 0.75
sec. Determine the tension in the cable during this
startup.
5 in
16 in
Problem 6-3:
The sports car shown has a wheel base of 112 in and
weighs 3400 lbs. The center of gravity has been
located as shown. The car has been tested to
accelerated from 0 to 60 mph in 8 sec. During this
test, determine the road force for each tire.
24 in
45 in
112 in
Problem 6-7:
The compressor mechanism shown is running at a
constant rate of 600 rpm, cw. The cylinder pressure
is 45 psig, and the piston weighs 0.5 lb. The weight
of all other links is negligible. For the instant shown,
determine the torque required to operate the
compressor.
1.5 in
650
8 in
2 in
45 psig
Problem 6-24:
A curve in a road, has a radius of 500 ft. The road is
slightly banked at a 100 angle. During a rain storm,
the coefficient of static friction between rubber tires
and the road is 0.4. Determine whether it is safe for a
2500 lb car to proceed through the curve at 55 mph.
500 ft
100
Problem 6-29:
For the position shown, the shaft is rotating at 400
rpm. Determine the compressive load on the spring.
The weights are 0.5 lb each
and the weight of the arms
is negligible.
4”
3”
3”
900
190
2”
2”
Inertial Torque
Newton’s 2nd Law also applies to links that
encounter angular inertia
SM = Ia
Define inertial torque: Ti = -Ia
Then:
SM + Ti = 0
Free Body Diagram
FBD
W
Fwind
Ti
a
Fi
a
v
Ff
FB
Problem 6-31:
The grinding disk, and shaft, shown is made of steel.
The motor that drives the disk is started and
accelerates to its rated speed of 1200 rpm in 1.25
seconds. Determine the torque transmitted to the
grinder shaft.
T
8 in
0.75 in
10 in
1 in
Problem 6-38:
Robotic arm BC has a mass of 15 kg and a moment of inertia
about its center of gravity of 3.5 kg m2. At the instant shown,
arm BC is lowering with an angular velocity of 3 rad/sec and
is accelerating at 8 rad/sec2. Determine the torque required to
operate joint B, and the reaction forces at that joint. .
250 mm
C
400
B
700 mm
Problem 6-46
For the windshield wiper linkage shown, determine
the instantaneous torque required to drive the
system and the side loads onto the motor shaft. The
motor rotates at a constant rate of 45 rpm,
counterclockwise. The friction force from the rubber
blade on the windshield is shown. The wiper and
arm assembly weighs 1.2 lbs, the center of gravity is
shown and the mass moment of inertia, relative to
an axis at the center of gravity, is 0.4 lb in s2. The
weight of all other links is negligible.
Problem 6-46 (con’t)
16 in
2 in
6 in
13 in
700
450
1.0 lb
3.5 in
14 in