CE 403 Optional FE Review:
Dynamics
Chris Rehmann
Engineering Mechanics (Statics and Dynamics)
Statics
• Resultants of force systems
• Concurrent force systems
• Equilibrium of rigid bodies
• Frames and trusses
• Centroid of area
• Area moments of inertia
• Friction
Dynamics
• Linear motion
• Angular motion
• Mass moments of inertia
• Impulse and momentum
• Work, energy and power
• Friction
Linear motion: USF question 4.1
Angular motion
What are the angular velocity and linear speed
of the tip of a 0.1 m long second hand on a
clock?
a.
b.
c.
d.
1 rad/s, 0.1 m/s
0.1 rad/s, 0.01 m/s
60 rad/s, 0.1 m/s
60 rad/s, 0.6 m/s
Linear motion: Newton’s law
A 5-kg block of steel initially at rest on a steel
plate is subjected to a constant force of 25 N.
The coefficient of friction is 0.4. How far will the
block have traveled in 10 seconds?
a.
b.
c.
d.
4m
24 m
54 m
250 m
Projectile motion: USF question 4.2
Dynamics: USF question 4.3
Uniform circular motion
A curve of radius 500 m at a speedway is banked at
an angle of 22°. If drivers of racecars do not wish to
rely on friction, at what speed should they take this
curve?
a.
b.
c.
d.
50 mph
60 mph
70 mph
100 mph
Ohanian (1985), ch. 6, ex. 13
Angular and linear motion
Two masses are suspended from a string that
runs without slipping over a pulley of radius R
and moment of inertia I. Determine the linear
acceleration of the masses if m1 = 5 kg, m2 = 5.1
kg, R = 0.1, and I = 10-3 kg m2.
Impulse
In a crash test, a 1700-kg car collides with a wall.
The collision lasts 0.12 seconds, and the initial
and final speeds are 13.6 m/s and -1.3 m/s,
respectively. What is the impulse?
Ohanian (1985), ch. 10, ex. 1
Work and energy: bobsled run
A bobsled run at Lake Placid descends 148 m
from its highest point to its lowest point.
Suppose that a sled, initially at rest, slides with
negligible friction. What speed will the sled
attain at the lowest point?
a.
b.
c.
d.
0 m/s
21 m/s
54 m/s
148 m/s
Ohanian (1985), ch. 7, ex. 6
Spring-mass: USF question 4.4
Vibrations: effective springs
If the spring constants are k1 = 1 N/m and k2 =
0.5 N/m, what are the effective spring constants
for the two situations below?
k1
k2
k1
k2
Work: variable force
A spring has a spring constant of 4x104 N/m, and
it is initially relaxed. How much work must be
done to compress the spring by 0.1 m?
a.
b.
c.
d.
2J
20 J
200 J
2000 J
Elastic collisions
A boxcar of mass 20 metric tons moving at 5 m/s collides
with a stationary boxcar of mass 65 metric tons.
What are the resulting velocities of both boxcars?
Inelastic collision: Lindeburg ex. 44.13
A golf ball is dropped from an initial height of
2.4 m, and it rebounds to a height of 1.8 m.
What is the coefficient of restitution?
a.
b.
c.
d.
0.5
0.67
0.75
0.87