99
Question 317
A particle of mass m is attached to an inextensible massless rope of length l as shown
in Fig. P3-17. The rope is attached at its other end to point A located at the top of
a xed cylinder of radius R . As the particle moves, the rope wraps
88
Chapter 3. Kinetics of Particles
Question 312
A particle of mass m is attached to a linear spring with spring constant K and unstretched length r0 as shown in Fig. P3-12. The spring is attached at its other end at
point P to the free end of a rigid mas
Chapter 4
Kinetics of a System of Particles
Question 41
A particle of mass m is connected to a block of mass M via a rigid massless rod of
length l as shown in Fig. P4-1. The rod is free to pivot about a hinge attached to
the block at point O . Furthermor
Kinetics
of particles
Objectives:
Apply Newtons Laws of Motion to single-particle problems
Precious moments
Orbital mechanics
Linear Momentum Balance (LMB)
Fi L
i
L mv
Fi m a
i
Cannonball
A cannonball with mass m is launched from a boat. Assume an air
Multiparticle
Systems
Center of Mass
rCM ?
mrCM
m i ri
i
m i ri/CM 0
i
Linear Momentum and Newton II
Li
L
d
m i ri
dt
Li m
d
rCM
dt
i
d
L
dt
ma CM
Fi ma CM
i
Conservation of Linear Momentum
Fi 0
i
L const
Kinetic and Potential Energy
Ek ? #
Ep ? #
Lets
1
Machining Experiments
This handout -based on Dr. Ts PhD Thesis- demonstrates linear system identication from a series of tool vibration measurements in turning of aluminium.
The motivation behind this work was to gather a consistent set of data to
valid
Problem
Simulink Model
m& + cx + kx = 0
x&
c
k
&
& = x x
x
m
m
25 .5
c
Divide
x_dotdot
1
s
10
xo
Add
m
Integrator
100
Initial value of x
Divide 1
1
s
1
Initial value of x
0
k
x_dot
_dot
x
xo
Scope
Integrator 1
Response
1
Amplitude (m)
0.5
0
-0.5
0
0.5
1
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64
Chapter 3. Kinetics of Particles
Question 35
A collar of mass m is constrained to move along a frictionless track in the form of a
logarithmic spiral as shown in Fig. P3-5. The equation for the spiral is given as
r = r0 ea
where r0 and a are constants
113
Question 322
A particle of mass m is attached to a linear spring with spring constant K and unstretched length r0 as shown in Fig. P3-22. The spring is attached at its other end to
a massless collar where the collar slides along a frictionless horizon
123
Question 325
A particle of mass m slides without friction along a track in the form of a parabola as
shown in Fig. P3-25. The equation for the parabola is
y=
r2
2a
where a is a constant, r is the distance from point O to point Q, point Q is the projec
140
Chapter 4. Kinetics of a System of Particles
Question 43
A block of mass m is dropped from a height h above a plate of mass M as shown in
Fig. P4-3. The plate is supported by three linear springs, each with spring constant K ,
and is initially in stat
152
Chapter 4. Kinetics of a System of Particles
Question 417
A dumbbell consists of two particles A and B each of mass m connected by a rigid
massless rod of length 2l. Each end of the dumbbell slides without friction along a
xed circular track of radius