Engineering Mechanics - Dynamics
Chapter 20
Problem 20-1 The ladder of the fire truck rotates around the z axis with angular velocity 1 which is increasing at rate 1. At the same instant it is rotat
Engineering Mechanics - Dynamics
Chapter 15
Problem 15-1 A block of weight W slides down an inclined plane of angle with initial velocity v0. Determine the velocity of the block at time t1 if the co
Engineering Mechanics - Dynamics
Chapter 21
a
Iyz
0
2m a h
2
h( a
y)
h a y dy 2 2
1 mah 6
Iyz
1 mah 6
Problem 21-7 Determine by direct integration the product of inertia Ixy for the homogen
Engineering Mechanics - Dynamics
Chapter 14
Problem 14-1 A woman having a mass M stands in an elevator which has a downward acceleration a starting from rest. Determine the work done by her weight a
Engineering Mechanics - Dynamics
Chapter 13
Problem 13-1 Determine the gravitational attraction between two spheres which are just touching each other. Each sphere has a mass M and radius r. Given:
Engineering Mechanics - Dynamics
Chapter 12
Problem 12-1 A truck traveling along a straight road at speed v1, increases its speed to v2 in time t. If its acceleration is constant, determine the dist
ME 2580 Dynamics
Principle of Impulse and Momentum for Particles
Recall that Newtons second law for a particle may be
written as F ma , where F is the resultant force acting
on the particle and a is i
ME 2580 Dynamics
Relative Motion of Two Particles
The figure shows the paths of motion of
two particles A and B. The vectors r A and
r B represent the position vectors of A and
B relative to a fixed p
ME 2580 Dynamics
Power and Efficiency
The work done by a force F as a particle moves
from position 1 to position 2 is
U12
t2
F dr F v dt .
t1
The power generated by F at any instant is P F v dU dt .
ME 2580 Dynamics
Conservation of Energy for Particles
Conservative and Nonconservative Forces
Consider a particle that moves from position 1 to position
2 along one path (forward path) and back again
ME 2580 Dynamics
Dependent Motion: Pulley Problems
When two or more masses are connected
through a series of pulleys by cables or
ropes that do not stretch, the positions,
velocities and accelerations
ME 2580 Dynamics
Conservation of Linear Momentum for Particles
Under certain circumstances, the net impulse on a
particle (or system of particles) is zero, so the linear
momentum of the particle (or s
ME 2580 Dynamics
Impact of Particles
When two particles collide, the net impulse on the system (the two particles) is zero, so
the motion of the system must satisfy the principle of conservation of li
ME 2580 Dynamics
Principle of Work and Energy
Recall that Newtons second law for a particle may be
written as F ma , where F is the resultant force acting
on the particle and a is its acceleration. Re
ME 2580 Dynamics
Kinetics of Particles: Newtons Second Law
Until now we have been studying kinematics, that is, the study of motion without
regard to the forces that cause (or result from) the motion.
ME 2580 Dynamics
Curvilinear Motion Rectangular Components
General Concepts:
Position, Velocity, and Acceleration
If a particle does not move in a straight line,
then its motion is said to be curvilin
ME 2580 Dynamics
Relative Acceleration of Two Points Fixed on a Rigid Body
The figure depicts a rigid body moving in two
dimensions. The two points P and Q are fixed on the
body. At any instant of tim
ME 2580 Dynamics
Relative Velocity of Two Points Fixed on a Rigid Body
The figure depicts a rigid body moving in two
dimensions. The two points P and Q are fixed on the body.
At any instant of time, t
ME 2580 Dynamics
Point Moving on a Rigid Body (Sliding Contact)
The relative motion of two points fixed on a rigid body may be calculated using the
relative velocity and relative acceleration equation
ME 2580 Dynamics
Acceleration Profiles A Second Example
Given: A car has the acceleration profile
shown where a (t ) is in (m/sec).
Find:
v(t ) and s (t ) the speed and position
of the car as function
ME 2580 Dynamics
Acceleration Profiles
a (t )
2
a (t ) (m/s )
Given: A car has an acceleration profile as
shown. Its initial position and velocity are
(0) (0)
zero. ( s= v= 0 )
0.3
15
5
v(t ) = a (t )
ME 2580 Dynamics
Rectilinear (Straight Line) Motion
General Concepts:
Position, Velocity, and Acceleration
A particle P has rectilinear motion when it moves in a straight line. As shown in the
figure,
ME 2580 Dynamics
Curvilinear Motion Radial and Transverse Components
Radial and Transverse Components
Another way to describe the motion of P as it
moves along a curved path is to use radial and
trans
ME 2580 Dynamics
Curvilinear Motion Normal and Tangential Components
Normal and Tangential Components
Normal and tangential components refer to
components that are normal and tangential to
the path of
HW Problems due Monday, Feb: 9:
1343,14. 16, 17, 44
13755, 59, 62, 72, 80
ME 2580: Dynamics
Week 4: Equations of Motion: Rectangular
Components, Normal & Tangential
Components, FBD's
Class Today
o Ann
ME 2580 Dynamics - Equation Sheet #1
Motion Tangent to Path:
s = s (t )
a = a (t )
a = a(s)
ds
dt
dv
a=
dt
dv
= a (t )
dt
v
v=
dv = a ( t ) dt
ds = v ( t ) dt
a ( t=
) a=
0 constant
v ( t=
) v0 + a0
HWPmblems due Monday, Feb 2:
12~162,166,168,177,181,182
12491201209, 217, 231
ME 2580: Dynamics
Week 3: Curvilinear Motion: Radiai &Transverse
and Cylindri-I Components; Absolute,
Dependent Motion: Re