CE3302 Dynamics
Spring 2012
Homework 22: Solutions
1. In the equilibrium position, the 10 kg cylinder causes a static deflection of 20 mm in the coiled spring.
If the cylinder is depressed an additional 20 mm and released from rest, calculate the resultin
CE3302 Dynamics
Spring 2012
Homework 23: Solutions
1. Assume that the mass and stiffness of the system shown are m 5 kips sec2 /in and k 40 kips/in .
If the system is set into free vibration with the initial conditions x(0) 0.7 in and x(0) 5.6 in/sec ,
de
CE3302 Dynamics
Spring 2012
Homework 20: Solutions
1. The 50 kg flywheel of a small hoisting engine has a radius of gyration 150 mm. If the power is cut off
when the angular velocity of the flywheel is 200 rpm clockwise, determine the time required for th
CE3302 Dynamics
Spring 2012
Homework 16: Solutions
h
36"
1. A 50 lb cabinet is mounted on casters that allow it to move freely on the floor (the coefficient of
friction is zero). If a 25 lb force is applied as shown, determine (a) the range of values of h
CE3302 Dynamics
Spring 2012
Homework 14: Solutions
1. At the instant shown, the angular velocity of bar D E is 15 rad/sec counterclockwise. Determine (a)
The angular velocity of bar A B , (b) the angular velocity of bar B D and (c) the velocity of the mid
CE3302 Dynamics
Spring 2012
Homework 21
1. The 2 oz bullet has a horizontal velocity of 1500 ft/sec as it strikes the 20 lb slender bar OA , which is
suspended from point O and is initially at rest. Determine the angular velocity which the bar with its
em
CE3302 Dynamics
Spring 2012
Homework 19: Solutions
1. The 3 kg slender rod AB is connected to a spring of constant k . The system is held at rest in the
horizontal position, when the spring is undeformed. When it is released, rod AB rotates downward
and s
CE3302 Dynamics
Spring 2012
Homework 18: Solutions
1. A slender rod of length l is pivoted about a point O located at a distance b from its mass center G . It
is released from rest from the horizontal position and swings freely. Determine (a) the distance
CE3302 Dynamics
Spring 2012
Homework 17: Solutions
A
O
AM
A
A
B
12
"
O
O
O
C
B
16.1 lb
32.2 lb
16.1 lb 16.1 lb
(a)
12
"
12
"
12
"
1. Each of the four drums are 12 inches in diameter and 64.4 lb in weight and has a radius of gyration
about its center of 9
CE3302 Dynamics
Spring 2012
Homework 12: Solutions
1. The angular velocity of the disk is defined by 2t 3 2t 2 1 rad/s , where t is in seconds.
Determine the magnitudes of the velocity and acceleration of point A on the disk when t 1 s .
Solution:
At t 1
CE3302 Dynamics
Spring 2012
Homework 15: Solutions
1. At the instant shown, the disk rotates about a fixed axis through O with angular velocity 10 rad/s
and angular acceleration 3 rad/s 2 in the directions shown. The slider A moves in the circular slot in
CE3302 Dynamics
Spring 2012
Homework 10:Solutions
1. Block B of mass 2 kg is initially at rest. Block A of mass 1.5 kg is traveling at a velocity shown with
a magnitude of 6 m/s before colliding with block B . If the coefficient of restitution for the col
CE3302 Dynamics
Spring 2012
Homework 13: Solutions
1. The wheel of radius r rolls without slipping, and its center O has a constant velocity v0 to the right.
Determine expressions for the magnitudes of the velocity v and acceleration a of point A on the r
CE3302 Dynamics
Spring 2012
Homework 11: Solutions
1. Particle A is instantaneously moving at a speed of 6 m/s in the direction shown. Determine the angular
momentum of particle A with respect to point O .
(k )
( )
j
(i )
Solution:
i
j
H O mA x A
yA
(v A
CE3302 Dynamics
Spring 2012
Homework 8: Solutions
1. The 2 kg block is pressed against a spring of constant 100 kN/m until the spring deforms
d 0.05 m from its undeformed length. If the block is then released on the smooth slope, determine
the highest poi
CE3302 Dynamics
Spring 2012
Homework 6: Solutions
1. A cylinder of mass m rests in a supporting carriage as shown ( 30, 45 ). Determine the
maximum acceleration a which the carriage may be given up the incline so that the cylinder does not
lose contact at
CE3302 Dynamics
Spring 2012
Homework 7
1. A 64.4 lb package is at rest on the horizontal surface when a constant force F of 50 lb is applied to it
as shown. The coefficient of kinetic friction between the package and the slope is 0.2. Determine the
distan
CE3302 Dynamics
Spring 2012
Homework 3
1. The path of a skier during the Winter Olympic Games is as shown. When the skier reaches point A ,
his speed is 25 m/s , which is increasing at a rate of 1 m/s 2 . Determine the magnitude of the skier's
acceleratio
CE3302 Dynamics
Spring 2012
Homework 9: Solutions
1. A 20 kg block is at rest on an incline when a constant force P is applied to it. The static and kinetic
coefficients of friction between the block and the incline are 0.4 and 0.3, respectively. Knowing
CE3302 Dynamics
Spring 2012
Homework 2
1. The position of a particle in curvilinear motion can be determined using the position vector in the form
of r (t ) 3sin( t )i 4cos(2 t ) j (5t 8) k ft . Determine the expressions that describe the velocity
and acc
CE3302 Dynamics
Spring 2012
Homework 5: Solutions
1. A truck loaded with a crate starts from rest and accelerates at a constant rate along a straight road for a
distance of 120 m. If the coefficient of static friction between the crate that the truck is s
CE3302 Dynamics
Spring 2012
Homework 1 Solutions
1. The acceleration of a particle is given by a 2t 10 , where a is in meters per second squared and t
is in seconds. Determine the velocity and displacement as functions of time. The initial displacement at
CE3302 Dynamics
Spring 2012
Homework 4
1. At a certain instant, cylinder B is moving down with a velocity of 6 m/s and an acceleration of 3 m /s 2 .
Determine the corresponding velocity and acceleration of cylinder A .
sB
sA
B
A
Solution:
Define the posit
CE 612
Spring 2006
Solutions to Assignment 4
3.1
A hydraulic jump is to be formed in a trapezoidal channel with a base width of 20 ft and
side slopes of 2:1. The upstream depth is 1.25 ft and Q=1000 cfs. Find the downstream
depth and the head loss in the
CE 612
Spring 2006
Solutions to Assignment 3
2.1
10 ft/s
Water is flowing at a depth of 10 ft with a velocity of 10 ft/s in a channel of rectangular
section. Find the depth and change in water surface elevation caused by a smooth
upward step in the channe
CE 612
Spring 2006
Solutions to Assignment 2
Classify each of the following flows as steady or unsteady from the viewpoint of the observer:
Flow
(a) Flow of river around bridge piers
(b) Movement of flood surge downstream
Observer
(1)
Standing on bridge
(
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