
International Edition---engineering Mechanics: Statics 4th Edition
4th Edition
ISBN: 9781305856240
Author: Pytel
Publisher: Cengage
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Chapter 1, Problem 1.70P
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An aluminum rod of length L
=
1m has mass density p = 2700 kg and
Young's modulus E = 70 GPa. The rod is fixed at both ends. The exact
natural eigenfrequencies of the rod are wexact
E
=
√
ρ
for n=1,2,3,. . . .
1. What is the minimum number of linear elements necessary to
determine the fundamental frequency w₁ of the system? Discretize
the rod in that many elements of equal length, assemble the global
system of equations KU = w² MU, and find the fundamental
frequency w₁. Compute the relative error e₁ = (w1 - wexact) /w exact
Sketch the fundamental mode of vibration.
2. Use COMSOL to solve the same problem. Show the steps necessary
to find the fundamental frequency and mode of the rod. What is the
relative error using linear elements and a normal mesh?
A ball with a mass of 5.0 kg is hanging from a string and is initially at rest.
A bullet with a mass of 10.0 g and a velocity of 200.0 m/s is fired at the ball.
The bullet embeds itself inside the ball.
How high (h) do the ball and the bullet rise?
Gravitational acceleration: g=9.81g = 9.81g=9.81 m/s².
Don't use chatgpt.
Need handwritten solution.
Mechanical engineering
Chapter 1 Solutions
International Edition---engineering Mechanics: Statics 4th Edition
Ch. 1 - A person weighs 30 lb on the moon, where...Ch. 1 - The radius and length of a steel cylinder are 40...Ch. 1 - Convert the following: (a) 400lbft to knm; (b)...Ch. 1 - A compact car travels 30 mi on one gallon of gas....Ch. 1 - The kinetic energy of a car of mass m moving with...Ch. 1 - In a certain application, the coordinate a and the...Ch. 1 - When a force F acts on a linear spring, the...Ch. 1 - In some applications dealing with very high...Ch. 1 - A geometry textbook gives the equation of a...Ch. 1 - A differential equation is d2ydt2=Ay2+Byt where y...
Ch. 1 - The position coordinate x of a particle is...Ch. 1 - A differential equation encountered in the...Ch. 1 - Determine the dimensions of constants A and B far...Ch. 1 - The typical power output of a compact car engine...Ch. 1 - Two 12-kg spheres are placed 400 mm apart. Express...Ch. 1 - Two identical spheres of radius 8 in. and weighing...Ch. 1 - A man weighs 170 lb on the surface of the earth....Ch. 1 - Use Eq. (1.4) to show that the weight of an object...Ch. 1 - Plot the earths gravitational acceleration g(m/s2)...Ch. 1 - Find the elevation h (km) where the weight of an...Ch. 1 - Calculate the gravitational force between the...Ch. 1 - The magnitudes of the two velocity vectors are...Ch. 1 - Determine the magnitudes of vectors v1 and v2 so...Ch. 1 - The pole AB is held up by the rope attached to B....Ch. 1 - Resolve the 20-kN force into components along the...Ch. 1 - The velocity vector of the boat has two...Ch. 1 - Two members of a truss apply the forces shown to...Ch. 1 - Two members of a truss apply the forces shown to...Ch. 1 - Determine the resultant of the position vectors A...Ch. 1 - Resolve the position vector A of the car (measured...Ch. 1 - Resolve the 360-lb force into components along the...Ch. 1 - The supporting cables AB and AC are oriented so...Ch. 1 - The two forces shown act on the structural member...Ch. 1 - The resultant of the two forces has a magnitude of...Ch. 1 - The forces acting on the bob of the pendulum are...Ch. 1 - A surveyor sights a target at C from points A and...Ch. 1 - Knowing that the resultant of the two forces is...Ch. 1 - To move the oil drum, the resultant of the three...Ch. 1 - The resultant of the 50-Ib and 30-lb forces is R....Ch. 1 - Obtain the rectangular representation of the force...Ch. 1 - The length of the position vector r is 240 mm....Ch. 1 - Determine the rectangular components of the 560-lb...Ch. 1 - The coordinates of points A and B are (-3, 0, 2)...Ch. 1 - The slider travels along the guide rod AB with the...Ch. 1 - Find the rectangular representation of the force...Ch. 1 - The magnitude of the force F is 160 lb. Find its...Ch. 1 - A rifle at A is fired at a target at B. If the...Ch. 1 - The pole OB is subjected to the 6004b force at B....Ch. 1 - The cables AB and AC are attached to the frame...Ch. 1 - The two forces are applied to the end of the boom...Ch. 1 - The magnitudes of the three forces are...Ch. 1 - Given that P=120lb and Q=130lb, find the...Ch. 1 - Knowing that P=90lb and that the resultant of P...Ch. 1 - If R is the resultant of the forces P and Q, find...Ch. 1 - The force R is the resultant of P and 0. Determine...Ch. 1 - The vertical post is secured by three cables. The...Ch. 1 - Compute the dot product A - B for each of the...Ch. 1 - Compute the cross product C=AB for each of the...Ch. 1 - Given r=4i6j+2km (position vector) F=20i+40j30kN...Ch. 1 - Compute AB and CB for the position vectors shown.Ch. 1 - Use the dot product to find the angle between the...Ch. 1 - Use the dot product to find the angle between the...Ch. 1 - Let A and B be two nonparallel vectors that lie in...Ch. 1 - Determine (a) the angle between the position...Ch. 1 - Find a unit vector that is perpendicular to both...Ch. 1 - The three points A(0,2,2),B(1,4,1), and C(3,0,0)...Ch. 1 - For the position vectors P and Q shown, determine...Ch. 1 - Compute the orthogonal Component of F=6i+20j12klb...Ch. 1 - Compute the value of the scalar a for which the...Ch. 1 - Resolve A=3i+5j4k in. into two vector...Ch. 1 - The force F=5i+12j+4k lb is applied to the handle...Ch. 1 - Determine the value of the scalar a if the...Ch. 1 - Resolve the force F=20i+30j+50klb into two...Ch. 1 - It can be show that a plane area may he...Ch. 1 - The coordinates of the corners of a triangle ABC...Ch. 1 - Show that |abc| equals the volume of a...
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