Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Chapter 2, Problem 2.45P
To determine
Whether an equilibrium state is stable or unstable when
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Suppose three forces with magnitudes of 198 N, 275 N, and 205 N are placed in equilibrium. If the 205-N force acts in the +y-direction, what is one of the two configurations in the xy-plane that the remaining forces may have? Give numerical values for the angles.
Q 03: a) Explain categories of equilibrium?
b) Define a dot product of two vectors A and B,
where A = Axi + Avi + Azk and B = Bxi + Byị + Bzk
Determine the equivalent force-couple system at the center O for each of the three cases of forces (F = 370 N) being applied along the edges of a square plate of side d = 480 mm. The couple is positive if
counterclockwise, negative if clockwise.
y
F
y
y
F
d
- x
F
Answers:
(a)
R =
j) N, Mo =
N-m
(b)
R =
j) N, Mo =
N-m
(c)
R =
j ) N, Mo =
N-m
+
Chapter 2 Solutions
Classical Dynamics of Particles and Systems
Ch. 2 - Prob. 2.1PCh. 2 - Prob. 2.2PCh. 2 - If a projectile is fired from the origin of the...Ch. 2 - A clown is juggling four balls simultaneously....Ch. 2 - A jet fighter pilot knows he is able to withstand...Ch. 2 -
In the blizzard of ’88, a rancher was forced to...Ch. 2 - Prob. 2.7PCh. 2 - A projectile is fired with a velocity 0 such that...Ch. 2 - Consider a projectile fired vertically in a...Ch. 2 - Prob. 2.11P
Ch. 2 - A particle is projected vertically upward in a...Ch. 2 -
A particle moves in a medium under the influence...Ch. 2 - A projectile is fired with initial speed 0 at an...Ch. 2 -
A particle of mass m slides down an inclined...Ch. 2 - A particle is projected with an initial velocity 0...Ch. 2 - A strong softball player smacks the ball at a...Ch. 2 - Prob. 2.19PCh. 2 - A gun fires a projectile of mass 10 kg of the type...Ch. 2 - Prob. 2.21PCh. 2 - Prob. 2.22PCh. 2 - A skier weighing 90 kg starts from rest down a...Ch. 2 - A block of mass m = 1.62 kg slides down a...Ch. 2 - A child slides a block of mass 2 kg along a slick...Ch. 2 - A rope having a total mass of 0.4 kg and total...Ch. 2 - A superball of mass M and a marble of mass m are...Ch. 2 - An automobile driver traveling down an 8% grade...Ch. 2 - A student drops a water-filled balloon from the...Ch. 2 - Prob. 2.31PCh. 2 - Two blocks of unequal mass are connected by a...Ch. 2 - A particle is released from rest (y = 0) and falls...Ch. 2 - Perform the numerical calculations of Example 2.7...Ch. 2 - Prob. 2.36PCh. 2 - A particle of mass m has speed υ = α/x, where x is...Ch. 2 - The speed of a particle of mass m varies with the...Ch. 2 - A boat with initial speed υ0 is launched on a...Ch. 2 - A train moves along the tracks at a constant speed...Ch. 2 - Prob. 2.42PCh. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - Consider a particle moving in the region x > 0...Ch. 2 - Prob. 2.48PCh. 2 - Prob. 2.49PCh. 2 - According to special relativity, a particle of...Ch. 2 - Let us make the (unrealistic) assumption that a...Ch. 2 - A particle of mass m moving in one dimension has...Ch. 2 - A potato of mass 0.5 kg moves under Earth’s...Ch. 2 - Prob. 2.55P
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- (a) Is it possible for an object to be in translation equilibrium ( the first condition) but not in rational equilibrium ( the second condition) ? Illustrate your answer with a simple example. (b) Can an object be in rational equilibrium yet not in translation equilibrium? justify your answer with a simple example.arrow_forwardThe diagram below shows a particle in equilibrium under the forces shown. Obtain an equation by resolving in the Ox direction, then obtain an equation by solving in the Oy direction, and then use these equation to find the unknown force and angle. y 45° 3 N 1 N P Ꮎ ; x 15√2 Narrow_forwardDetermine what should be the magnitude of P and F to keep theconcurrent force system in equilibrium.arrow_forward
- Determine the equivalent force-couple system at the center O for each of the three cases of forces (F = 340 N) being applied along the edges of a square plate of side d = 230 mm. The couple is positive if counterclockwise, negative if clockwise. y y F d F -d- F Answers: (a) R=( i i+ i j) N, Mo = i N-m (b) R= ( i i+ j) N, Мо- N-m (c) R= ( i i+ j) N, Mo = N-marrow_forwardA particle's potential energy as a function of position is given by U = 2 x³ – 3 x² – 9 x + 15, with x in meters and U in joules. Find the positions of any stable and unstable equilibria. Express your answers using three significant figures separated by a comma 5 ΑΣΦ x1, x2 = ? marrow_forwardShow that when A+B=C then A2+B2+2ABcos , where is the angle between vectors A and B .arrow_forward
- a) Cables AC and BC are connected to lifting points A & B, and joined together at C as shown in Figure Q1a. The angle = 200 and angle B = 50°. If the tension in each cable is 3.75 KN, calculate the force (F) and the angle a required to maintain point C in static equilibrium. Give your answers for F in kilonewtons (kN) and the angle a in degrees to two decimal places. A 3 F α B Oarrow_forwardIf three coplanar concurrent forces acting at a point be in equilibrium, then each force is proportional to the sine of the angle between the other two. F F, F sin B sin y %3D sin a F, 10arrow_forward63. To find the resultant of a concurrent force system, express each force as a Cartesian vector and add the i, j. k components of all the forces in the system. True False 64. A position vector ir ates one point in space relative to another point. True False 65. The tensile force developed in a continuous cable that passed over a frictionless pulley must have a constant magnitude throughout the cable to keep it in equilibrium. O True False 66. A cable can support only a compressive or "pulling" force. True False 67. In equilibrium, IF includes all the known and unknown forces which act on the particle. True O Falsearrow_forward
- 4. The 500-kg uniform beam is subjected to the three external loads shown. Compute the reactions at the support point O. The x-y plane is vertical. 15 kN-m 130% × 8 kN A B Lief 1.4 kN 1.8 m 1.8 m 1.2 m +arrow_forwardThe combined action of the three forces on the base at O may be obtained by establishing their resultant through O. Determine the magnitudes of R and the accompanying couple M. Assume F1 = 640 Ib, F2 = 590 lb, F3 = 690 Ib, a = 7.3 ft, b = 2.3 ft, c = 2.9 ft, and 0 = 47. F, 9. a Answers: R= i Ib M= i Ib-ftarrow_forwardDraw the free-body diagram showing all the forces (refer to the figure) A в E 6 ft 3 ft C 2 ft D1 ft 160 b 140 D 300 b Establish the 2nd condition of equilibrium (rotational equilibrium) using A. Point A as the pivot pt. B. Point B as the pivot pt.arrow_forward
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