EBK ENGINEERING MECHANICS
15th Edition
ISBN: 9780137616909
Author: HIBBELER
Publisher: VST
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Chapter 21, Problem 42P
To determine
Derive the Euler equations of motion.
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2. Derive the equation of motion for the system shown in the figure below using Newton-Euler
method.
K1
cm
M, I cm
M2
Inextensible
K2
PROBLEM1:
Determine the equation of motion of the following systems:
1080
al*k
www
0.51
ghiv
Vin &
Mass Less, Rigid
L
J
Figure 2-Problem 1-2
a3*m
Question 1
Atwood's machine: Figure 1.4 is a sketch of Atwood's machine. It consists of masses
m¡ and m2 suspended by a massless inextensible string over a frictionless, massless
pulley. Evaluate the Lagrangian and obtain the equation of motion.?
V=0
X2 = 1 – x,
m2
m,
Figure 1.4 Atwood's machine.
Answer.
Chapter 21 Solutions
EBK ENGINEERING MECHANICS
Ch. 21 - Show that the sum of the moments of inertia of a...Ch. 21 - Prob. 2PCh. 21 - Prob. 3PCh. 21 - Determine the moments of inertia Ix and Iy of the...Ch. 21 - Prob. 5PCh. 21 - Determine by direct integration the product of...Ch. 21 - Prob. 9PCh. 21 - Prob. 10PCh. 21 - Determine the moment of inertia Ixx of the...Ch. 21 - Prob. 13P
Ch. 21 - Prob. 14PCh. 21 - Prob. 15PCh. 21 - The bent rod has a weight of 1.5 lb/ft. Locate the...Ch. 21 - If a body contains no planes of symmetry, the...Ch. 21 - Prob. 23PCh. 21 - Prob. 25PCh. 21 - Prob. 28PCh. 21 - Prob. 29PCh. 21 - Prob. 30PCh. 21 - The 2-kg thin disk is connected to the slender rod...Ch. 21 - Prob. 33PCh. 21 - Prob. 36PCh. 21 - Prob. 37PCh. 21 - Prob. 40PCh. 21 - Prob. 41PCh. 21 - Prob. 42PCh. 21 - Prob. 48PCh. 21 - Prob. 51PCh. 21 - Prob. 54PCh. 21 - Show that the angular velocity of a body, in terms...Ch. 21 - A thin rod is initially coincident with the Z axis...Ch. 21 - The top consists of a thin disk that has a weight...Ch. 21 - Prob. 66PCh. 21 - Prob. 69PCh. 21 - Prob. 70PCh. 21 - Prob. 73PCh. 21 - Prob. 74PCh. 21 - Prob. 77P
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- Q4) Derive the equation of motion of figure 4. www Slender bar of mass m Figure 4arrow_forwardA car is modeled as shown in Figure. Derive the equations of motion and find matrix M, C, and K. Mass = M, mass moment of inertia = JG .000 m1 k₂ F1 1 k2 000 k₁ k₁ m2 F2, X2 ellarrow_forwardDetermine the governing equation of motion for the system shown below as well as zeta, wn and tau D.arrow_forward
- derive the differential equation of motion. k. exxxe Larrow_forward* F2 # 3 E Problem 4. EOM Derivation Derive the equation of motion for the following system: We want to measure the spin rate w of the rotating shaft of a turbine. To do it we push a small mass m against the end of the shaft. The shaft makes friction contact with the drag cup mounted on the mass. The frictional torque is b (w). Assume that the rotational spring torque is ke and that the moment of inertia of mass m is J. J Rotating Shaft F3 @ $ 4 R b J, m Drag Cup F4 Q Search % 5 F5 T 0 Wall * A 6 F6 Y 2 * F7 & 7 PrtScn U F8 4 8 Home 6. F9 9 End F10 Po 0arrow_forwardPROBLEM1: Determine the equation of motion of the following systems: مد exiz ملية كريتا عامرات C, p(x,t) = (x) (1) m 20 k, ه a Figure I- Problem1-1 (ma massless rod .. ه سلم aarrow_forward
- * Find the equations of motion of the systems if you know: =mở tan6 5 =- In(ø) 16 R= Q = 0arrow_forwardConsider a satellite moving in a torque-free environment. The inertial frame and satellite body-fixed frame are represented by N-frame and B-frame, where {^₁, ŵ2, ñ3} and {b₁, 62, 63} are right-handed vector bases fixed in N-frame and B-frame, respectively. {1;} is aligned with the principal axis of inertia, where ☎₁ and 3 are associated with the minimum and maximum moments of inertia, respectively. Denote the satellite angular velocity by w = wib; and the inertia tensor about the CoM by Ic. Suppose that I at time t = 0 is given by: Ic(t = 0) = 2ñ₁ñ₁ +2.25 ñ¿Ñ₂ +2.25 ñ³Ñ3 – 0.75 ñ¿ñ3 −0.75 3₂ (dimensionless) Express the satellite inertia tensor about the CoM in B-frame. Determine [BN] at time t = 0, i.c., the direction cosine matrix (DCM) that represents the orientation of B-frame relative to N-frame.arrow_forward1. Draw the free-body diagram of the systmes depicted below and derive the differential equation describing the equation of motion (EOM) for each system. X (a) m - 3 kg k = 10 N m k₁ = N 3 kg m = www k₂ = 2 N m z (t) (b) (c) 1 = 7 m m = = 2 kgarrow_forward
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