EBK ENGINEERING MECHANICS
15th Edition
ISBN: 9780137569830
Author: HIBBELER
Publisher: VST
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Chapter 2, Problem 17FP
To determine
The force as a Cartesian
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3. The figure shows a frame under the
influence of an external loading made up
of five forces and two moments. Use the
scalar method to calculate moments.
a. Write the resultant force of the
external loading in Cartesian vector
form.
b. Determine the
& direction
of the resultant moment of the
external loading about A.
15 cm
18 cm
2.2 N-m
B
50 N
45°
10 cm
48 N.m
250 N
60 N
20
21
50 N
25 cm
100 N
A
118,
27cm 5, 4:1
The 2-mass system shown below depicts a disk which rotates about its center and has rotational
moment of inertia Jo and radius r. The angular displacement of the disk is given by 0. The spring
with constant k₂ is attached to the disk at a distance from the center. The mass m has linear
displacement & and is subject to an external force u. When the system is at equilibrium, the spring
forces due to k₁ and k₂ are zero. Neglect gravity and aerodynamic drag in this problem. You may
assume the small angle approximation which implies (i) that the springs and dampers remain in
their horizontal / vertical configurations and (ii) that the linear displacement d of a point on the
edge of the disk can be approximated by d≈re.
Ө
K2
www
m
4
Cz
777777
Jo
Make the following assumptions when analyzing the forces and torques:
тв
2
0>0, 0>0, x> > 0, >0
Derive the differential equations of motion for this dynamic system. Start by sketching
LARGE and carefully drawn free-body-diagrams for the disk and the…
A linear system is one that satisfies the principle of superposition. In other words, if an input u₁
yields the output y₁, and an input u2 yields the output y2, the system is said to be linear if a com-
bination of the inputs u = u₁ + u2 yield the sum of the outputs y = y1 + y2.
Using this fact, determine the output y(t) of the following linear system:
given the input:
P(s) =
=
Y(s)
U(s)
=
s+1
s+10
u(t) = e−2+ sin(t)
=e
Chapter 2 Solutions
EBK ENGINEERING MECHANICS
Ch. 2 - Determine the magnitude of the resultant force...Ch. 2 - Two forces act on the hook. Determine the...Ch. 2 - Determine the magnitude of the resultant force and...Ch. 2 - Resolve the 30-lb force into components along the...Ch. 2 - The force F = 450 lb acts on the frame. Resolve...Ch. 2 - If force F is to have a component along the u axis...Ch. 2 - Determine the magnitude of the resultant force FR...Ch. 2 - Resolve the force F1 into components acting along...Ch. 2 - Resolve the force F2 into components acting along...Ch. 2 - Prob. 10P
Ch. 2 - Determine the angle for connecting member A to...Ch. 2 - Determine the magnitude and direction of the...Ch. 2 - Determine the magnitude and direction of the...Ch. 2 - Determine the magnitude and direction of FA SO...Ch. 2 - If the resultant force of the two tugboats is 3...Ch. 2 - If FB = 3 kN and = 45, determine the magnitude of...Ch. 2 - If the resultant force of the two tugboats is...Ch. 2 - Resolve each force acting on the post into its x...Ch. 2 - Determine the magnitude and direction of the...Ch. 2 - Prob. 9FPCh. 2 - If the resultant force acting on the bracket is to...Ch. 2 - If the magnitude of the resultant force acting on...Ch. 2 - Determine the magnitude of the resultant force and...Ch. 2 - Resolve each force acting on the gusset plate into...Ch. 2 - Determine the magnitude of the resultant force...Ch. 2 - Prob. 39PCh. 2 - Determine the magnitude of the resultant force and...Ch. 2 - Determine the magnitude of the resultant force and...Ch. 2 - Express F1, F2, and F3 as Cartesian vectors.Ch. 2 - Prob. 43PCh. 2 - Determine the magnitude and orientation of FB so...Ch. 2 - Prob. 48PCh. 2 - Express F1, F2, and F3 as Cartesian vectors.Ch. 2 - Prob. 56PCh. 2 - If the resultant force acting on the bracket is...Ch. 2 - Prob. 58PCh. 2 - If F = 5 kN and = 30, determine the magnitude of...Ch. 2 - Determine the coordinate direction angles of the...Ch. 2 - Prob. 14FPCh. 2 - Prob. 15FPCh. 2 - Prob. 16FPCh. 2 - Prob. 17FPCh. 2 - Prob. 18FPCh. 2 - Prob. 61PCh. 2 - Prob. 66PCh. 2 - Determine the magnitude and coordinate direction...Ch. 2 - Specify the magnitude and coordinate direction...Ch. 2 - Prob. 73PCh. 2 - Prob. 74PCh. 2 - Prob. 75PCh. 2 - Prob. 77PCh. 2 - Prob. 79PCh. 2 - Prob. 81PCh. 2 - Prob. 82PCh. 2 - If the direction of the resultant force acting on...Ch. 2 - Express the position vector rAB in Cartesian...Ch. 2 - Prob. 20FPCh. 2 - Express the force as a Cartesian vector. Prob....Ch. 2 - Prob. 22FPCh. 2 - Prob. 23FPCh. 2 - Prob. 24FPCh. 2 - Determine the length of the connecting rod AB by...Ch. 2 - Prob. 88PCh. 2 - Prob. 90PCh. 2 - Prob. 91PCh. 2 - Determine the magnitude and coordinate direction...Ch. 2 - Prob. 98PCh. 2 - Prob. 25FPCh. 2 - Determine the angle between the force and the...Ch. 2 - Prob. 27FPCh. 2 - Prob. 28FPCh. 2 - Find the magnitude of the projected component of...Ch. 2 - Prob. 30FPCh. 2 - Determine the magnitudes of the components of the...Ch. 2 - Determine the components of F that act along rodAC...Ch. 2 - Determine the magnitudes of the components of F =...Ch. 2 - Prob. 111PCh. 2 - Prob. 112PCh. 2 - Determine the angle between the two cables...Ch. 2 - Determine the angle between the cables AB and AC....Ch. 2 - Determine the magnitude of the projected component...Ch. 2 - Determine the magnitude of the projected component...Ch. 2 - Determine the magnitudes of the projection of the...Ch. 2 - Determine the magnitude of the resultant force FR...Ch. 2 - Prob. 5RPCh. 2 - Prob. 6RPCh. 2 - Prob. 7RPCh. 2 - Prob. 8RP
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