MasteringEngineering: Lecture 7
1 of 7
https:/session.masteringengineering.com/myct/itemView?view=solutio.
Further Simplification of a Force and Couple System
Description: In this tutorial, students will replace force-couple systems with an equivalent for

MasteringEngineering: Lecture 8
1 of 11
https:/session.masteringengineering.com/myct/itemView?view=solutio.
Equilibrium in Three Dimensions
Description: Learning Goal: To be able to solve three-dimensional equilibrium problems using the equations of
equil

Soiurt cw"
section
Name (print neatly):
UC Merced
Engineering 057 Statics and Dynamics
Exam 1: 75 minutes
October 15, 2015
Directions: Students may use calculators and two-sides of an 8 1/2 x 11 note sheet. To receive
maximum credit, you must remember to

Quiz 2
Wednesday September 18, 2012
Given: the forces and couple acting in the beam as shown in the diagram.
Find: represent the resultant of the three forces and couple by a forcecouple system at point A.
Diagram:
3 kN
1.5 m
3.5 m
2.5 m
A
10 kN *m
160o
5

MasteringEngineering: Lecture 2
1 of 5
http:/session.masteringengineering.com/myct/itemView?view=solution.
Cartesian Vector Addition
Description: Includes Math Remediation. In this tutorial, students will find the Cartesian components of a force and
use t

487.
The gear reducer is subject to the couple moments shown.
Determine the resultant couple moment and specify its
magnitude and coordinate direction angles.
z
M2 = 80 lb ft
M1 = 60 lb ft
30
45
SOLUTION
x
Express Each:
M 1 = 560i6 lb # ft
M 2 = 801-cos 3

645.
The skewed truss carries the load shown. Determine the
force in members AB, BF, and EF and state if these
members are in tension or compression. Assume that all
joints are pinned.
d/ 2
C
d
D
P
d
P
SOLUTION
a + MF = 0;
B
E
- P(2d) + P(d) + FAB (d) = 0

MasteringEngineering: Lecture 8
1 of 3
http:/session.masteringengineering.com/myct/itemView?view=solution.
Equations of Equilibrium
Description: In this tutorial, students will determine the reaction forces on a static beam by using the equations of
equil

565.
Due to an unequal distribution of fuel in the wing tanks, the
centers of gravity for the airplane fuselage A and wings B
and C are located as shown. If these components have
weights WA = 45 000 lb, WB = 8000 lb, and WC = 6000 lb,
determine the normal

33.
The lift sling is used to hoist a container having a mass of
500 kg. Determine the force in each of the cables AB and
AC as a function of u. If the maximum tension allowed in
each cable is 5 kN, determine the shortest lengths of cables
AB and AC that

514.
The overhanging beam is supported by a pin at A and
the two-force strut BC. Determine the horizontal and
vertical components of reaction at A and the reaction at B
on the beam.
1m
A
SOLUTION
1.5 m
Equations of Equilibrium: Since line BC is a two-forc

MasteringEngineering: Lecture 6
1 of 7
http:/session.masteringengineering.com/myct/itemView?view=solution.
Moment of a Couple
Description: Includes Math Remediation. In this tutorial, students will calculate the moment of a couple and the net
moment of tw

MasteringEngineering: Lecture 4
1 of 7
http:/session.masteringengineering.com/myct/itemView?view=solution.
Coplanar Force Systems
Description: In this tutorial, students will use the spring equation to solve for unknown forces in two dimensions and find
t

MasteringEngineering: Lecture 1
1 of 6
http:/session.masteringengineering.com/myct/itemView?view=solution.
Finding Errors Using Dimensional Homogeneity
Description: Learning Goal: To understand how dimensional homogeneity can be used to find errors in alg

21.
Determine the magnitude of the resultant force FR = F1 + F2
and its direction, measured counterclockwise from the positive
x axis.
y
F1
250 lb
30
SOLUTION
x
FR = 2(250) + (375) - 2(250)(375) cos 75 = 393.2 = 393 lb
2
2
Ans.
45
393.2
250
=
sin 75
sin u

11.
Round off the following numbers to three significant
figures: (a) 58 342 m, (b) 68.534 s, (c) 2553 N, and
(d) 7555 kg.
SOLUTION
a) 58.3 km
b) 68.5 s
c) 2.55 kN
d) 7.56 Mg
Ans.
19.
A rocket has a mass of 250(103) slugs on earth. Specify
(a) its mass in

MasteringEngineering: Lecture 10
1 of 10
http:/session.masteringengineering.com/myct/itemView?view=solution.
The Method of Sections
Description: Includes Math Remediation. Learning goal: To apply the method of sections to find the forces in specific
memb

Given: 140 lb Force, F, is directed along the
diagonal of the rectangular parallelpiped whose
sides are in the ratio 2:3:6.
Find: Express F in Cartesian vector form.
Diagram:
Z
140 lb
2
Y
3
X
Calculations:
6
calculations
uF
F F (
)
uF
(0 3)i (0 6 ) j ( 2

Name (print neatly): J 5 a2]
UC Merced
Engineering 057 Statics and Dynamics
Exam 2: 75 minutes
December 8, 2015
Directions: Students may use calculators and two-sides of a 8 1/2 x 11 note sheet. To receive
maximum credit, remember to show your approach an

Name (print neatly): Sb \UTi 0L)
UC Merced
Engineering 057 Statics and Dynamics
Exam 1: 75 minutes
March 10, 2015
Directions: Students may use calculators and two-sides of a 8 V2 x 11 note sheet. To receive
maximum credit, remember to show your approach

Name (print neatly): S ("D ) MT? OIL)
UC Merced
Engineering 057 Statics and Dynamics
Exam 2: 75 minutes
May 5, 2015
Directions: Students may use Calculators and two-sides of a 8 1/2 x 11 note sheet. To receive
maximum credit, remember to show your approac

Name(printneatly):_section_
UC Merced
Engineering 057 Statics and Dynamics
Exam 1: 75 minutes
March 8, 2016
Directions: Students may use calculators and two-sides of an 8 x 11 note sheet. To receive
maximum credit, you must remember to show your FBD and s

< \
Name (print neatly): 3 o 07:00 section
UC Merced
Engineering 057 Statics and Dynamics
Exam 1: 75 minutes
March 8, 2016
Directions: Students may use calculators and two-sides of an 8 1/2 x 11 note sheet. To receive
maximum credit, you must remember to

MasteringEngineering: Lecture 3
1 of 6
https:/session.masteringengineering.com/myct/itemView?view=solution&.
Position Vectors
Description: Includes Math Remediation. In this tutorial, students will find the position vectors for two points that
have a comm

96.
Locate the centroid y of the area.
y
y
1
1 x2
4
1m
x
2m
SOLUTION
Area and Moment Arm: The area of the differential element is
y
1
1
1
'
= a1 - x 2 b .
dA = ydx = a1 - x2 b dx and its centroid is y =
4
2
2
4
Centroid: Due to symmetry
x = 0
Ans.
Applyin

122.
When a train is traveling along a straight track at 2 m/s, it
begins to accelerate at a = 160 v-42 m>s2, where v is in m/s.
Determine its velocity v and the position 3 s after the
acceleration.
s
SOLUTION
a =
dv
dt
dt =
dv
a
v
3
dt =
0
L
3 =
dv
-4
2

12155.
The race car travels around the circular track with a speed of
16 m>s. When it reaches point A it increases its speed at
at = (4 v1>4) m>s2, where v is in m>s. Determine the
3
magnitudes of the velocity and acceleration of the car when
it reaches p

47.
Determine the moment of each of the three forces about
point A.
F1
F2
250 N 30
300 N
60
A
2m
3m
4m
SOLUTION
The moment arm measured perpendicular to each force from point A is
d1 = 2 sin 60 = 1.732 m
B
F3
d3 = 2 sin 53.13 = 1.60 m
Using each force whe

77.
Determine the internal normal force, shear force, and
moment at points C and D in the simply-supported beam.
Point D is located just to the left of the 2500-lb force.
2500 lb
500 lb/ft
A
3 ft
SOLUTION
With reference to Fig. a, we have
a + MA = 0;
By(1

135.
The water-park ride consists of an 800-lb sled which slides
from rest down the incline and then into the pool. If the
frictional resistance on the incline is Fr = 30 lb, and in
the pool for a short distance Fr = 80 lb, determine how
fast the sled is