B mg F OA F OA mg 2mg N A B A x y ME 274 – Summer 2020 SOLUTION Final Examination (AM) Problem No. 1 Given: Particle B (having a mass of m) is connected to ground at O with a link OB (having a length of L and negligible mass). OB is released from rest with a horizontal orientation. At its bottom-most position, B strikes stationary block A, which has a mass of 2m. The coefficient of restitution for this impact is e = 0.8 . Find: Determine the maximum height h above the line of impact that B reaches after impacting A. Leave your answer in terms of, at most, m, g and L. SOLUTION From 1 (release) to 2 (immediately before impact): FBD of B Work/energy: T 1 + V 1 + U 1 →2 nc ( ) = T 2 + V 2 ⇒ mgL = 1 2 mv B2 2 ⇒ ! v B2 = − 2 gL ˆ i From 2 to 3 (immediately after impact): FBD of A, B and link OB Linear impulse/momentum and COR: F x ∑ = 0 ⇒ mv B2 = mv B3 + 2mv A3 ⇒ v A3 = v B2 − v B3 ( ) /2 e = v B3 − v A3 v A2 − v B2 ⇒ v B3 = v A3 − ev B2 = v B2 − v B3 ( ) /2 − ev B2 ⇒ 1 + 2 ( ) v B3 = 1 − 2e ( ) v B2 ⇒ v B3 = − 1 3 1 − 2e ( ) 2 gL From 3 to 4 (maximum height): FBD (same as FBD for from 1 to 2): Work/energy: T 3 + V 3 + U 3 →4 nc ( ) = T 4 + V 4 ⇒ 1 2 mv B3 2 = mgh ⇒ h = 1 2 v B3 2 g = 1 2 1 − 2e 3 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 2 gL ( ) 2 g = 1 − 2e 3 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 L = L 25 A B m 2m g L line of impact h O From July 16 tutorial session
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ME 274 – Summer 2020 SOLUTION Final …...2A B Om L 2m g L Flineofimpact 1h B mg F OA F OA Bmg 2mg N A B A x y A B Om L 2m g L lineofmpact h B mg F OA OA mg ( 2mg N A B A x From
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A
B
m
L
2m
g
L
line of impact h
O B
mg
FOA
FOA
mg 2mg
N A
B A
x
y
A
B
m
L
2m
g
L
line of impact h
O B
mg
FOA
FOA
mg 2mg
N A
B A
x
y
ME 274 – Summer 2020 SOLUTION Final Examination (AM) Problem No. 1 Given: Particle B (having a mass of m) is connected
to ground at O with a link OB (having a length of L and negligible mass). OB is released from rest with a horizontal orientation. At its bottom-most position, B strikes stationary block A, which has a mass of 2m. The coefficient of restitution for this impact is e = 0.8 .
Find: Determine the maximum height h above the
line of impact that B reaches after impacting A. Leave your answer in terms of, at most, m, g and L.
SOLUTION From 1 (release) to 2 (immediately before impact): FBD of B Work/energy:
T1 +V1 +U1→2
nc( ) = T2 +V2 ⇒ mgL = 12
mvB22 ⇒ !vB2 = − 2gLi
From 2 to 3 (immediately after impact): FBD of A, B and link OB Linear impulse/momentum and COR:
From 3 to 4 (maximum height): FBD (same as FBD for from 1 to 2): Work/energy:
T3 +V3 +U3→4nc( ) = T4 +V4 ⇒ 1
2mvB3
2 = mgh ⇒
h = 12
vB32
g= 1
21− 2e
3⎛⎝⎜
⎞⎠⎟
2 2gL( )2g
= 1− 2e3
⎛⎝⎜
⎞⎠⎟
2
L = L25
A
B
m
L
2m
g
L
line of impact h
O
From July 16 tutorial session
ME 274 – Spring 2009 Name
Final Examination
PROBLEM NO. 2 – 20 pts
Given: A simple pendulum, consisting of a particle A of mass mA and a rigid massless
link OA of length L, is released from rest when OA is horizontal. At the instant
when OA has rotated into a vertical orientation, particle A strikes stationary
particle B, of mass mB, causing B to slide along a horizontal track. Let e
represent the coefficient of restitution for the impact of particles A and B.
Find: For this problem, determine
a) the velocity of the particle A immediately prior to impacting particle B.
b) the velocity of the particle B immediately after being struck by particle A.
c) the distance x that particle B slides over the rough portion of the surface
before coming to rest.
Use the following parameters in your analysis: mA = 2 kg, mB = 3 kg, L = 3 m, e = 0.6,
and μk = 0.2 (over the rough portion of the path of B).
A
B
g
3
4
L
m F smooth
A
B
F
N A
NB
mg
θ
x
y
From July 21 tutorial session
ME 274 – Fall 2008 Name
Examination No. 3
PROBLEM NO. 1
Given: A thin, homogeneous bar having a length of L and mass m moves within a
HORIZONTAL plane. Ends A and B of the bar are constrained to move along
smooth walls that are perpendicular to each other. A force F acts at the center
of mass G of the bar in the x-direction. The bar is released from rest when ! =
53.13°.
Find: Determine the angular acceleration of the bar on release. Use m = 100 kg, L
= 5 meters and F = 500 N. Use the figure provided below for the FBD of your
analysis. As always, clearly show the four steps of your analysis.
A
B
G F
smooth
smooth !
B
G x
y
A
ME 274 – Summer 2020 SOLUTION Final Examination (AM) Problem No. 2 Given: A thin, homogeneous bar AB has a length of L and a mass
of m. The bar is held in place against a smooth horizontal surface at A and a smooth vertical surface at B, with the bar having an orientation as shown in the figure. With a horizontal force F acting to the left at end A of the bar, the bar is released from rest.
Find: Determine the angular acceleration of the bar on release.
Express your answers in terms of, at most, m, L, F and g. SOLUTION 1. FBD 1. Newton/Euler Fx∑ = −F + NB = maGx ⇒ NB = maGx + F
Fy∑ = −mg + N A = maGy ⇒ N A = m g + aGy( )
MG∑ = N AL2
cosθ⎛⎝⎜
⎞⎠⎟− NB
L2
sinθ⎛⎝⎜
⎞⎠⎟− F
L2
sinθ⎛⎝⎜
⎞⎠⎟= IGα ⇒
m g + aGy( ) L2
cosθ⎛⎝⎜
⎞⎠⎟− maGx + F( ) L
2sinθ
⎛⎝⎜
⎞⎠⎟− F
L2
sinθ⎛⎝⎜
⎞⎠⎟= 1
12mL2⎛
⎝⎜⎞⎠⎟α ⇒
(1)
g + aGy( )cosθ − aGx +Fm
⎛⎝⎜
⎞⎠⎟
sinθ − Fm
sinθ = 16
Lα
3. Kinematics
!aB = !aA +!α × !rB/ A −ω 2!rB/ A
aB j = aAi + α k( )× −Lcosθ i + Lsinθ j( ) = aA − Lαsinθ( ) i + −Lαcosθ( ) j ⇒
j : aB = −Lαcosθ
!aG = !aB +
!α × !rG / B −ω 2!rG / B
= −Lαcosθ( ) j + α k( )× L2
cosθ i − L2
sinθ j⎛⎝⎜
⎞⎠⎟= L
2αsinθ
⎛⎝⎜
⎞⎠⎟
i + − L2αcosθ
⎛⎝⎜
⎞⎠⎟
j
4. Solve Using equation (1):
g − L2αcosθ
⎛⎝⎜
⎞⎠⎟
cosθ − L2αsinθ + 2 F
m⎛⎝⎜
⎞⎠⎟
sinθ = 16
Lα ⇒
!α =
gcosθ − 2 F / m( )sinθ
1/ 6( )L+ L / 2( ) cos2θ + sin2θ( )⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
k
= 32L
gcosθ − 2 F / m( )sinθ⎡⎣ ⎤⎦ k = 0.9 gL− 2.4 F
mL⎡
⎣⎢
⎤
⎦⎥ k
A
B
g
3
4
L
m F smooth
g
A
B
O
C
no slip
3R
2R
m
m
Position1(releasedfromrest)
A B
O
C
Position2(ABhorizontal)
A B
O
C = IC
N f
mg
mg
datum
A B
O
C
2R 2R
2R 2R
2R g
A
B
O
C
no slip
3R
2R
m
m
Position1(releasedfromrest)
A B
O
C
Position2(ABhorizontal)
A B
O
C = IC
N f
mg
mg
datum
A B
O
2R 2R
2R 2R
2R VO
C = IC
ME 274 – Summer 2020 SOLUTION Final Examination (AM) Problem No. 3 Given: A thin, homogeneous bar AB (having a mass
of m) is pinned to a homogeneous disk at ends A and B, with A and B at a radial distance of 2R from the disk’s center C. The disk has a mass of m and an outer radius of 3R. The system is released from rest at a position where A is on the same horizontal line as O and B located directly above O. The disk is able to roll without slipping on a horizontal surface, as shown in the figure.
Find: Determine the angular speed of the disk when the disk has rotated to a position
where AB is horizontal under the disk center O. Express your answer in terms of, at most, m, R and g.
SOLUTION
1. FBD 2. Work/energy
T1 = 0 ; I .A.R.V1 = mgR ; "+ " above datum
T2 =12
IC( )bωb2 + 1
2IC( )d ωd
2 = 12
IC( )b + IC( )d⎡⎣
⎤⎦ω
2 ; ωd =ωb =ω
V2 = −mg 2R( ) ; "− " below datum
U1→2nc( ) = 0
where:
IC( )d = 12
m 3R( )2 + m 3R( )2 = 272
mR2
IC( )b =1
12m 2 2R( )2 + m 3R − 2R( )2 = 2
3+ 3− 2( )2⎡
⎣⎢
⎤
⎦⎥mR2
Therefore:
T1 +V1 +U1→2
nc( ) = T2 +V2 ⇒ mgR = 12
IC( )b + IC( )d⎡⎣
⎤⎦ω
2 − 2mgR
3. Kinematics – none needed
4. Solve
ω =mgR 1+ 2( )IC( )b + IC( )d
= 1+ 2856+ 3− 2( )2
gR
g
A
B
O
C
no slip
3R
2R
m
m
Position1(releasedfromrest)
A B
O
C
Position2(ABhorizontal)
yB t( ) 2m
k k 2k
3k A
B
m
x yA t( )
2m
k k 2k
3k A
B
m
x
yB t( ) 2m
k k 2k
3k A
B
m
x
2k yB − x( )
k yB − x( ) 2mg
N2 N1
3kx
ME 274 – Summer 2020 Name Quiz 8 Problem No. 1 Derive the differential equation of motion (EOM) for the system below in terms of the coordinate of x. Base B has a prescribed motion of: xB t( ) = bsinΩt . Provide all details of your work, including FBDs.
From Quiz 8
ME 274 – Summer 2020 SOLUTION Final Examination (AM) Problem No. 4 Given: A system is made up of a cart B
(having a mass of m) and block A (having a mass of 2m). The system is interconnected by a set of springs, as shown in the figure. Cart B is given a prescribed motion of yB t( ) = bsinΩt . The springs are all unstretched when
x = yB = 0 .
Find: For this problem:
a) Derive the dynamical equation of motion (EOM) for this system in terms of the coordinate x. You must clearly show your four steps in your derivation, including appropriate FBD(s).
b) What is the numerical value for the natural frequency for the system? c) Determine the particular solution of your EOM derived in a) above. Leave
your answer in terms of b. d) Does the response found in c) above show A moving in-phase or out-of-
phase with B? Use the following parameter values: m = 10 kg , k = 4000 N / m and Ω = 20 rad / s . SOLUTION 1. FBD 2. Newton
Fx∑ = k yB − x( ) + 2k yB − x( )− 3kx = 2m!!x ⇒
2m!!x + 6kx = 3kbsinΩt
3. Kinematics - none needed 4. EOM - standard form
!!x + 3 km
x = 3k2m
bsinΩt ⇒
ωn =3km
=3( )4000
10= 20 3 rad / s
Solution
xP t( ) = A sinΩt + B cosΩt ⇒
−Ω2 +ωn2( )A sinΩt + −Ω2 +ωn
2( )cosΩt = 3k2m
bsinΩt ⇒
A = 3k / 2m−Ω2 +ωn
2
⎡
⎣⎢⎢
⎤
⎦⎥⎥bsinΩt = 600
−202 + 20 3( )2⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥bsin20t = 3
4bsin20t ⇒
IN PHASE
Chapter3
Question C3.4The vertical shaft OA rotates about a fixed axis with a constant rate of ⌦ = 8 rad/s. The armAB is pinned to OA and is being raised at a constant rate of ✓ = 10 rad/s. An observer and xyzaxes are attached to AB. The XY Z axes are stationary. What is the angular acceleration vectorfor arm AB when ✓ = 90�?
ME 274 - Fall 2005 Name Examination No. 1 PROBLEM NO. 3 Part (a) – 5 points Vertical shaft OA rotates about a fixed axis with a constant rate of ! = 8 rad/sec. Arm AB is pinned to OA and is being raised at a constant rate of
˙ ! = 10 rad /sec . An observer and the xyz axes are attached to AB. The XYZ axes are stationary. What is the angular acceleration of arm AB when " = 90°? Write your answer as a vector.
5 ft
"
O
A
B ! x
y Y
X Chapter3
Question C3.4The vertical shaft OA rotates about a fixed axis with a constant rate of ⌦ = 8 rad/s. The armAB is pinned to OA and is being raised at a constant rate of ✓ = 10 rad/s. An observer and xyzaxes are attached to AB. The XY Z axes are stationary. What is the angular acceleration vectorfor arm AB when ✓ = 90�?
ME 274 - Fall 2005 Name Examination No. 1 PROBLEM NO. 3 Part (a) – 5 points Vertical shaft OA rotates about a fixed axis with a constant rate of ! = 8 rad/sec. Arm AB is pinned to OA and is being raised at a constant rate of
˙ ! = 10 rad /sec . An observer and the xyz axes are attached to AB. The XYZ axes are stationary. What is the angular acceleration of arm AB when " = 90°? Write your answer as a vector.
5 ft
"
O
A
B ! x
y Y
X
L
L
Chapter3
Question C3.4The vertical shaft OA rotates about a fixed axis with a constant rate of ⌦ = 8 rad/s. The armAB is pinned to OA and is being raised at a constant rate of ✓ = 10 rad/s. An observer and xyzaxes are attached to AB. The XY Z axes are stationary. What is the angular acceleration vectorfor arm AB when ✓ = 90�?
ME 274 - Fall 2005 Name Examination No. 1 PROBLEM NO. 3 Part (a) – 5 points Vertical shaft OA rotates about a fixed axis with a constant rate of ! = 8 rad/sec. Arm AB is pinned to OA and is being raised at a constant rate of
˙ ! = 10 rad /sec . An observer and the xyz axes are attached to AB. The XYZ axes are stationary. What is the angular acceleration of arm AB when " = 90°? Write your answer as a vector.
5 ft
"
O
A
B ! x
y Y
X Chapter3
Question C3.4The vertical shaft OA rotates about a fixed axis with a constant rate of ⌦ = 8 rad/s. The armAB is pinned to OA and is being raised at a constant rate of ✓ = 10 rad/s. An observer and xyzaxes are attached to AB. The XY Z axes are stationary. What is the angular acceleration vectorfor arm AB when ✓ = 90�?
ME 274 - Fall 2005 Name Examination No. 1 PROBLEM NO. 3 Part (a) – 5 points Vertical shaft OA rotates about a fixed axis with a constant rate of ! = 8 rad/sec. Arm AB is pinned to OA and is being raised at a constant rate of
˙ ! = 10 rad /sec . An observer and the xyz axes are attached to AB. The XYZ axes are stationary. What is the angular acceleration of arm AB when " = 90°? Write your answer as a vector.
5 ft
"
O
A
B ! x
y Y
X
L
L
ME 274 – Summer 2020 SOLUTION Final Examination (AM) Problem No. 5 PART A – 4 points Shaft OA is rotating about the fixed Y-axis with a constant rotational speed of Ω . Arm AB is being raised at a constant rate of !θ . It is desired to use the following moving reference frame kinematics to describe the acceleration of end B:
!aB = !aA + !aB/ A( )rel
+!α × !rB/ A + 2
!ω × !vB/ A( )rel
+!ω ×
!ω × !rB/ A( )
(i) If an observer attached to OA is used for this equation, what are the following two
terms in the above equation?
!vB/ A( )rel= L "θ j
!aB/ A( )rel= −L "θ 2i
(ii) If an observer attached to AB is used for this equation, what are the following two
terms in the above equation?
!vB/ A( )rel=!0
!aB/ A( )rel=!0
From Conceptual Question C3.4
Chapter3
Question C3.4The vertical shaft OA rotates about a fixed axis with a constant rate of ⌦ = 8 rad/s. The armAB is pinned to OA and is being raised at a constant rate of ✓ = 10 rad/s. An observer and xyzaxes are attached to AB. The XY Z axes are stationary. What is the angular acceleration vectorfor arm AB when ✓ = 90�?
ME 274 - Fall 2005 Name Examination No. 1 PROBLEM NO. 3 Part (a) – 5 points Vertical shaft OA rotates about a fixed axis with a constant rate of ! = 8 rad/sec. Arm AB is pinned to OA and is being raised at a constant rate of
˙ ! = 10 rad /sec . An observer and the xyz axes are attached to AB. The XYZ axes are stationary. What is the angular acceleration of arm AB when " = 90°? Write your answer as a vector.
5 ft
"
O
A
B ! x
y Y
X
A B
O
E
ωOA x
y
A B
O
E
ωOA x
y
a
b c
d
C = ICAB
vA vB
ω AB
ω BE
ME 274 – Summer 2020 SOLUTION Final Examination (AM) Problem No. 5 PART B – 4 points The four-bar mechanism shown below is made up of links OA, AB and BE. Let ωOA ,
ω AB and ω BE represent the angular speeds of these links. Assume that the figure of the mechanism below has been drawn to scale.
i. Which of the three speeds ωOA , ω AB and ω BE is the LARGEST?
ii. Which of the three speeds ωOA , ω AB and ω BE is the SMALLEST? You must provide justification for your answers above.
OA : vA = aωOA
AB : vA = bω AB
Therefore:
aωOA = bω AB ⇒ ωOA = b
aω AB >ω AB
AB : vB = cω AB
BE : vB = dω BE
Therefore:
bω AB = dω BE ⇒ ω AB = d
bω BE >ω BE
From June 24 tutorial session
Chapter 2: Planar Rigid Body Kinematics Homework
Homework 2.B.10
Given: The mechanism shown below is made up on links AB, BD and DE. Link AB is knownto be rotating counterclockwise with an angular speed of !AB. At the instant shown, link BD ishorizontal.
Find: For this problem:
(a) Locate the instant center for link BD.
(b) Using the instant center approach, determine the angular speeds of links BD and DE (in termsof !AB). Also, determine the sense of rotation (clockwise or counterclockwise) for links BDand DE.
A
B D
E
2 ft
! AB
1 ft
30°
Freeform c�2018 2-55
ME 274 – Summer 2020 SOLUTION Final Examination (AM) Problem No. 5 PART C – 4 points An L-shaped bar is pinned to ground at end O. At an instant when the bar is rotating CCW with an angular speed of ω , particle P impacts end B of the bar, as shown below. The coefficient of restitution for this impact is: 0 ≤ e <1. All motion occurs in a horizontal plane. Circle all correct statements below in regard to the kinetics of the system of bar+P during the time of impact:
a) Linear momentum is conserved for the system. !F∑ ≠!0
b) Angular momentum about point O is conserved for the system. !
MO∑ =!0
c) Energy is conserved for the system. e ≠ 1
d) None of the above. You must provide justification for your answer above.
ω
P
B A
O
v
HORIZONTALplane
ω
P
B A
O
vrel
HORIZONTALplane rough, µk
ω
P
B A
O
v
HORIZONTALplane
P
B A
O Ox
Oy
ME 274 – Summer 2020 SOLUTION Final Examination (AM) Problem No. 5 PART D – 4 points Blocks A and B (having masses of m and 2m, respectively) are connected by a lightweight, rigid rod. In System 1, a force F acts to the left on block A. In System 2, the same force acts to the left on block B. Let F1 and F2 represent the magnitude of the load
carried by the rod in Systems 1 and 2, respectively.
Circle the answer below that most accurately describes the magnitudes of F1 and F2 :
a) F1 > F2
b) F1 = F2
c) F1 < F2
d) More information is needed to answer this question.
You must provide justification for your answer above.
For either system:
F∑ = F = 3ma ⇒ a = F3m
For System 1:
F∑ = F − F1 = ma ⇒ F1 = F − ma = F − m F
3m⎛⎝⎜
⎞⎠⎟= 2
3F
For System 2:
F∑ = F2 = ma ⇒ F2 = ma = m F
3m⎛⎝⎜
⎞⎠⎟= 1
3F
Chapter4
Question C4.1Blocks A and B (having masses of m and 2m, respectively) are connected by a lightweight, rigidrod. In System 1, a force F acts to the left on block A. In System 2, the same force acts to theleft on block B. Let F1 and F2 represent the magnitude of the load carried by the rod in Systems1 and 2, respectively. Circle the answer below that most accurately represents the magnitudes ofF1 and F2:
(a) F1 > F2
(b) F1 = F2
(c) F1 < F2
(d) More information is needed to answer this question
Provide a justification for your answer.
ME 274 – Spring 2007 Name
Examination No. 2
PROBLEM NO. 3 Instructor
Part (a) – 5 points
Blocks A and B (having masses of m and 2m, respectively) are connected by a
lightweight rod. In System 1 (shown below left), a force F acts to the left on block A. In
System 2 (shown below right), the same force F acts to the left on block B. Let F1 and F2
represent the magnitudes of the load carried by the rod in Systems 1 and 2, respectively.
Circle the answer below that most accurately represents the sizes of F1 and F2:
a) F1 > F2
b) F1 = F2
c) F1 < F2
d) More information is needed in order to assess the relative sizes of F1 and F2.
Provide a justification for your answer
F A B
m 2m
System 1
F1
F A B
m 2m
System 2
F2
Chapter4
Question C4.1Blocks A and B (having masses of m and 2m, respectively) are connected by a lightweight, rigidrod. In System 1, a force F acts to the left on block A. In System 2, the same force acts to theleft on block B. Let F1 and F2 represent the magnitude of the load carried by the rod in Systems1 and 2, respectively. Circle the answer below that most accurately represents the magnitudes ofF1 and F2:
(a) F1 > F2
(b) F1 = F2
(c) F1 < F2
(d) More information is needed to answer this question
Provide a justification for your answer.
ME 274 – Spring 2007 Name
Examination No. 2
PROBLEM NO. 3 Instructor
Part (a) – 5 points
Blocks A and B (having masses of m and 2m, respectively) are connected by a
lightweight rod. In System 1 (shown below left), a force F acts to the left on block A. In
System 2 (shown below right), the same force F acts to the left on block B. Let F1 and F2
represent the magnitudes of the load carried by the rod in Systems 1 and 2, respectively.
Circle the answer below that most accurately represents the sizes of F1 and F2:
a) F1 > F2
b) F1 = F2
c) F1 < F2
d) More information is needed in order to assess the relative sizes of F1 and F2.
Provide a justification for your answer
F A B
m 2m
System 1
F1
F A B
m 2m
System 2
F2
F F1
A
F2
A
Chapter4
Question C4.1Blocks A and B (having masses of m and 2m, respectively) are connected by a lightweight, rigidrod. In System 1, a force F acts to the left on block A. In System 2, the same force acts to theleft on block B. Let F1 and F2 represent the magnitude of the load carried by the rod in Systems1 and 2, respectively. Circle the answer below that most accurately represents the magnitudes ofF1 and F2:
(a) F1 > F2
(b) F1 = F2
(c) F1 < F2
(d) More information is needed to answer this question
Provide a justification for your answer.
ME 274 – Spring 2007 Name
Examination No. 2
PROBLEM NO. 3 Instructor
Part (a) – 5 points
Blocks A and B (having masses of m and 2m, respectively) are connected by a
lightweight rod. In System 1 (shown below left), a force F acts to the left on block A. In
System 2 (shown below right), the same force F acts to the left on block B. Let F1 and F2
represent the magnitudes of the load carried by the rod in Systems 1 and 2, respectively.
Circle the answer below that most accurately represents the sizes of F1 and F2:
a) F1 > F2
b) F1 = F2
c) F1 < F2
d) More information is needed in order to assess the relative sizes of F1 and F2.
Provide a justification for your answer
F A B
m 2m
System 1
F1
F A B
m 2m
System 2
F2
F F1
A
F2
A
From Conceptual Question C4.1
Chapter4
Question C4.1Blocks A and B (having masses of m and 2m, respectively) are connected by a lightweight, rigidrod. In System 1, a force F acts to the left on block A. In System 2, the same force acts to theleft on block B. Let F1 and F2 represent the magnitude of the load carried by the rod in Systems1 and 2, respectively. Circle the answer below that most accurately represents the magnitudes ofF1 and F2:
(a) F1 > F2
(b) F1 = F2
(c) F1 < F2
(d) More information is needed to answer this question
Provide a justification for your answer.
ME 274 – Spring 2007 Name
Examination No. 2
PROBLEM NO. 3 Instructor
Part (a) – 5 points
Blocks A and B (having masses of m and 2m, respectively) are connected by a
lightweight rod. In System 1 (shown below left), a force F acts to the left on block A. In
System 2 (shown below right), the same force F acts to the left on block B. Let F1 and F2
represent the magnitudes of the load carried by the rod in Systems 1 and 2, respectively.
Circle the answer below that most accurately represents the sizes of F1 and F2:
a) F1 > F2
b) F1 = F2
c) F1 < F2
d) More information is needed in order to assess the relative sizes of F1 and F2.
Provide a justification for your answer
F A B
m 2m
System 1
F1
F A B
m 2m
System 2
F2
ME 274 – Summer 2020 SOLUTION Final Examination (AM) Problem No. 5 PART E – 4 points Particle P, having a mass of m, is able to slide on a smooth homogeneous arm of mass m, with the arm pinned to ground at end O. At Position 1, P has a speed of vP1 , and is at a
radial position of R1 . At Position 2, P has slid outward on the arm to a position of R2
(where R2 > R1 ), and the bar is rotating about O with an angular speed of ω2 , with
!R2 > 0 . All motion is in a horizontal plane.
Choose the response below that most accurately describes the speed of P at Position 2,
vP2 :
a) vP2 < R2ω2
b) vP2 = R2ω2
c) vP2 > R2ω2
You must provide justification for your answer above.
!vP2 = "R2eR + R2ω2eθ ⇒ vP2 = "R2
2 + R2ω2( )2 > R2ω2 ; since !R2 ≠ 0
P
v1
Position1
R1
P
ω2
R2
Position2
m m
ME 274 – Summer 2020 Name Examination No. 2 (PM) PROBLEM NO. 3 (continued) PART B – 4 points Particle P, having a mass of m, is able to slide on a smooth, HORIZONTAL surface. P is connected to ground at pin O with an elastic band of stiffness k. At Position 1, P has a speed of vP1 , with the band having a length of R1 . At Position 2, the band has stretched
to a length of R2 (where R2 > R1), and OP is rotating about O with an angular speed of
ω2 and with !R2 < 0 .
Choose the response below that most accurately describes the speed of P at Position 2,
vP2 :
a) vP2 < R2ω2
b) vP2 = R2ω2
c) vP2 > R2ω2
d) More information is needed in order to answer this question.
If you want partial credit on your work, provide a justification for your answer here.