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:

Fx∑ = 0 ⇒ mvB2 = mvB3 + 2mvA3 ⇒ vA3 = vB2 − vB3( ) / 2

e =vB3 − vA3vA2 − vB2

⇒ vB3 = vA3 − evB2 = vB2 − vB3( ) / 2 − evB2 ⇒

1+ 2( )vB3 = 1− 2e( )vB2 ⇒ vB3 = − 13

1− 2e( ) 2gL

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.

R1

vP1

P

O

R2

P

ω2

Position1 Position2

O

m

k

From Exam 2