ME 274 – Summer 2014 Name Final Examination PROBLEM NO. 4 – 20 points Given: Particles A and B (each of mass m) are attached to rigid bar OA with OA

having negligible mass. A particle P (of mass m) strikes particle A with a speed of vP1 in the direction shown in the figure. On impact with A, particle P immediately sticks to A.

Find: Determine the angular velocity of OA immediately after P sticks to A. Clearly

indicate the four steps in a neat and orderly presentation of your work.

B

A

O

L / 2

L / 2

PvP1

θ

HORIZONTAL*PLANE*

m

m

m

Work appearing above this line will NOT be graded

ME 274 – Spring 2010 Name Examination No. 3 PROBLEM NO. 2 Given: A T-shaped bar consisting of a bar (of mass m, length L) welded to the end of

another bar (m, L) that is pinned at O. A bullet (mass mB) strikes a T-shaped bar at end C with a speed vB. The bullet becomes embedded in the bar immediately after the impact. All motion of the system is in a HORIZONTAL PLANE.

Find: Determine the angular velocity of the T-shaped bar immediately after impact.

Use the following parameters in your analysis: L = 2, m = 3 kg, mB = 0.02 kg, vB = 150 m/s.

O

A B

m, L

m, L vB

D C

mB

2L

L

2L

HORIZONTAL PLANE

ME 274 – Spring 2009 Name

Examination No. 3

PROBLEM NO. 3

Part (a) – 10 points

A thin, homogeneous bar (of mass m and length L) is translating

without rotation in a horizontal plane with a speed of vG1 when pin

O on the bar strikes a stationary stop. Immediately after impact

point O sticks to the stop.

Determine the angular velocity of the bar immediately after

impact. Leave your answer in terms of (at most) m, L and vG1.

HINT: Energy is NOT conserved during impact.

L/4

G

HORIZONTAL PLANE

vG1

O

L/4

L/2

ME 274 – Summer 2014 Name Examination No. 2 PROBLEM NO. 3 For Parts A-C, you must provide justification (written words, drawings and/or equations) for all answers. For Part D, you do NOT need to provide justification. PART A – 5 points A rigid body has a mass of m, with its center of mass located at point G. Consider points A and B on the body, where A, B and G are collinear. If the mass moment of inertia of the body about point B is IB = 15 kg ⋅m

2 , determine the mass of moment of inertia of the body about point A, IA . Use m = 10 kg and d = 0.5 m .

G

A

B d

d

ME 274 – Summer 2014 Name Examination No. 2 PROBLEM NO. 3 (continued) PART C – 5 points A particle P is free to slide on a smooth bar of negligible mass. The bar is free to rotate in a horizontal plane about a vertical axis passing through end O of the bar. A spring of stiffness k and unstretched length R0 is connected between P and O. The spring is compressed to half of its unstretched length and released when the bar has a rotational speed of ω1 . After release, P reaches a position when the spring is unstretched. At this position, the rotational speed of the bar is ω2 . Suppose now the experiment is repeated except the stiffness of the spring is doubled to a value of 2k. As a result of this change, the value of ω2 is now:

a) decreased. b) the same. c) increased. d) unknown. More information is needed to answer this question.

Provide a justification for your answer.

Question C4.13A particle P is free to slide on a smooth, lightweight bar. The bar is free to rotate in a horizontalplane about a vertical axis passing through end O of the bar. A spring of sti↵ness k and unstretchedlength R0 is connected between P and O. The spring is compressed to half of its unstretched lengthand released when the bar has a rotational speed of !1. After release, P reaches a position whenthe spring is unstretched. At this position, the rotational speed of the bar is !2.

Suppose now the experiment is repeated except the sti↵ness of the spring is doubled to a value of2k. As a result of this change, the value of !2 is now:

(a) Decreased

(b) The same

(c) Increased

(d) More information is needed in order to answer this question.

ME 274 – Spring 2007 Name

Examination No. 2

PROBLEM NO. 3 Instructor

Part (d) – 5 points

A particle P is free to slide on a smooth, lightweight bar. The bar is free to rotate in a

horizontal plane about a vertical shaft passing through O. A spring of stiffness k and

unstretched length R0 is connected between P and O. The spring is compressed to half of

its unstretched length and released when the bar has a rotational speed of !1. After

release P reaches a position where the spring is unstretched. At this position, the

rotational speed of the bar is !2.

Suppose now that the experiment is repeated except the stiffness of the spring is doubled

to a value of 2k. As a result, the value of !2 is:

a) is decreased.

b) remains the same.

c) is increased.

d) more information is needed to answer this question.

Provide a justification for your answer.

P O

R0/2

HORIZONTAL PLANE

k

P

O

R0

k

!2

!1

ME 274 – Summer 2014 Name Examination No. 2 PROBLEM NO. 3 (continued) PART D – 5 points Consider the system shown below where A, B and E masses of m, 2m and 2m, respectively. The system starts from rest with θ = 0 . Consider the motion of the system through to a second position where θ = 90° . Answer the following.

TRUE or FALSE: Mechanical energy is conserved for each particle individually.

TRUE or FALSE: Mechanical energy is conserved for the total system of A+B+E.

TRUE or FALSE: Linear momentum in the vertical direction is conserved for the total system A+B+E

TRUE or FALSE: Angular momentum about C is conserved for the system of E alone.

TRUE or FALSE: Angular momentum about point O is conserved for the system of A+B. You do NOT need to provide justification for your answers here.

Question C4.20Consider the system shown below where A, B and E masses of m, 2m and 2m, respectively. Thesystem starts from rest with ✓ = 0. Consider the motion of the system through a second positionwhen ✓ = 90�. Answer the following.

TRUE or FALSE: Energy is conserved for each particle individually.

TRUE or FALSE: Energy is conserved for the total system of A+B+E.

TRUE or FALSE: Linear momentum in the horizontal direction is conserved for the total systemof A+B+E.

TRUE or FALSE: Linear momentum in the vertical direction is conserved for the total system ofA+B+E.

TRUE or FALSE: Angular momentum about point O is conserved for the system of A+B.

Particle kinetics; Work/energy equation IV-38 ME274

Example IV.2.6 The system shown is made up of particles A, B and E, having masses of 5 kg, 20 kg and 80 kg, respectively). Lightweight bars OB and OA are welded together with a right angle between the two bars, with these bars welded to the pulley at O. Consider the mass of the pulleys to be negligible. The system is released from rest when ! = 0 . Determine the speed of particle E when ! = 90° . Use r = 0.1 meters and L = 0.5 meters.

g

!

2L

L

A

B

E

r O C

ME 274 – Summer 2014 Name Final Examination PROBLEM NO. 5 For Parts A-D, you must provide justification (written words, drawings and/or equations) for all answers. PART A – 5 points

Consider the homogeneous disks A and B with mA > mB and RA > RB . The disks are released from rest. Circle the answer below that most accurately describes the relative sizes of the acceleration of the disk’s center O on release:

a) (aO )A > (aO )B b) (aO )A = (aO )B c) (aO )A < (aO )B

θno slip

RAmA

O

Cθ

no slip

RBmB

OC

g