Unformatted text preview: gid Body Kinetics HChapter V: Rigid
omework Problems ME 274 Body Kinetics Homework V7 roblem V5
Problem V.5 pallet/winch/roller system is used to move crate B of mass M, where the pallet A has a
Given: A
ass of m. Determine the pallet/winch/roller system is used to move crate B of mass M, where the pallet A has
a mass of m. a) maximum winch force that can be applied to the pallet such that the crate does
not tip and
Find: Determine: a) the maximum winch force that can be applied to the pallet such that the
crate does not friction required between the crate and pallet to ensure
b) the coefficient of statictip, and b) the coeﬃcient of static friction required between the crate and pallet to
ensure that tipping occurs
that tipping occurs prior to slip. prior to slip.
d1 d1
d2 G
d2 B
A Use = 4 kg, M parameters 0 your and d = m m.
se the following: mthe1following= 65 kg, d1 =in .3 m, analysis: 0.6= 16kg , M = 80kg , d1 = 0.3m and d2 = 0.6m.
2 V8 Chapter V: Rigid Body Kinetics Homework netics Homework Problems V6 ME 274 Problem V.6
Given: The center of mass G of the disk shown below (mass m) is oﬀset by a distance e from the of mass G of the disk shown below (mass position shown,aG is directly above O as the wheel rolls without slip
geometric center O. At the m) is offset by distance e from the
center O. If Gthrough the bottom of a as the wheel rolls without slip through
is in the position shown circular path shown.
of a circular path shown, find the normal force N that is exerted by the path on
Find: For this position, determine the normal force N that is exerted by the path on the disk. C
! R e
O G
r Use the following e = 0.05 m, ! = 3 analysis: R = 1. m,
llowing: R = 1.25 m, r = 0.25 m, parameters in yourrad/s, and m = 505kg. r = 0.2m, e = 0.1m, ω = 4rad/sec and
m = 75kg . Problem V9
A thin, homogeneous bar AB (having a length of L and mass m) is pinned to ground at
pointChapter V: Rigid a distance of L/4 from end A). A homogeneous disk of mass M
O (where O is at Body Kinetics Homework
and radius r is welded to the bar AB with end B being at the center of the disk. A constant
forceProblemend A in such a way that the line of action of F is always perpendicular to
F acts at V.9
OA. At instant “1”, the system is released from rest with AB being horizontal. V11 Given: A thin, homogeneous bar system made up of of L and mass m) is pinned to ground at
a) Draw a free body diagram of theAB (having a lengthbar AB and the disk. List
point O (where O is at a distance of L/4 from end A). A homogeneous disk of mass M and radius r
which, if any, nonconservative forces do work on this system. is welded to the bar AB with end B being at the center of the disk. A constant force F acts at end b) Determine thethat the velocity of bar ABis always perpendicular to OA. The system is released
A in such a way angular line of action of F when AB reaches its vertical position
(instant “2”). Note that since the
from rest with AB being horizontal.disk is welded to AB, the disk has the same
angular velocity as bar AB.
Find: For this problem: a) determine the angular disk as particle of mass M reaches
c) Repeat your calculations in b) but here treat the velocityaof bar AB when AB (that its vertical
position, and b) ! 0
is, consider r repeat your calculations in a) but here treat the disk as a particle of mass M.
). F
M r m
A
L/4 O 3L/4 B g
VERTICAL PLANE
Use the following parameters in your analysis: L = rs r 1 1 e m = 40kg , ,
Use the following parameters in your analysis: L = 2.5 mete3m,, r == mmt,er , m = 40 kgM = 50kg and
M = F = g and. F = 100 Newtons .
50 k 100N Chapter V: Rigid Body Kinetics Homework V13 Problem V.11
Given: ConsiderBody Kinetics Homework Problems
Rigid the three systems (each of total mass m) shown below where: (I) 274
ME made up on a
particle of mass m supported within a massless ring by massless spokes, (II) made up of identical,
P total mass
thin spokes of roblem V11 m in a massless ring, and (III) a thin ring of mass m. Each system is
Consider the three systems (each of total mass m) shown below where: (I) made up on a
released from prest, with eachssystem rolling withoutring by massless spokes, (II) made up of
article of mass m upported within a massless slipping on a rough incline.
identical, thin spokes of total mass m in a massless ring, and (III) a thin ring of mass m.
Each the velocity of the mass center O of each system when each system has made
Find: Determine system is released from rest, with each system rolling without slipping on a rough
ncline. Determine the velocity of the inclines. Rank the speeds of O system
two complete irevolutions in rolling down the mass center O of each system when eachfor the three systems.
has made two complete revolutions in rolling down the inclines. Rank the speeds of O for
Explain in words why the speeds endwords why those rankings.with those rankings.
up with the speeds end up
the three systems. Explain in g
O O R
no slip ! (I) massless ring, massless
spokes and particle of
mass m O R R no slip ! (II) massless ring and
identical spokes (with
total mass of spokes m) no slip ! (III) thin ring of mass m Chapter V: Rigid Body Kinetics Homework V17 Rigid Body KineticsProblemProblems
Homework V.15 ME 274 Given: The center of the homogeneous disk of mass m shown below has an initial velocity of v0
Problem V15
up the slope. The center of the homogeneous disk of mass m shown below has an initial velocity of v0
Find: Find the of the of the disk after an elapsed time of ∆t, assuming that
up the slope. Find the velocityvelocitydisk after an elapsed time of !t, assuming that the the disk rolls without
slip.
disk rolls without slip. O r ! ◦
Use m 8 kg, r = 0.3 m, ! = in your analysis: / = and
Use the following: the=following parameters 36.87°, v0 = 36 m msec 10kg ,!rt = 105secs . = 30 , v0 = 30m/sec and
= 0. m , θ ∆t = 12sec. V20
Body Kinetics Homework Problems Problem V.18 Chapter V: Rigid Body Kinetics Homework
ME 274 blem V18 Given: The slender bar, shown below, of mass m and length L has a downward velocity vG at
the instant shown. Assume that the pivot at the end of bar becomes attached to the support after
slender bar, shown below, of mass m and length L has a downward velocity at the
falling h. nt shown. Assuming that the pivot at the end of bar becomes attached to the support
falling h, determine the angular the angular the bar immediately after impact.
Find: Determine velocity of velocity of the bar immediately after impact. Use the following parameters in your analysis: m = 4kg , L = 0.4m, vG = 3m/sec and h = 4m. the following: m = 3 kg, L = 0.3 m, vG = 4 m/s and h = 3 m. V24
etics Homework Problems Problem V.22 22 (6/109) Chapter V: Rigid Body Kinetics Homework
ME 274 Given: A slender, homogeneous bar of mass m is released from rest. omogeneous bar of mass m is released from rest. Determine the contact force
Find: Determine the contact force on the bar due to the smooth horizontal surface on release.
ue to the smooth horizontal surface. V26 Chapter V: Rigid Body Kinetics Homework Problem V.24 mework Problems 6/117) Given: A constant frictional torque Mf from the bearings at O resist the motion of the pulley
ME downward with a speed of v .
system shown. The system is released with A traveling 274
A1
Find: Determine the speed of block A after it drops through a distance of d. nal torque M f from the bearings at O
of the pulley system shown. If the
with A traveling downward with a
ermine the speed of block A after it
istance of d. m, kO A Use the following parameters in your analysis: m = 12kg , Mf = 3N m, vA1 = 0.3m/sec, d = 1.5m
and kO = 210mm. parameters in your analysis: m = 12 kg , M f = 3 N ! m ,
d = 1.5 meters and kO = 210 mm . Chapter V: Rigid Body Kinetics Homework V37 Rigid Body Kinetics Homework Problems ME 274 Problem V.35 Problem V35 Given: Bars OA and AB each have a mass of m and a length of L. B is constrained to move in
Bthe horizontal direction only. mass of mMO is appliedof L. B OA at O. The system isin
ars OA and AB each have a A couple and a length to link is constrained to move released from
rest when thedangle between A couple AB is applied. at O. Theall surfacesreleased from
the horizontal irection only. OA and M is θ = θ1 Assume system is are smooth. rest when the angle between OA and AB is !1. Assume all surfaces are smooth.
Find: Determine the of point B when ! when
Determine the velocity velocity of point B = !2. θ = θ2 .
B O
! MO L L g A
Use the following parameters for your analysis: mm 10 12kgL = 2 m2.!m= θ 80°, 36.87◦ ,0° = 0 and
Use the following parameters in your analysis: = = kg, , L = , 5 1 , 11 = !2 = 3 θ2
and MO 6040m.
M = = N Nm.
O V38 Chapter V: Rigid Body Kinetics Homework Rigid Body Kinetics Homework Problems ME 274 Problem V.36 Problem V36 Given: A uniform, disk (of mass m and radius r) is pinned at is applied to amass O. Force F is
A uniform disk (m r) is pinned at its center of mass O. Force F its center of rope
applied toaround the disk. The diskthe released from rest.released from rest. Assume that the rope
wrapped a rope wrapped around is disk. The disk is
does not seconds,
After 2 slip on the disk. a) determine the angular velocity of the disk.
Find: At time t, determine: a) the angular velocity of the disk, and b) the reaction force components on)theeterminepin O.
b d disk at the reaction force components at the pin. r O F Use the following parameters in your analysis: m = 15kg , r = 0.4m, F = 200N and t = 2sec. Use the following parameters for your analysis: m = 10 kg, r = 0.3 m, F = 250 N. Rigid Body Kinetics Homework Problems ME 274 Problem V49
Chapter V: Rigid Body Kinetics Homework V51 Given: An inextensible cable connects block B with point A on a rigid, homogeneous
disk. At the instant shown, point A is directly above the disk’s center O. Block
Problem V.49
B has a mass of m = 40 kg, and the disk has a mass of M = 20 kg. The disk is
able to roll without slipping on a rough horizontal surface with C being the
Given: An inextensible cable connects block B with point A on a rigid, homogeneous disk. At the
contact oint
instant shown, pointpA is .directly above the disks center O. Block B has a mass of m, and the disk
has a mass of M . The disk is able to roll without slipping on a rough horizontal surface with C
Find:
If the system is released is released the rest.
being the contact point. The system from rest atfromposition shown, find the angular acceleration of the disk. Write your answer as a vector. Find: Determine the angular acceleration of the disk immediately after release. M A
R/2 O
no slip R C
B m Use the following parameters in your analysis: M = 20kg and m = 40kg . inetics Homework Problems ME 274 V50
V52 Chapter V: Rigid Body Kinetics Homework Particle B (having a mass of m = 10 kg) initially travels on a smooth
HORIZONTAL surfaceV.50 a speed of vB1 = 20 m/sec. This particle strikes
Problem with
point E on a stationary thin homogeneous bar (having a mass of M = 15 kg),
Given: being pinned to ground. The coefficient of restitution
with end A of the bar Particle B (having a mass of m) initially travels on a smooth HORIZONTAL surface with
a speed of v the This point E is known to be e a stationary thin homogeneous bar (having a mass
between the particle and B 1 . bar atparticle strikes point E on = 0.6.
Furthermore,of Mcontact surface of the bar beingpoint E is smooth. The coeﬃcient of restitution between the
the ), with end A between B and pinned to ground.
particle and the bar at point E is known to be e. Furthermore, the contact surface between B and
point E is smooth. Determine the angular velocity of the bar immediately after being impacted
by the particle. Write your answer as a vector. Find: Determine the angular velocity of the bar immediately after being impacted by the particle. A B
d m M
L vB1
E ! Use the following parameters in your analysis: L = 3m, d = 2m, m = 10kg , M = 15kg , e = 0.6,
θ = 60◦ and vB 1 = 20m/sec. Problem V51
Given: A homogeneous, thin bar AB (of length L = 3 meters and mass m = 50 kg) is
Chapter V: Rigid Body Kinetics Homework
pinned to a block at A. The block has a mass of M = 100 kg and is constrained
to move along a smooth horizontal surface. A horizontal force F = 200 N is
Problem V.51 the bar’s center of mass G at an instant when the bar is vertical and
applied to
at rest. V53 Given: A homogeneous, thin bar AB (of length L and mass m) is pinned to a block at A. The
block has a this problem, is constrained to move along a smooth horizontal surface. A horizontal
Find:
For mass of M and
force F is) applied to the bar’s centerdiagramsG atthe bar and the block below.vertical and at rest.
a Complete the free body of mass for an instant when the bar is b) Determine the angular acceleration of the bar for the instant when the
Find: Determine F is angular acceleration of the bar for the instant when the force F is applied to
force the applied to the bar.
the bar. M g A F G L m B
Use the following parameters in your analysis: L = 3m, m = 50kg , M = 100kg and F = 200N . Rigid Body Kinetics Homework Problems ME 274 Problem V54
Chapter V: Rigid Body Kinetics Homework
Given: A drum has a mass of M = 30 kg, outer radius of R = 0.5 m, inner radius of r
= 0.25 m, a centroidal radius of gyration of kG = 0.6 m and centroid at the
Problem V.54
geometric center G. A cable is wrapped around the inner radius of the drum
and is connected to particle A having a mass of m = 10 kg. The cable is also
Given: A drum has aover an ideal pulley.radius of R, stiffness K = 100 ,N/m is attached
wrapped mass of M , outer A spring of inner radius of r a centroidal radius of
gyration of kGbetween G of at the geometric center G. A cable is released from rest with theradius
and centroid the drum and ground. The system is wrapped around the inner
of the drum and is connected to particle A having a mass of m. The cable is also wrapped over an
spring unstretched.
V56 ideal pulley. A spring of stiﬀness K is attached between G of the drum and ground. The system is
released from rest with the spring unstretched. Find: Determine the speed of A after it has dropped 2 meters. Find: Determine the speed of A after it has dropped through a distance of d. pulley has
negligible mass M R K
r G
no slip m A Use the following parameters in your analysis: M = 30kg , m = 10kg , R = 0.5m, r = 0.25m,
kG = 0.3m, K = 100N/m and d = 2m. Rigid Body Kinetics Homework Problems ME 274 V60 Chapter V: Rigid Body Kinetics Homework Problem V58
Given: Link AB (having a mass of m with uniform mass distribution and length L) is
Problem V.58
supported by a vertical cable OA (of length 0.6L and negligible mass) at A,
and end B is constrained to move within a smooth slot, as shown below. The
Given: Link AB (having a mass of m with uniform mass distribution and length L) is supported
bar is released from rest when it is horizontal. by a vertical cable OA (of length 0.6L and negligible mass) at A, and end B is constrained to move
within a smooth slot, as shown below. The bar is released from rest when it is horizontal. Find: Determine the angular acceleration of AB on release. Use the following
parameters: m = acceleration of meters.
Find: Determine the angular40 kg and L = 2AB on release. g O
0.6 L
massless
cable m, L B A
! smooth Use the following parameters in your analysis: m = 40kg and L = 2m. Rigid Body Kinetics Homework Problems V62 Problem V60 M Chapter V: Rigid Body Kinetics Homework Given: The compound wheel shown rolls without slipping up the incline on its hub
and is pulled by a constant force T = 100 N applied to a cord wrapped arou
Given: The compound wheel shown rollsouter rim. The wheel starts from rest, hubs and is of m = 40 kg, and has
its without slipping up the incline on its has a mass pulled
by a constant force T applied to a cord wrappedgaround its outer rim. The mass O of kOfrom.15 meters. Assume
radius of yration about its center of wheel starts = 0 rest,
has a mass of m, and has a radius of gyration about not center of mass O of kO . Assume that the
the cable does its slip on the wheel.
Problem V.60 cable does not slip on the wheel. F velocity The angular after its center wheel after itsacenter O hasd up 2 meters up
Find: Determine the angularind:
of the wheel velocity of the O has moved distance of moved
incline.
the incline.
F no slip
R/2 O
R ! Use the following parameters in your analysis: m = 40kg , R = 0.2m, d = 2m, T = 100N and
kO = 0.15m. ...
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 Fall '09

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