Eccentric Impact

1

• Eccentric Impact
• e - (vB2 vA2)/(vB1 vA1)
• Where e is the coefficient of restitution and
  varies from 0 1
• vA and vB are the velocities along the line of
  impact for the
• two objects
• If e 0 the objects stick together and along the
  line of impact their velocities are equal.
• Use both linear and angular impulse momentum to
  solve the problem.
• If e 1 perfectly elastic use conservation of
  energy and both linear and angular impulse
  momentum to solve the problem.
• If 0 lt e lt 1 use coefficient of restitution
  equation along the line of impact

2

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.

3
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.

State 2 just before impact
State 3 just after impact
State 4 at max height
4
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.
• Use conservation of energy from 1 to 2
• T1 V1 T2 V2
• 0 mgL/2

Datum
State 2 just before impact
State 3 just after impact
State 4 at max height
5
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.
• Use conservation of energy from 1 to 2
• T1 V1 T2 V2
• 0 mgL/2 (1/2)(1/3)mL2w22 0

Datum
State 2 just before impact
State 3 just after impact
State 4 at max height
6
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.
• Use conservation of energy from 1 to 2
• T1 V1 T2 V2
• 0 mgL/2 (1/2)(1/3)mL2w22 0 ? w2 (3g/L)1/2

Datum
State 2 just before impact
State 3 just after impact
State 4 at max height
7
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.
• Use conservation of energy from 1 to 2
• T1 V1 T2 V2
• 0 mgL/2 (1/2)(1/3)mL2w22 0 ? w2 (3g/L)1/2
• vA vB w2k x Li

Datum
State 2 just before impact
State 3 just after impact
State 4 at max height
8
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.
• Use conservation of energy from 1 to 2
• T1 V1 T2 V2
• 0 mgL/2 (1/2)(1/3)mL2w22 0 ? w2 (3g/L)1/2
• vA vB w2k x Li - L (3g/L)1/2j

Datum
State 2 just before impact
State 3 just after impact
State 4 at max height
9
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.
• Use conservation of energy from 1 to 2
• T1 V1 T2 V2
• 0 mgL/2 (1/2)(1/3)mL2w22 0 ? w2 (3g/L)1/2
• vA vB w2k x Li - L (3g/L)1/2j
• Use coefficient of restitution from 2 to 3
• e - (vF3 vA3)/(vF2 vA2)
• .

Datum
State 2 just before impact
State 3 just after impact
State 4 at max height
10
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.
• Use conservation of energy from 1 to 2
• T1 V1 T2 V2
• 0 mgL/2 (1/2)(1/3)mL2w22 0 ? w2 (3g/L)1/2
• vA vB w2k x Li - L (3g/L)1/2j
• Use coefficient of restitution from 2 to 3
• e - (vF3 vA3)/(vF2 vA2)
• .5 - (0 vA3)/(0 L (3g/L)1/2)

Datum
State 2 just before impact
State 3 just after impact
State 4 at max height
11
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.
• Use conservation of energy from 1 to 2
• T1 V1 T2 V2
• 0 mgL/2 (1/2)(1/3)mL2w22 0 ? w2 (3g/L)1/2
• vA vB w2k x Li - L (3g/L)1/2j
• Use coefficient of restitution from 2 to 3
• e - (vF3 vA3)/(vF2 vA2)
• .5 - (0 vA3)/(0 L (3g/L)1/2) ? vA3
  (L/2)(3g/L)1/2

Datum
State 2 just before impact
State 3 just after impact
State 4 at max height
12
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.
• Use conservation of energy from 1 to 2
• T1 V1 T2 V2
• 0 mgL/2 (1/2)(1/3)mL2w22 0 ? w2 (3g/L)1/2
• vA vB w2k x Li - L (3g/L)1/2j
• Use coefficient of restitution from 2 to 3
• e - (vF3 vA3)/(vF2 vA2)
• .5 - (0 vA3)/(0 L (3g/L)1/2) ? vA3
  (L/2)(3g/L)1/2
• w3 (1/2)(3g/L)1/2

Datum
State 2 just before impact
State 3 just after impact
State 4 at max height
13
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.
• Use conservation of energy from 1 to 2
• T1 V1 T2 V2
• 0 mgL/2 (1/2)(1/3)mL2w22 0 ? w2 (3g/L)1/2
• vA vB w2k x Li - L (3g/L)1/2j
• Use coefficient of restitution from 2 to 3
• e - (vF3 vA3)/(vF2 vA2)
• .5 - (0 vA3)/(0 L (3g/L)1/2) ? vA3
  (L/2)(3g/L)1/2
• w3 (1/2)(3g/L)1/2
• Use conservation of energy from 3 to 4
• T3 V3 T4 V4

Datum
State 2 just before impact
State 3 just after impact
State 4 at max height
14
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.
• Use conservation of energy from 1 to 2
• T1 V1 T2 V2
• 0 mgL/2 (1/2)(1/3)mL2w22 0 ? w2 (3g/L)1/2
• vA vB w2k x Li - L (3g/L)1/2j
• Use coefficient of restitution from 2 to 3
• e - (vF3 vA3)/(vF2 vA2)
• .5 - (0 vA3)/(0 L (3g/L)1/2) ? vA3
  (L/2)(3g/L)1/2
• w3 (1/2)(3g/L)1/2
• Use conservation of energy from 3 to 4
• T3 V3 T4 V4
• (1/2)(1/3)mL2(1/4)(3g/L) 0

Datum
State 2 just before impact
State 3 just after impact
State 4 at max height
15
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.
• Use conservation of energy from 1 to 2
• T1 V1 T2 V2
• 0 mgL/2 (1/2)(1/3)mL2w22 0 ? w2 (3g/L)1/2
• vA vB w2k x Li - L (3g/L)1/2j
• Use coefficient of restitution from 2 to 3
• e - (vF3 vA3)/(vF2 vA2)
• .5 - (0 vA3)/(0 L (3g/L)1/2) ? vA3
  (L/2)(3g/L)1/2
• w3 (1/2)(3g/L)1/2
• Use conservation of energy from 3 to 4
• T3 V3 T4 V4
• (1/2)(1/3)mL2(1/4)(3g/L) 0 0 (L/2)mgsinq

Datum
State 2 just before impact
State 3 just after impact
State 4 at max height
16
State 1

• Problem 17.104 The uniform slender rod AB is in
• equilibrium in the position shown when end A is
  given a
• slight nudge, causing the rod to rotate
  counterclockwise
• and hit the horizontal surface. Knowing that the
• coefficient of restitution between the knob at A
  and the
• horizontal surface is e .5, determine the
  maximum
• angle of rebound q of the rod.
• Use conservation of energy from 1 to 2
• T1 V1 T2 V2
• 0 mgL/2 (1/2)(1/3)mL2w22 0 ? w2 (3g/L)1/2
• vA vB w2k x Li - L (3g/L)1/2j
• Use coefficient of restitution from 2 to 3
• e - (vF3 vA3)/(vF2 vA2)
• .5 - (0 vA3)/(0 L (3g/L)1/2) ? vA3
  (L/2)(3g/L)1/2
• w3 (1/2)(3g/L)1/2
• Use conservation of energy from 3 to 4
• T3 V3 T4 V4
• (1/2)(1/3)mL2(1/4)(3g/L) 0 0 (L/2)mgsinq
• Sinq 1/4 ? q 14.480

Datum
State 2 just before impact
State 3 just after impact
State 4 at max height
17

• 17.111 A slender rod AB is released from rest
• in the position shown. It swings down to a
• vertical position and strikes a second and
• identical rod CD which is resting on a
• frictionless surface. Assuming that the
• coefficient of restitution between rods is 0.4,
• determine the velocity of rod CD immediately
• after impact.

18

• 17.111 A slender rod AB is released from rest
• in the position shown. It swings down to a
• vertical position and strikes a second and
• identical rod CD which is resting on a
• frictionless surface. Assuming that the
• coefficient of restitution between rods is 0.4,
• determine the velocity of rod CD immediately
• after impact.

State 1
19

• 17.111 A slender rod AB is released from rest
• in the position shown. It swings down to a
• vertical position and strikes a second and
• identical rod CD which is resting on a
• frictionless surface. Assuming that the
• coefficient of restitution between rods is 0.4,
• determine the velocity of rod CD immediately
• after impact. From state 1 to state 2
• T1 V1 T2 V2
• 0 0 (1/2)(1/3)mL2w2 mgL/2
• w (3g/L)1/2

State 1
20

• 17.111 A slender rod AB is released from rest
• in the position shown. It swings down to a
• vertical position and strikes a second and
• identical rod CD which is resting on a
• frictionless surface. Assuming that the
• coefficient of restitution between rods is 0.4,
• determine the velocity of rod CD immediately
• after impact. From state 1 to state 2
• T1 V1 T2 V2
• 0 0 (1/2)(1/3)mL2w2 mgL/2
• w (3g/L)1/2 ? vA vB wk x Lj Lwi

State 1
21

• 17.111 A slender rod AB is released from rest
• in the position shown. It swings down to a
• vertical position and strikes a second and
• identical rod CD which is resting on a
• frictionless surface. Assuming that the
• coefficient of restitution between rods is 0.4,
• determine the velocity of rod CD immediately
• after impact. From state 1 to state 2
• T1 V1 T2 V2
• 0 0 (1/2)(1/3)mL2w2 mgL/2
• w (3g/L)1/2 ? vA vB wk x Lj Lwi
• From 2 to 3 Coefficient of restitution and
  angular momentum about B
• e -(vA3 vC3)/(vA2 vC2)

State 1
22

• 17.111 A slender rod AB is released from rest
• in the position shown. It swings down to a
• vertical position and strikes a second and
• identical rod CD which is resting on a
• frictionless surface. Assuming that the
• coefficient of restitution between rods is 0.4,
• determine the velocity of rod CD immediately
• after impact. From state 1 to state 2
• T1 V1 T2 V2
• 0 0 (1/2)(1/3)mL2w2 mgL/2
• w (3g/L)1/2 ? vA vB wk x Lj Lwi
• From 2 to 3 Coefficient of restitution and
  angular momentum about B
• e -(vA3 vC3)/(vA2 vC2)
• .4 -(vA3 vC3)/(Lw 0)

State 1
23

• 17.111 A slender rod AB is released from rest
• in the position shown. It swings down to a
• vertical position and strikes a second and
• identical rod CD which is resting on a
• frictionless surface. Assuming that the
• coefficient of restitution between rods is 0.4,
• determine the velocity of rod CD immediately
• after impact. From state 1 to state 2
• T1 V1 T2 V2
• 0 0 (1/2)(1/3)mL2w2 mgL/2
• w (3g/L)1/2 ? vA vB wk x Lj Lwi
• From 2 to 3 Coefficient of restitution and
  angular momentum about B
• e -(vA3 vC3)/(vA2 vC2)
• .4 -(vA3 vC3)/(Lw 0)
• -.4Lw vA3 vC3

State 1
24

• 17.111 A slender rod AB is released from rest
• in the position shown. It swings down to a
• vertical position and strikes a second and
• identical rod CD which is resting on a
• frictionless surface. Assuming that the
• coefficient of restitution between rods is 0.4,
• determine the velocity of rod CD immediately
• after impact. From state 1 to state 2
• T1 V1 T2 V2
• 0 0 (1/2)(1/3)mL2w2 mgL/2
• w (3g/L)1/2 ? vA vB wk x Lj Lwi
• From 2 to 3 Coefficient of restitution and
  angular momentum about B
• e -(vA3 vC3)/(vA2 vC2)
• .4 -(vA3 vC3)/(Lw 0)
• -.4Lw vA3 vC3
• IB2 MBt IB3
• (1/3)mL2w 0 (1/3)mL2w3 mLvC3

State 1
25

• 17.111 A slender rod AB is released from rest
• in the position shown. It swings down to a
• vertical position and strikes a second and
• identical rod CD which is resting on a
• frictionless surface. Assuming that the
• coefficient of restitution between rods is 0.4,
• determine the velocity of rod CD immediately
• after impact. From state 1 to state 2
• T1 V1 T2 V2
• 0 0 (1/2)(1/3)mL2w2 mgL/2
• w (3g/L)1/2 ? vA vB wk x Lj Lwi
• From 2 to 3 Coefficient of restitution and
  angular momentum about B
• e -(vA3 vC3)/(vA2 vC2)
• .4 -(vA3 vC3)/(Lw 0)
• -.4Lw vA3 vC3
• IB2 MBt IB3
• (1/3)mL2w 0 (1/3)mL2w3 mLvC3
• (1/3)Lw (1/3)vA3 vC3

State 1
26

• 17.111 A slender rod AB is released from rest
• in the position shown. It swings down to a
• vertical position and strikes a second and
• identical rod CD which is resting on a
• frictionless surface. Assuming that the
• coefficient of restitution between rods is 0.4,
• determine the velocity of rod CD immediately
• after impact. From state 1 to state 2
• T1 V1 T2 V2
• 0 0 (1/2)(1/3)mL2w2 mgL/2
• w (3g/L)1/2 ? vA vB wk x Lj Lwi
• From 2 to 3 Coefficient of restitution and
  angular momentum about B
• e -(vA3 vC3)/(vA2 vC2)
• .4 -(vA3 vC3)/(Lw 0)
• -.4Lw vA3 vC3
• IB2 MBt IB3
• (1/3)mL2w 0 (1/3)mL2w3 mLvC3
• (1/3)Lw (1/3)vA3 vC3
• vC3 (7/20)Lw (7/20)L(3g/L)1/2

State 1
27

• Problem 17.91 The uniform slender rod AB of
  weight 5
• lb and length 2.5 ft forms an angle b 300 with
  the
• vertical as it strikes the smooth corner shown
  with a
• vertical velocity v1 of magnitude 8 ft/s and no
  angular
• velocity. Assuming impact is perfectly plastic,
  determine
• (a) the angular velocity of the rod immediately
  after
• impact, (b) the magnitude of the impulse on the
  rod.

5
28

• Problem 17.91 The uniform slender rod AB of
  weight 5
• lb and length 2.5 ft forms an angle b 300 with
  the
• vertical as it strikes the smooth corner shown
  with a
• vertical velocity v1 of magnitude 8 ft/s and no
  angular
• velocity. Assuming impact is perfectly plastic,
  determine
• (a) the angular velocity of the rod immediately
  after
• impact, (b) the magnitude of the impulse on the
  rod.

y
x
AX
5
AY
29

• Problem 17.91 The uniform slender rod AB of
  weight 5
• lb and length 2.5 ft forms an angle b 300 with
  the
• vertical as it strikes the smooth corner shown
  with a
• vertical velocity v1 of magnitude 8 ft/s and no
  angular
• velocity. Assuming impact is perfectly plastic,
  determine
• (a) the angular velocity of the rod immediately
  after
• impact, (b) the magnitude of the impulse on the
  rod.
• HA1 Imp HA2
• (m v) r IA
  w
• (5/g)(-8)(2.5/2)sin30 0 (1/3)(5/g)(2.5)2w

y
x
AX
5
AY
30

• Problem 17.91 The uniform slender rod AB of
  weight 5
• lb and length 2.5 ft forms an angle b 300 with
  the
• vertical as it strikes the smooth corner shown
  with a
• vertical velocity v1 of magnitude 8 ft/s and no
  angular
• velocity. Assuming impact is perfectly plastic,
  determine
• (a) the angular velocity of the rod immediately
  after
• impact, (b) the magnitude of the impulse on the
  rod.
• HA1 Imp HA2
• (5/g)(-8)(2.5/2)sin30 0 (1/3)(5/g)(2.5)2w
• w - (12/5) rad/s

y
x
AX
5
AY
31

• Problem 17.91 The uniform slender rod AB of
  weight 5
• lb and length 2.5 ft forms an angle b 300 with
  the
• vertical as it strikes the smooth corner shown
  with a
• vertical velocity v1 of magnitude 8 ft/s and no
  angular
• velocity. Assuming impact is perfectly plastic,
  determine
• (a) the angular velocity of the rod immediately
  after
• impact, (b) the magnitude of the impulse on the
  rod.
• HA1 Imp HA2
• (5/g)(-8)(2.5/2)sin30 0 (1/3)(5/g)(2.5)2w
• w - (12/5) rad/s
• vG vA wk x rG/A

y
x
AX
5
AY
32

• Problem 17.91 The uniform slender rod AB of
  weight 5
• lb and length 2.5 ft forms an angle b 300 with
  the
• vertical as it strikes the smooth corner shown
  with a
• vertical velocity v1 of magnitude 8 ft/s and no
  angular
• velocity. Assuming impact is perfectly plastic,
  determine
• (a) the angular velocity of the rod immediately
  after
• impact, (b) the magnitude of the impulse on the
  rod.
• HA1 Imp HA2
• (5/g)(-8)(2.5/2)sin30 0 (1/3)(5/g)(2.5)2w
• w - (12/5) rad/s
• vG vA wk x rG/A
• vG 0i (12/5)k x (2.5/2)(sin30i cos30j)

y
x
AX
5
AY
33

• Problem 17.91 The uniform slender rod AB of
  weight 5
• lb and length 2.5 ft forms an angle b 300 with
  the
• vertical as it strikes the smooth corner shown
  with a
• vertical velocity v1 of magnitude 8 ft/s and no
  angular
• velocity. Assuming impact is perfectly plastic,
  determine
• (a) the angular velocity of the rod immediately
  after
• impact, (b) the magnitude of the impulse on the
  rod.
• HA1 Imp HA2
• (5/g)(-8)(2.5/2)sin30 0 (1/3)(5/g)(2.5)2w
• w - (12/5) rad/s
• vG vA wk x rG/A
• vG 0i (12/5)k x (2.5/2)(sin30i cos30j)
• vG 2.6i 1.5j

y
x
AX
5
AY
34

• Problem 17.91 The uniform slender rod AB of
  weight 5
• lb and length 2.5 ft forms an angle b 300 with
  the
• vertical as it strikes the smooth corner shown
  with a
• vertical velocity v1 of magnitude 8 ft/s and no
  angular
• velocity. Assuming impact is perfectly plastic,
  determine
• (a) the angular velocity of the rod immediately
  after
• impact, (b) the magnitude of the impulse on the
  rod.
• HA1 Imp HA2
• (5/g)(-8)(2.5/2)sin30 0 (1/3)(5/g)(2.5)2w
• w - (12/5) rad/s
• vG vA wk x rG/A
• vG 0i (12/5)k x (2.5/2)(sin30i cos30j)
• vG 2.6i 1.5j
• L1X ImpX L2X

y
x
AX
5
AY
35

• Problem 17.91 The uniform slender rod AB of
  weight 5
• lb and length 2.5 ft forms an angle b 300 with
  the
• vertical as it strikes the smooth corner shown
  with a
• vertical velocity v1 of magnitude 8 ft/s and no
  angular
• velocity. Assuming impact is perfectly plastic,
  determine
• (a) the angular velocity of the rod immediately
  after
• impact, (b) the magnitude of the impulse on the
  rod.
• HA1 Imp HA2
• (5/g)(-8)(2.5/2)sin30 0 (1/3)(5/g)(2.5)2w
• w - (12/5) rad/s
• vG vA wk x rG/A
• vG 0i (12/5)k x (2.5/2)(sin30i cos30j)
• vG 2.6i 1.5j
• L1X ImpX L2X
• (5/g)0 ImpX (5/g)2.6

y
x
AX
5
AY
36

• Problem 17.91 The uniform slender rod AB of
  weight 5
• lb and length 2.5 ft forms an angle b 300 with
  the
• vertical as it strikes the smooth corner shown
  with a
• vertical velocity v1 of magnitude 8 ft/s and no
  angular
• velocity. Assuming impact is perfectly plastic,
  determine
• (a) the angular velocity of the rod immediately
  after
• impact, (b) the magnitude of the impulse on the
  rod.
• HA1 Imp HA2
• (5/g)(-8)(2.5/2)sin30 0 (1/3)(5/g)(2.5)2w
• w - (12/5) rad/s
• vG vA wk x rG/A
• vG 0i (12/5)k x (2.5/2)(sin30i cos30j)
• vG 2.6i 1.5j
• L1X ImpX L2X
• (5/g)0 ImpX (5/g)2.6 ? ImpX .403 lb s

y
x
AX
5
AY
37

• Problem 17.91 The uniform slender rod AB of
  weight 5
• lb and length 2.5 ft forms an angle b 300 with
  the
• vertical as it strikes the smooth corner shown
  with a
• vertical velocity v1 of magnitude 8 ft/s and no
  angular
• velocity. Assuming impact is perfectly plastic,
  determine
• (a) the angular velocity of the rod immediately
  after
• impact, (b) the magnitude of the impulse on the
  rod.
• HA1 Imp HA2
• (5/g)(-8)(2.5/2)sin30 0 (1/3)(5/g)(2.5)2w
• w - (12/5) rad/s
• vG vA wk x rG/A
• vG 0i (12/5)k x (2.5/2)(sin30i cos30j)
• vG 2.6i 1.5j
• L1X ImpX L2X
• (5/g)0 ImpX (5/g)2.6 ? ImpX .403 lb s
• L1Y ImpY L2Y

y
x
AX
5
AY
38

• Problem 17.91 The uniform slender rod AB of
  weight 5
• lb and length 2.5 ft forms an angle b 300 with
  the
• vertical as it strikes the smooth corner shown
  with a
• vertical velocity v1 of magnitude 8 ft/s and no
  angular
• velocity. Assuming impact is perfectly plastic,
  determine
• (a) the angular velocity of the rod immediately
  after
• impact, (b) the magnitude of the impulse on the
  rod.
• HA1 Imp HA2
• (5/g)(-8)(2.5/2)sin30 0 (1/3)(5/g)(2.5)2w
• w - (12/5) rad/s
• vG vA wk x rG/A
• vG 0i (12/5)k x (2.5/2)(sin30i cos30j)
• vG 2.6i 1.5j
• L1X ImpX L2X
• (5/g)0 ImpX (5/g)2.6 ? ImpX .403 lb s
• L1Y ImpY L2Y
• (5/g)(-8) ImpY (5/g)(- 1.5)

y
x
AX
5
AY
39

• Problem 17.91 The uniform slender rod AB of
  weight 5
• lb and length 2.5 ft forms an angle b 300 with
  the
• vertical as it strikes the smooth corner shown
  with a
• vertical velocity v1 of magnitude 8 ft/s and no
  angular
• velocity. Assuming impact is perfectly plastic,
  determine
• (a) the angular velocity of the rod immediately
  after
• impact, (b) the magnitude of the impulse on the
  rod.
• HA1 Imp HA2
• (5/g)(-8)(2.5/2)sin30 0 (1/3)(5/g)(2.5)2w
• w - (12/5) rad/s
• vG vA wk x rG/A
• vG 0i (12/5)k x (2.5/2)(sin30i cos30j)
• vG 2.6i 1.5j
• L1X ImpX L2X
• (5/g)0 ImpX (5/g)2.6 ? ImpX .403 Ns
• L1Y ImpY L2Y
• (5/g)(-8) ImpY (5/g)(- 1.5) ? ImpY 1.01 lb s

y
x
AX
5
AY