The slender bar AB (IAB = 12 mL²) with a mass of mAB 20.0 kg and length of L = = 2.40 m, is supported by a pin at A, and is initially at rest. Ball C, with a mass of mc = 1.500 kg, strikes the bar with a velocity of vo = 40.0 m/s at 0.500 m above end B, as shown in Figure 1. The coefficient of restitution between the bar and the ball is e = = 0.600. Figure 1 C Vo 0.500 m A D Variables used: w' angular velocity of the bar immediately after impact VG' - velocity of the bar at its centroid immediately after impact velocity of the ball immediately after impact Vc 2.40 m VD' - velocity of the bar at point of impact with the ball at D, immediately after impact B 1) [20%] Determine the velocity of ball C immediately after impact, vč. 2) [20%] Determine the angular velocity of bar AB immediately after impact, w'. 3) [10%] 4) [10%] Determine the velocity of bar AB at its centroid immediately after impact, VG'. Determine the horizontal impulse at A. 5) [10%] Determine the vertical impulse at A. The inertia-force diagram for the slender bar AB is shown in Figure 2. A force F = 84.1 kN is acting 0. 500 m above end B. At this instant, the acceleration of the centroid of the bar aĠ in terms of its angular acceleration αAB is given as aG = aGx î+ 200 1 -αAB Ĵ. Figure 2 Ay A MABAGY G IABαAB MABAGX B A Ax G 2.40 m W F 0.500 m B 6) [10%] Determine the angular acceleration of the bar, αAB. 7) [10%] Determine the horizontal reaction force at A. 8) [10%] Determine the vertical reaction force at A.
The slender bar AB (IAB = 12 mL²) with a mass of mAB 20.0 kg and length of L = = 2.40 m, is supported by a pin at A, and is initially at rest. Ball C, with a mass of mc = 1.500 kg, strikes the bar with a velocity of vo = 40.0 m/s at 0.500 m above end B, as shown in Figure 1. The coefficient of restitution between the bar and the ball is e = = 0.600. Figure 1 C Vo 0.500 m A D Variables used: w' angular velocity of the bar immediately after impact VG' - velocity of the bar at its centroid immediately after impact velocity of the ball immediately after impact Vc 2.40 m VD' - velocity of the bar at point of impact with the ball at D, immediately after impact B 1) [20%] Determine the velocity of ball C immediately after impact, vč. 2) [20%] Determine the angular velocity of bar AB immediately after impact, w'. 3) [10%] 4) [10%] Determine the velocity of bar AB at its centroid immediately after impact, VG'. Determine the horizontal impulse at A. 5) [10%] Determine the vertical impulse at A. The inertia-force diagram for the slender bar AB is shown in Figure 2. A force F = 84.1 kN is acting 0. 500 m above end B. At this instant, the acceleration of the centroid of the bar aĠ in terms of its angular acceleration αAB is given as aG = aGx î+ 200 1 -αAB Ĵ. Figure 2 Ay A MABAGY G IABαAB MABAGX B A Ax G 2.40 m W F 0.500 m B 6) [10%] Determine the angular acceleration of the bar, αAB. 7) [10%] Determine the horizontal reaction force at A. 8) [10%] Determine the vertical reaction force at A.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![The slender bar AB (IAB
=
12
mL²) with a mass of mAB 20.0 kg and length of L
=
=
2.40 m,
is
supported by a pin at A, and is initially at rest. Ball C, with a mass of mc
=
1.500 kg, strikes the
bar with a velocity of vo = 40.0 m/s at 0.500 m above end B, as shown in Figure 1. The
coefficient of restitution between the bar and the ball is e = = 0.600.
Figure 1
C
Vo
0.500 m
A
D
Variables used:
w'
angular velocity of the bar immediately after impact
VG' - velocity of the bar at its centroid immediately after impact
velocity of the ball immediately after impact
Vc
2.40 m
VD' - velocity of the bar at point of impact with the ball at D,
immediately after impact
B
1) [20%]
Determine the velocity of ball C immediately after impact, vč.
2) [20%]
Determine the angular velocity of bar AB immediately after impact, w'.
3) [10%]
4) [10%]
Determine the velocity of bar AB at its centroid immediately after impact, VG'.
Determine the horizontal impulse at A.
5) [10%] Determine the vertical impulse at A.
The inertia-force diagram for the slender bar AB is shown in Figure 2. A force F = 84.1 kN is
acting 0. 500 m above end B. At this instant, the acceleration of the centroid of the bar aĠ in terms
of its angular acceleration αAB is given as aG = aGx î+
200
1
-αAB Ĵ.
Figure 2
Ay
A
MABAGY
G
IABαAB
MABAGX
B
A
Ax
G
2.40 m
W
F
0.500 m
B
6) [10%]
Determine the angular acceleration of the bar, αAB.
7) [10%]
Determine the horizontal reaction force at A.
8) [10%]
Determine the vertical reaction force at A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23067924-0c25-4da4-bd00-385725079ded%2F90770cc5-26b9-488a-b236-89aed7842675%2Fu3rjn7j_processed.png&w=3840&q=75)
Transcribed Image Text:The slender bar AB (IAB
=
12
mL²) with a mass of mAB 20.0 kg and length of L
=
=
2.40 m,
is
supported by a pin at A, and is initially at rest. Ball C, with a mass of mc
=
1.500 kg, strikes the
bar with a velocity of vo = 40.0 m/s at 0.500 m above end B, as shown in Figure 1. The
coefficient of restitution between the bar and the ball is e = = 0.600.
Figure 1
C
Vo
0.500 m
A
D
Variables used:
w'
angular velocity of the bar immediately after impact
VG' - velocity of the bar at its centroid immediately after impact
velocity of the ball immediately after impact
Vc
2.40 m
VD' - velocity of the bar at point of impact with the ball at D,
immediately after impact
B
1) [20%]
Determine the velocity of ball C immediately after impact, vč.
2) [20%]
Determine the angular velocity of bar AB immediately after impact, w'.
3) [10%]
4) [10%]
Determine the velocity of bar AB at its centroid immediately after impact, VG'.
Determine the horizontal impulse at A.
5) [10%] Determine the vertical impulse at A.
The inertia-force diagram for the slender bar AB is shown in Figure 2. A force F = 84.1 kN is
acting 0. 500 m above end B. At this instant, the acceleration of the centroid of the bar aĠ in terms
of its angular acceleration αAB is given as aG = aGx î+
200
1
-αAB Ĵ.
Figure 2
Ay
A
MABAGY
G
IABαAB
MABAGX
B
A
Ax
G
2.40 m
W
F
0.500 m
B
6) [10%]
Determine the angular acceleration of the bar, αAB.
7) [10%]
Determine the horizontal reaction force at A.
8) [10%]
Determine the vertical reaction force at A.
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