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Problem 12.128
Pin B weighs 4 oz and is free to slidein a horizontal plane along the rotatingarm OC and along the circular slot DEof radius b = 20 in. Neglecting frictionand assuming that = 15 rad/s and = 250 rad/s2 for the position = 20o,determine for that position (a) theradial and transverse components ofthe resultant force exerted on pin B,(b) the forces P and Q exerted on pinB, respectively, by rod OC and the wallof slot DE.
...
Solving Problems on Your OwnProblem 12.128
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1. Kinematics: Examine the velocity and acceleration of theparticle. In polar coordinates:
v = r er + r e
a = (r - r 2 ) er + (r + 2 r ) e
.
.. .
.
... . r = r er
eer
Pin B weighs 4 oz and is free to slidein a horizontal plane along the rotatingarm OC and along the circular slot DEof radius b = 20 in. Neglecting frictionand assuming that = 15 rad/s and..
.
= 250 rad/s2 for the position = 20o, determine for that position(a) the radial and transverse components of the resultant forceexerted on pin B, (b) the forces P and Q exerted on pin B,respectively, by rod OC and the wall of slot DE.
Solving Problems on Your OwnProblem 12.128
Pin B weighs 4 oz and is free to slidein a horizontal plane along the rotatingarm OC and along the circular slot DEof radius b = 20 in. Neglecting frictionand assuming that = 15 rad/s and..
.
= 250 rad/s2 for the position = 20o, determine for that position(a) the radial and transverse components of the resultant forceexerted on pin B, (b) the forces P and Q exerted on pin B,respectively, by rod OC and the wall of slot DE.
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B CD
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2. Kinetics: Draw a free body diagram showing the appliedforces and an equivalent force diagram showing the vectorma or its components.
Solving Problems on Your OwnProblem 12.128
Pin B weighs 4 oz and is free to slidein a horizontal plane along the rotatingarm OC and along the circular slot DEof radius b = 20 in. Neglecting frictionand assuming that = 15 rad/s and..
.
= 250 rad/s2 for the position = 20o, determine for that position(a) the radial and transverse components of the resultant forceexerted on pin B, (b) the forces P and Q exerted on pin B,respectively, by rod OC and the wall of slot DE.
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B CD
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3. Apply Newton’s second law: The relationship between theforces acting on the particle, its mass and acceleration is givenby F = m a . The vectors F and a can be expressed in terms ofeither their rectangular components or their radial and transversecomponents. With radial and transverse components:
Fr = m ar = m ( r - r 2 ) and F = m a = m ( r + 2 r ) .. . .. . .
Problem 12.128 Solution
Kinematics.b
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r = 2 b cos
r = - 2 b sin
r = - 2 b sin - 2 b cos 2..
. .
...
= 20o
= 15 rad/s
= 250 rad/s2..
.
Problem 12.128 Solution
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r = 2 b cos , r = - 2 b sin , r = - 2 b sin - 2 b cos 2... . ...
For: b = 20/12 ft, = 20o,
= 15 rad/s = 250 rad/s2
r = 2 (20/12 ft) cos 20o = 3.13 ft
r = - 2 (20/12 ft) sin 20o (15 rad/s) = - 17.1 ft/s
r = -2(20/12 ft) sin 20o (250 rad/s2 ) - 2(20/12 ft) cos 20o (15 rad/s)2
r = - 989.79 ft/s2
.
. ..
..
..
Problem 12.128 Solution
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EKinetics; draw a free body diagram.
r
O A
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r
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B
Fr
F
mar
ma
=
(a) Radial and transversecomponents of the resultant forceexerted on pin B.
Problem 12.128 Solution
r
O A
B
r
O A
B
Fr
F
mar
ma
=
Apply Newton’s second law.
+ Fr = mar: Fr = m ( r - r 2 )
Fr = [- 989.79 - ( 3.13 )(152 )] = -13.16 lb Fr = 13.16 lb
+ F = ma: F = m ( r + 2 r )
F = [(3.13)(250) + 2 (-17.1)(15)] = 2.1 lb
(4/16)32.2
.
.
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..
(4/16)32.2
..
F = 2.10 lb
Problem 12.128 Solution
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r
O A
B
r
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Fr
F
=Q
P
Fr = - Q cos
-13.16 = - Q cos 20o
Q = 14.00 lb 40o
F = - Q sin + P
2.10 = - 14.0 sin 20o + P
P = 6.89 lb 20o
