b

b

r

O

A

B CD

E

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

b

b

r

O

A

B CD

E

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.

b

b

r

O

A

B CD

E

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.

b

b

r

O

A

B CD

E

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

b

r

O

A

B CD

E

b

r

O

A

B

b

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

b

r

O

A

B

b

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

b

b

r

O

A

B CD

EKinetics; draw a free body diagram.

r

O A

B

r

O A

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

.

.

.

..

(4/16)32.2

..

F = 2.10 lb

Problem 12.128 Solution

b

b

r

O

A

B CD

E

r

O A

B

r

O A

B

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