Problem 3.154

The force P has a magnitudeof 250 N and is applied at theend C of a 500 mm rod ACattached to a bracket at A andB. Assuming = 30o and = 60o, replace P with (a) anequivalent force-couplesystem at B , (b) an equivalentsystem formed by two parallelforces applied at A and B.

P

C

B

A200 mm

300 mm

Solving Problems on Your Own

The force P has a magnitudeof 250 N and is applied at theend C of a 500 mm rod ACattached to a bracket at A andB. Assuming = 30o and = 60o, replace P with (a) anequivalent force-couplesystem at B , (b) an equivalentsystem formed by two parallelforces applied at A and B.

1. Replace a force with an equivalent force-couple system at aspecified point. The force of the force-couple system is equal tothe original force, while the required couple vector is equal to themoment of the original force about the given point.

P

C

B

A200 mm

300 mm

Problem 3.154

Problem 3.154 Solution

P

C

B

A200 mm

300 mm

Replace a force with an equivalentforce-couple system at a specifiedpoint.

(a) Equivalence requires:

F : F = P or F = 250 N 60o

MB : M = _ (0.3 m)(250 N) = _75 N

The equivalent force couple system at B is:

F = 250 N 60o, M = 75 N . m

Problem 3.154 Solution

(b) Require: The two force systems are equivalent.

P

C

B

A200 mm

300 mm

B

A

C

60o

250 N30o

C

B

A FB

FA

xy

=

B

A

C

60o

250 N30o

C

B

A FB

FA

xy

=

Problem 3.154 Solution

Equivalence then requires:

Fx : 0 = FA cos + FB cos

FA = _ FB or cos = 0

Fy : _250 = _ FA sin _ FB sin

If FA = _ FB then _ 250 = 0 reject

Consequently cos = 0 or = 90o and FA + FB = 250

Problem 3.154 Solution

B

A

C

60o

250 N30o

C

B

A FB

FA

xy

=

Also:

MB : _ (0.3 m)( 250 N) = (0.2 m) FA

or FA = _ 375 N

and FB = + 675 N

FA = 375 N 60o, FB = 625 N 60o

+