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Asignatura: Física, Profesor: , Carrera: Ingeniería en Informática, Universidad: UC3M
Tipo: Ejercicios
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Determine the vertical force P which must be applied at G to maintain the
equilibrium of the linkage.
Assuming
A δ y
it follows
C A A δ y = δ y = δ y
E C A δ y = δ y = δ y
D A A A δ y = δ y = δ y = δ y
G A A A δ y = δ y = δ y = δ y
Then, by Virtual Work
Determine the vertical force P which must be applied at G to maintain the
equilibrium of the linkage.
Link ABC
Link DEFG
Assume
δθclockwise
Then for point C
and for point D
And for link DEFG
D δ x = δφ
∴ 5 δ θ = 15 δφ
or
δφ = δθ
Then
4 2 2 in. 3
G δ δφ δθ
Now cos 45 G G δ y = δ °
2 cos 45 3
δθ
in. 3
δθ
Then, by Virtual Work.
δθ δθ P δθ
or P =40 lb W
Determine the couple M which must be applied to member DEFG to
maintain the equilibrium of the linkage.
Assuming
A δ y
it follows
C A A δ y = δ y = δ y
E C A δ y = δ y = δ y
D A A A δ y = δ y = δ y = δ y
E A A
y y y
δ δ δφ= = = δ
Then, by Virtual Work:
A A A δ y δ y M δ y
M = + 6000 N mm⋅ M = 6.00 N m⋅ W
An unstretched spring of constant 4 lb/in. is attached to pins at points C
and I as shown. The pin at B is attached to member BDE and can slide
freely along the slot in the fixed plate. Determine the force in the spring
and the horizontal displacement of point H when a 20-lb horizontal force
directed to the right is applied ( a ) at point G , ( b ) at points G and H.
First note:
xG = 3 xD ⇒ δ xG = 3 δ xD
xH = 4 xD ⇒ δ xH = 4 δ xD
xI = 5 xD ⇒ δ xI = 5 δ xD
( a ) Virtual Work δ U = 0: FG δ xG − FSP δ xI = 0
thus, FSP = 12.00 lb T W
Now FSP = k ∆ xI
Thus, ∆ x (^) I =3 in.
and
δ x D = δ xH = δ xI
∴ ∆ xH = ∆ xI
3 in. 5
= or ∆ x (^) H = 2.40 in. W
( b ) Virtual Work: δ U = 0: FG δ xG + FH δ xH − FSP δ xI = 0
thus, FSP = 28.0 lb T W
Now FSP = k ∆ xI
Thus, ∆ x (^) I =7 in.
From part ( a )
∆ x (^) H = ∆ xI
7 in. 5
= or ∆ x (^) H = 5.60 in. W
Now SP I F = k ∆ x
I = ∆ x
Thus, 3 in. I ∆ x =
From part ( a )
H I ∆ x = ∆ x
3 in. 5
= or 2.40 in. H ∆ x = W
Knowing that the maximum friction force exerted by the bottle on the
cork is 300 N, determine ( a ) the force P which must be applied to the
corkscrew to open the bottle, ( b ) the maximum force exerted by the base
of the corkscrew on the top of the bottle.
From sketch
A C y = y
Thus, 4 A C δ y = δ y
( a ) Virtual Work:
A C δ U = P δ y − F δ y =
( b ) Free body: Corkscrew
Σ F (^) y = 0: R + P − F = 0
The mechanism shown is acted upon by the force P ; derive an expression
for the magnitude of the force Q required for equilibrium.
Virtual Work:
Have x (^) A =2 sin l θ
δ x (^) A = 2 cos l θ δθ
and yF =3 cos l θ
δ yF = − 3 sin l θ δθ
Virtual Work: δ U = 0: Q δ x (^) A + P δ yF = 0
tan 2
Q = P θW
Knowing that the line of action of the force Q passes through point C ,
derive an expression for the magnitude of Q required to maintain
equilibrium
Have 2 cos ; 2 sin A A y = l θ δ y = − l θ δθ
CD l CD l
θ θ = δ = δθ
Virtual Work:
P l Q l
θ θ δθ δθ
sin 2 cos /
θ
θ
