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HOMEWORK 2

EQUILIBRIUM OF PARTICLES

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1. Determine theforce P required tomaintain the 200-kgengine in the positionfor which q = 30o.The diameter of the

pulley at B isnegligible.

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2. The collar A of mass m may slide freely on thehorizontal frictionless rod. The spring attached to

the collar has a stiffness of 10 N/cm and it isundeformed when the collar is directly belowsupport B. Determine the magnitude of the force Prequired to maintain equilibrium.

9 cm

12 cm

B

AP

m

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3. A scale is constructed using the 10 kg mass A, the 2 kgpan P and the pulley and cord arrangement. Cord BCA is 2 mlong. If s = 0.75 m, determine the mass D in the pan. Neglectthe size of the pulley.

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5. The pipe is held in

place by the vice. Ifthe bolt exerts aforce of 250 N on thepipe in the directionshown, determine theforces F A and F B thatthe smooth contactsat A and B exert onthe pipe.

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6. Determine the mass of each of the two cylindersif they cause a sag of s = 0.5 m when supported from

the rings at A and B. Note that s = 0 when thecylinders are removed.

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7. Two particles weighing 800 N and 200 N are held in

equilibrium on frictionless perpendicular surfaces by a cable

which makes an angle q with the horizontal.

a) Determine the normal forces acting from the surfaces on

the particles,

b) Tension in the cable,

c) Angle q .

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2 m

A

B

C

y

10 m

8. The pail and its contents have mass of 60 kg. If cableBAC is 15 m long, determine the distance y of the pulley

for equilibrium. Neglect the mass of the pulley. Also findthe tension in the cable.

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9. A small peg P rests on a spring that is contained inside thesmooth pipe. When the spring is compressed so that s = 0.15

m, the spring exerts an upward force of 60 N on the peg.

B

A

x

0.3 m

yx

z

y

s

C

P

0.2 m0.4 m

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Determine thepoint ofattachment A (x,

y, 0) of cord PAso that thetension in cordsPB and PC equals

30 N and 50 N,respectively.

http://images.google.com/url?sa=i&rct=j&q=metal+spring&source=images&cd=&cad=rja&docid=dBpMB8OyVTmvlM&tbnid=uQFxmMPENo080M:&ved=0CAUQjRw&url=http://www.calypsoushaka.co.za/Newsletter&ei=8SVOUdnGLcSsPLfQgTg&bvm=bv.44158598,d.ZWU&psig=AFQjCNE0PZqBqMPFkWN4vFqLJHYuz0cSJw&ust=1364162413190132

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10. Straight bar AB is fixed in space. Spring CD has a stiffnessof 3 N/mm and its unstretched length is 200 mm. If there is nofriction between collar C and bar AB,

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determine the weight W of the collar thatproduces the equilibriumcondition shown and thereaction between thecollar and bar AB.

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x y

z

11. Determine the tensions in cables AB , AC , and ADfor equilibrium.

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12. Determine the stretch in each of the two springsrequired to hold the 20 kg crate in the equilibrium position

shown. Each spring has an unstretched length of 2 m and astiffness of k = 300 N/m.

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13. Determine theforce in each

cable used to liftthe 9.50 Mg surgearrester atconstant velocity.

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