6b- equilibrium slides

8/16/2019 6b- Equilibrium Slides

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Equilibrium


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Conditions for Equilibrium

• A body is said to be in equilibrium ifthe:

1. The resultant of all the forces actingon a body is equal to zero (∑F ! orFnet!"(linear acceleration !ms

#$".

$. The resultant of all the moments ortorques (T" acting on the body isequal to zero (∑T!% Tnet!"

(angular acceleration !ms#$".


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&arallel forces


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&rinci'le of oments

• )um of u'*ard forces sum ofdo*n*ard forces

• )um of anticloc+*ise moments sum of cloc+*ise moments

• , A moment or torque about a 'ointis found by multi'lying the force bythe 'er'endicular distance from theline of action of the force to the'oint.


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Ti's to -ote

• The 'iot 'oint is chosen such that*e eliminate all the un+no*n forcesat a 'oint.

• Turning e/ect% moment and torqueall hae the same meaning and are ameasure of the ability of a force to

rotate a body about a 'oint.• 0emember not to confuse -m in

moments *ith -m in oule (Energy".


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Triangle of Forces(2ector Triangle"

• This is a quic+ method if determining*hether or not the forces are inequilibrium using scaled ector

dra*ings.

• 3f the forces are not in equilibriumthe triangle *ill not close.

• 3f three forces are in equilibrium%they can be re'resented inmagnitude and direction by the three

sides of a triangle ta+en in order.


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E4am'le: 5adder &roblem


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Ti' to -ote

• The three forces (6% 0 and F" mustall 'ass through the same 'oint inorder to balance their resultant.


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E4am'le 1: Triangle ofForces

• A uniform ladder of *eight $!!- andlength 1$m is 'laced at an angle of 7!! tothe horizontal% *ith one end 8 leaning

against a smooth *all and the other end Aon the ground. Calculate the reaction force0 of the *all at 8 and the force (F" of theground at A.


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)olution

• 9se an a''ro'riate scale to re'resentthe forces gien. ere *e are gienthe *eight (6 $!!-" ( E.g 1cm

;!-"

• Com'lete the ector triangle

• easure the lengths of the sides ofthe triangle used to re'resent F and0 to determine their magnitudes


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E4am'le $: Triangle ofForces

• Consider the three forces sho*nbelo*. Find the angles that the


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)olution


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E4am'le >: Triangle offorces

• A massie iron ball ($!! +g" is used tos'eed u' demolition *or+. 3t hangs from asingle steel cable. 3t is hauled bac+ using a

horizontal ro'e% then released% to s*inginto the doomed building. 3f the ro'ecannot safely tolerate a tension of morethan 1!!! -% 6hat is the ma4imum angle

from the ertical for the steel su''ortingcable?


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)olution

• 1" Choose a suitable scale for the ectordiagram

• E.g 1cm ;!!-

• $" @ra* lines of length 'ro'ortional to themagnitude of the +no*n forces acting at the'oint ta+en in order.

• >" Com'lete the triangle and measure the

length of the un+no*n force

• " 9sing a 'rotractor% measure the angle at*hich the force is acting from the 'oint.


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&ractice: Tension in the ro'e

• Calculate the tension in the *iresu''orting the


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3nclined 'lane


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E4am'le

• A car of *eight 6 is 'ositioned on aroad slo'ing at an angle of >!! to thehorizontal. The frictional force on the

car is !!!- acting u' the road along8C. Find 6 and the normal reactionforce 0 of the road on the car.


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Ti' to -ote

• The acceleration do*n the slo'e isinde'endent of the mass of the obBect.

• A''lying -e*tons second la* for the

resultant force acting do*n the slo'e:• ∑F ma

• mgsinD ma

•

Therefore% a gsinD


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Cou'le

• T*o equal and o''osite forces *hoselines of action do not coincide are said tofrom a cou'le (E.g o'ening a bottle ca'"

• These t*o forces tends to 'roduce somerotation

• The torque (T or " due to a cou'le isequal to the magnitude of one of theforces (F" 4 perpendicular distance bet*een their lines of action (d".


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E4am'le: Cou'le

• 6hat is the magnitude of the torquedue to the cou'le sho*n in the gurebelo*?

Ans: -m


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E4am'le

• T*o 'arallel forces F act in o''ositedirections along the sides A@ and C8of a rectangular 'late A8C@. T*o

equal and o''osite forces of $- actalong the sides C@ and A8 as sho*n.Calculate F if the 'late does not

rotate. F >-

6b- equilibrium slides

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