answer a and b questions uliun Watch Y In a two-dimensional tug-of-war, Alex, Be

Question

answer a and b questions

uliun Watch Y In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the picture. The tire remains stationary in spite Alex pulls with force A of magnitude 218 N, and Charles pulls of the three pulls. with force. c of magnitude 188 N. Note that the direction of F C is not given. What is the magnitude of Betty's if force B Charles pulls in (a) the direction drawn in the picture or (b) the other possible direction for equilibrium? Alex Charles Betty 152

Explanation / Answer

a) Now the divide the force acting on the tug-of-war along the horizontal x - direction and vertical y-direction

Fx = 0

==> Fc cos@ - FA cos62 = 0

==> cos@ = FA cos62 / Fc

= 218 cos62 / 188

= 0.5443

==> @ = 57.01 deg

Now along the vertical direction

Fy = 0

==> FA sin62 + Fc sin57.01 - FB = 0

==> FB = 218 sin62 + 188 sin57.01

= 350.18 N

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(b)

along the horizontal direction

FA cos62 + Fc cos (270-@ ) = 0

==> cos (270 -@ ) = - FA cos62 / Fc

- sin@ = - 218 * cos62 / 188

@ = 33.0 deg

along the vertical direction

FA sin62 - Fc sin33 - FB = 0

==> FB = 218 sin62 - 188 sin33

= 90.07 N

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