In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the overhead view of the figure. The tire remains stationary in spite of the three pulls. Alex pulls with force of magnitude 227 N, and Charles pulls with force of magnitude 175 N. Note that the direction of Charles' force is not given. What is the magnitude of Betty's force?
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ΣFx= -F(A) •cos47 +F(C)cosφ=0
ΣFy= F(A) •sin47 +F(C) sinφ –F(B) =0
-227•0.68 +175•cosφ=0
227•0.73 +175•sinφ –F(B) = 0
154.36 =175•cosφ
cosφ=154.36/175 = 0.88
φ= 28.36°
sin28.36°=0.47.
166 +175•sinφ –F(B) = 0
F(B) =166 +175•sinφ=
=166 +175•0.47 = 249 N
ΣFy= F(A) •sin47 +F(C) sinφ –F(B) =0
-227•0.68 +175•cosφ=0
227•0.73 +175•sinφ –F(B) = 0
154.36 =175•cosφ
cosφ=154.36/175 = 0.88
φ= 28.36°
sin28.36°=0.47.
166 +175•sinφ –F(B) = 0
F(B) =166 +175•sinφ=
=166 +175•0.47 = 249 N
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 given angle is 142°). The tire remains stationary in spite of the three pulls. Alex pulls with force Upper F Overscript right-arrow EndScripts Subscript Upper A of magnitude 219 N, and Charles pulls with force Upper F Overscript right-arrow EndScripts Subscript Upper C of magnitude 187 N. Note that the direction of Upper F Overscript right-arrow EndScripts Subscript Upper C is not given. What is the magnitude of Betty's force Upper F Overscript right-arrow EndScripts Subscript Upper B if Charles pulls in (a) the direction drawn in the picture or (b) the other possible direction for equilibrium?
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