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Any time you have to climb a ladder, you want the ladder to remain in static equilibrium. At

Any time you have to climb a ladder, you want the ladder to remain in static equilibrium. At

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Any time you have to climb a ladder, you want the ladder to remain in static equilibrium. At what angle should a 60-kg painter place his ladder against the wall in order to climb two-thirds of the way up the ladder and have the ladder remain in static equilibrium? The ladder's mass is 10 kg and its length is 6.0 m. The exterior wall of the house is very smooth, meaning that it exerts a negligible friction force on the ladder. The coefficient of static friction between the floor and the ladder is 0.50.
Transcribed Image Text:Any time you have to climb a ladder, you want the ladder to remain in static equilibrium. At what angle should a 60-kg painter place his ladder against the wall in order to climb two-thirds of the way up the ladder and have the ladder remain in static equilibrium? The ladder's mass is 10 kg and its length is 6.0 m. The exterior wall of the house is very smooth, meaning that it exerts a negligible friction force on the ladder. The coefficient of static friction between the floor and the ladder is 0.50.
Given , F loor = mpig+meg L= Gm M= bekg =686N Sfyc0 Friction force M FNi Fioo Co. 50) C686) = 343M L=6m wall smooth TN, Froor mcng Ffloor Et=0 X 2 Cose + X 4 cos.@ t Fx 6 sin@-Mx€s mcg X6. X 2C0S@ + 1o x9.8 x4 cos O + 343 x6sinô- 686 cose-o 11 76 Cos Le) t 392 (oS 6 + 2058 sin @ - 4116 Cose- 2548 Cos ☺.+2058Sin 6 60 cos e cos e -25 48 +2058 tan Ce) =o +2548 > 2058tan 8=2548 2058 2058 + 2 548 tan e=26, =e=tan C26) =51.1 21 21 angie made byg ladder with verticol wall= 90-51.1= 38.9
Transcribed Image Text:Given , F loor = mpig+meg L= Gm M= bekg =686N Sfyc0 Friction force M FNi Fioo Co. 50) C686) = 343M L=6m wall smooth TN, Froor mcng Ffloor Et=0 X 2 Cose + X 4 cos.@ t Fx 6 sin@-Mx€s mcg X6. X 2C0S@ + 1o x9.8 x4 cos O + 343 x6sinô- 686 cose-o 11 76 Cos Le) t 392 (oS 6 + 2058 sin @ - 4116 Cose- 2548 Cos ☺.+2058Sin 6 60 cos e cos e -25 48 +2058 tan Ce) =o +2548 > 2058tan 8=2548 2058 2058 + 2 548 tan e=26, =e=tan C26) =51.1 21 21 angie made byg ladder with verticol wall= 90-51.1= 38.9
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