.com/ibiscms/modlibis/view.php?id 1564272 3/25/2015 01:00 PM A 25/100 Print calc

Question

.com/ibiscms/modlibis/view.php?id 1564272 3/25/2015 01:00 PM A 25/100 Print calculator Periodic Table uestion 2 o 4 A ladder is leaning against a vertical wall, and both ends of the ladder are at the point of slipping. The coefficient of friction between the ladder and the horizontal surface is 0.155 and the coefficient of friction between the ladder and the wall is 0.153. Determine the maximum angle with the vertical the ladder can make without falling on the ground. Number O Previous Give Up & View Solution Check Answer O Next i E

Explanation / Answer

Here ,

for simlification , let mass of ladder = 1 kg

length of ladder = 1 m

representing angle alpha by a

let the friction at the verticle is fv

and normal force at the wall is Nv

Normal force at the ground is N

friction at the ground is f

Now , as both the ends are about to slip

f = 0.155N

fv = 0.153 Nv

Now , balancing forces in y - direction ,

m*g = N + 0.153 Nv

9.8 = N + 0.153 Nv ---(1)

balancing the horizontal forces

Nv - 0.155 N = 0 ---(2)

solving 1 and 2

N = 9.57 N

Nv = 1.49 N

Now , balancing the torque about the base of ladder,

mg*l*sin(a)/2 - Nv*l*cos(a) - 0.153Nv*l*sin(a) = 0

4.9*sin(a) - 1.49*cos(a) - 0.153*1.49*sin(a) = 0

solving for a

a = 17.7 degree

the maximum angle ladder can make is 17.7 degree

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