Question #107263

A uniform ladder 10m long and weighing 59N rets against a smooth vertical wall. If the ladder is just on the verge of slipping when it makes a 50 degree angle with the ground, find the coefficient of static friction between the ladder and the ground.

Expert's answer

As per the given question,

Length of the uniform ladder(L)=10m

Weight of the ladder =59N

Angle between the ladder and the ground ="50^\\circ"

Let the reaction on the bottom of the ladder "N_1" and reaction on the wall "N_2"

Now, taking the torque about the center of the ladder

"N_1\\times\\dfrac{L}{2} \\sin 50-\\mu N_1\\dfrac{L}{2}\\cos 50=N_2\\times \\dfrac{L}{2}\\cos 50"

"N_2=N_1\\tan 50-\\mu N_1--------(i)"

Now, balancing horizontal force

"N_2=\\mu N_1-------(ii)"

From equation (i) and (ii)

"2\\mu N_1=N_1\\tan 50"

"\\mu=\\dfrac{\\tan 50}{2}=0.59"

"\\mu =0.59"

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