An 11.0 m, 230 N uniform ladder rests against a smooth wall. The coefficient of

Question

An 11.0 m, 230 N uniform ladder rests against a smooth wall. The coefficient of static friction between the ladder and the ground is 0.60, and the ladder makes a 50.0° angle with the ground. How far up the ladder can an 860 N person climb before the ladder begins to slip? Note: a few of you will encounter an odd bug in this problem. The random numbers WebAssign generates for you may say the person can climb, say, 11.5m up a ladder that's only 11m long. If that happens, just input 11.5m as your answer and the system should accept it.

Please show your work

Explanation / Answer

we need to balance the forces and moments.
now along the vertical direction the two forces acting downwards are 230 N and 860 N weight of the ladder and person.
so , normal reaction will be N = 230 + 860
N = 1090 N
so , frictional force will be mu * N = F = 0.6 * 1090 = 654 N

now taking the moment about the wall we will have,

230 * (11/2 ) * cos 50 + 860 * d cos 50 + 654 * 11* sin 50 = 1090 * 11 cos 50
813.12 + 552.79 d +5510.92 = 7707.02
=>
d = 2.5018 m ( from top of ladder)

so from the bottom it will be 11- 2.5018 = 8.498 m

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