A 5 kg, 3.4 m ladder is propped against a 2.4 m wall with the edge of the wall c

Question

A 5 kg, 3.4 m ladder is propped against a 2.4 m wall with the edge of the wall contacting the ladder at 2.6 m of its length (meaning there is 0.8 m of the ladder above the edge of the wall). a) Determine the normal force of the wall on the ladder. (assume a horizontal normal force) This ladder is mounted on an icy patch of asphalt and an 80 kg person was only able to climb 1.5 m up the length of the ladder before it started to slip. b) Determine the components of force acting at the base of the ladder before it starts to slip. c) From this determine the coefficient of static friction.

Explanation / Answer

a] Balancing torque about base of ladder,

mg*L/2 cos theta = N *h

5*9.8*3.4/2*1/2.6 = N*2.4

N = [5*9.8*1.7/2.6]/2.4 = 13.35 N answer

b] Force at base of ladder : Fx = friction = 13.35 N

Fy =normal at base = mg = 49 N

So F = 13.35 i + 49 j N

c] u >= f/N = 13.35/49 = 0.272 (greater than or equal to)

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