Question 8.10: DON'T CLIMB THE LADDER GOAL Apply the two conditions of equi...
DON’T CLIMB THE LADDER
GOAL Apply the two conditions of equilibrium.
PROBLEM A uniform ladder 10.0 \mathrm{~m} long and weighing 50.0 \mathrm{~N} rests against a frictionless vertical wall as in Figure 8.17 \mathrm{a}. If the ladder is just on the verge of slipping when it makes a 50.0^{\circ} angle with the ground, find the coefficient of static friction between the ladder and ground.
STRATEGY Figure 8.17 \mathrm{~b} is the force diagram for the ladder. The first condition of equilibrium, \sum \overrightarrow{\mathbf{F}}_{i}=0, gives two equations for three unknowns: the magnitudes of the static friction force f and the normal force n, both acting on the base of the ladder, and the magnitude of the force of the wall, P, acting on the top of the ladder. The second condition of equilibrium, \Sigma \tau_{i}=0, gives a third equation (for P ), so all three quantities can be found. The definition of static friction then allows computation of the coefficient of static friction.
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