An 85-kg person stands on a lightweight ladder, as shown in the figure(Figure 1)

Question

An 85-kg person stands on a lightweight ladder, as shown in the figure(Figure 1) . The floor is rough; hence, it exerts both a normal force f1, and a frictional force f2, on the ladder. The wall, on the other hand, is frictionless; it exerts only a normal force, f3

Part A

Suppose the person climbs higher on the ladder. As a result, is the ladder more likely, less likely, or equally likely to slip?

Part B

Choose the best explanation from among the following:

1-The magnitude of f2 must increase as the person moves upward. 2-When the person is higher, the ladder presses down harder on the floor . 3-The forces are the same regardless of the person's position . f3

Explanation / Answer

Balancing forces in vertical direction,

f1 - mg =0

in horizontal,

f2 - f3 = 0

balancing moment about floor point,

mgcos@ x (h/sin@) - f3 sin@ x L = 0

f3 = mgh cos@ / sin@ ^2 L

here everthing constant except h

so f3 = Kh

as heihgh increases, f3 increaases.

and f2 = f3

so friction by floor needed more and more.

but maximum value of fcrition is limited.

f2 _maximum = uk. mg

when f2 reaches beyond the maximum value of friction.

ladder start slipping . ( more likely )

B) the magnitude f2 must incxrease as the person moves upwards.

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