A14.0 m uniform ladder weighing 490 n rests against a frictionless wall. the ladder makes a 63.0°-angle with the horizontal.
(a) find the horizontal and vertical forces (in n) the ground exerts on the base of the ladder when an 820-n firefighter has climbed 3.80 m along the ladder from the bottom. (horizontal force, vertical force)
(b) if the ladder is just on the verge of slipping when the firefighter is 9.10 m from the bottom, what is the coefficient of static friction between ladder and ground?
(c) what if? if oil is spilled on the ground, causing the coefficient of static friction to drop to half the value found in part (b), what is the maximum distance (in m) the firefighter can climb along the ladder from the bottom before the ladder slips?

a) N = 1310 N

b)

c)

Given :

length of ladder, = 14 m

weight of ladder, = 490 N

position of firefighter, = 3.8 m

weight of firefighter, = 820 N

angle of ladder,

Solution :

Let force of the wall on the ladder be , force of friction on base of ladder be and normal force on base of ladder be N.

Now, in x direction

In y direction,

a)

b)

c)

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Explanation:

Given:

length of ladder

weight of ladder

position of firefighter

weight of firefighter

angle of ladder

Unknown:

force of the wall on the ladder

force of friction on base of ladder

normal force on base of ladder

From the free body diagram of the sketch you get 3 equations:

Solving the equations gives:

a)

b)

c) Using the result from b and solving for

causes

fossil fuels burn

cities become more industrialized

human population grows worldwide