In the figure, a ladder of weight 200 N and length 10 meters leans against a smo
ID: 1290699 • Letter: I
Question
In the figure, a ladder of weight 200 N and length 10 meters leans against a smooth wall (no friction on wall). A firefighter of weight 600 N climbs a distance x up the ladder. The coefficient of friction between the ladder and the floor is 0.5. What is the maximum value of x if the ladder is not to slip? Please show work
In the figure, a ladder of weight 200 N and length 10 meters leans against a smooth wall (no friction on wall). A firefighter of weight 600 N climbs a distance x up the ladder. The coefficient of friction between the ladder and the floor is 0.5. What is the maximum value of x if the ladder is not to slip? Please show workExplanation / Answer
Let:
M be the mass of the person,
d be the person's distance (measured along the ladder) from its foot,
m be the mass of the ladder,
L be the length of the ladder,
R be the upward reaction of the ground at the foot of the ladder,
F be the friction force at the foot of the ladder,
S be the horizontal reaction of the wall on the top of the ladder,
u be the coefficient of friction between the ladder and the ground,
a be the angle between the ladder and the ground,
g be the acceleration due to gravity.
Resolving horizontally and vertically:
F = S ...(1)
R = (M + m)g ...(2)
Moments about the foot of the ladder:
SL sin(a) = (mL / 2 + Md)g cos(a)
Substituting for S from (1) and rearranging:
F = (mL / 2 + Md)g cos(a) / [ L sin(a) ] ...(3)
F <= uR
Substituting for F from (3) and R from (2):
(mL / 2 + Md)g cos(a) <= u(M + m)gL sin(a)
Mgd <= u(M + m)gL tan(a) - mLg / 2
d <= (L / M)[ u(M + m) tan(a) - m / 2 ].
d = 10/600[.5(600+200) tan 50 - 200/2
d = 6.27 m
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.