A painter weighing 600 N climbs a very light ladder propped against the side of a house at an angle of 60° with the horizontal.
The ladder is 5.00 m long. The coefficient of static friction between ladder and ground is 0.40. Assume friction between the ladder and the wall is negligible.
a. How high up the ladder ( d in figure) can the painter go before the ladder slips?
b. Could the painter climb at all without the ladder slipping if the contact between the ladder and the ground were frictionless?
c. How large the coefficient of friction between the ladder and the floor needs to be for the painter to be able to climb 4.5 m without the ladder slipping?
Solution
a)
let s = distance he can climb up the ladder,
c = length of ladder
m = mass of ladder M = mass of man
TH = angle of ladder with wall
f = friction coefficient
s = (2cf(m+M) - cm*tanTH)/(2MtanTH)
m = 0 -->
s = (2cf)/(2tanTH)
s = 5*0,4/tan30 ---> if 60° is the angle with the ground:
s = 3,464 m ----> he can climb up the ladder
------
(if 60° is the angle with the wall:
s = 5*0,4/tan60
s = 1,154 m up the ladder)
b) no , the ladder would not stand without friction with ground and wall
.
A painter weighing 600 N climbs a very light ladder propped against th.docx
1. A painter weighing 600 N climbs a very light ladder propped against the side of a house at an
angle of 60° with the horizontal.
The ladder is 5.00 m long. The coefficient of static friction between ladder and ground is 0.40.
Assume friction between the ladder and the wall is negligible.
a. How high up the ladder ( d in figure) can the painter go before the ladder slips?
b. Could the painter climb at all without the ladder slipping if the contact between the ladder and
the ground were frictionless?
c. How large the coefficient of friction between the ladder and the floor needs to be for the
painter to be able to climb 4.5 m without the ladder slipping?
Solution
a)
let s = distance he can climb up the ladder,
c = length of ladder
m = mass of ladder M = mass of man
TH = angle of ladder with wall
f = friction coefficient
s = (2cf(m+M) - cm*tanTH)/(2MtanTH)
m = 0 -->
s = (2cf)/(2tanTH)
s = 5*0,4/tan30 ---> if 60° is the angle with the ground:
s = 3,464 m ----> he can climb up the ladder
2. ------
(if 60° is the angle with the wall:
s = 5*0,4/tan60
s = 1,154 m up the ladder)
b) no , the ladder would not stand without friction with ground and wall
