For the fire truck shown in the figure on the right, the base of the extension l
ID: 2993306 • Letter: F
Question
For the fire truck shown in the figure on the right, the base of the extension ladder is rotated 75 degree counter-clockwise. The 25-m ladder is elevated 60 degree from the horizontal. The ladder weight is 40 kN and is regarded as concentrated at a point 10 m up from the base of the ladder. A 900-N fireman and the 500-N young lady that he is rescuing are at the top of the ladder. What is the moment at the base of the ladder tending to tip over the truck? What is the moment about the horizontal axis having unit vector p shown in the diagram?Explanation / Answer
Given:
ladder weight, w = 40 kN
man weight weight, w1 = 900N
woman weight , w2 = 500 N
ladder length, L = 25 m
Solution:
THe total moment about the axis at 75º from the -ve y axis.
The total moment is given by M = wlcos + w1Lcos w2 Lcos
Where is the inclination of the ladder with the ground. = 60º and l = length at which the weight of the ladder acts.
M = 40000(10)cos60 + 900(25)cos60 + 500(25)cos60 = 217500 Nm
The moment Mx which tends to tip the truck is found by resolving the component of total momentum about the x axis.
Mx = Msin75 = 210088.87 Nm
Result:
The moment at the base of the truck tending to tip over the truck is Mx = 210088.87 Nm
The moment about the horizontal axis is M = 217500 Nm