* 248. Fig. 3.1 shows a firefighter of total weight 840 N in equilibrium at the top of a
ladder that is pivoted at point P.
I
C
ladder
112m
5.0m
P.
Fig. 3.1
The ladder leans towards a burning building at an angle such that the centre of gravity C
of the firefighter is 12 m above and 5.0 m to the right of P. The firefighter holds a hose
that directs a high-speed jet of water horizontally into a burning building.
(a) i) Calculate the moment M of the firefighter's weight about P.
moment =
[2]
Well, well, well, looks like we have a balancing act on our hands! Let's see if we can solve this pickle.
To calculate the moment of the firefighter's weight about point P, we need to multiply the weight by the perpendicular distance to the point of rotation. In this case, the weight of the firefighter is given as 840 N, and the perpendicular distance from point P to the centre of gravity C is 12 m.
So, the moment M would be 840 N multiplied by 12 m, which would give us...
*dramatic drumroll*
The moment is... 10080 Nm!
Voila! We have our answer. Keep calm and carry on with your firefighting endeavors!
To calculate the moment (M) of the firefighter's weight about point P, we need to multiply the weight (840 N) by the perpendicular distance from the weight to point P.
Given that the center of gravity (C) of the firefighter is 12 m above and 5.0 m to the right of P, the perpendicular distance can be calculated using the Pythagorean theorem:
r² = 12² + 5.0²
r² = 144 + 25
r² = 169
r = √169
r = 13 m
The moment (M) can then be calculated as:
M = weight × perpendicular distance
M = 840 N × 13 m
M = 10,920 Nm
Therefore, the moment (M) of the firefighter's weight about point P is 10,920 Nm.
To calculate the moment (M) of the firefighter's weight about point P, we need to use the formula for the moment of a force:
Moment (M) = Force (F) × Distance (d)
In this case, the force is the weight of the firefighter (840 N) and the distance is the perpendicular distance from the point P to the line of action of the force.
Since the firefighter is in equilibrium, the moments acting on him must add up to zero. This means that the moment of the weight about P must be equal and opposite to the moment of the hose's water jet about point P.
Given that the center of gravity of the firefighter is 12 m above and 5.0 m to the right of point P, we can calculate the distance as follows:
Distance = √(12^2 + 5.0^2) = √(144 + 25) = √169 = 13 m
Now we can calculate the moment:
Moment = 840 N × 13 m = 10,920 Nm
Therefore, the moment (M) of the firefighter's weight about point P is 10,920 Nm.