Answer :
Answer:
a) x=3.63m b) [tex]P_{2}=1.55kN[/tex]
Explanation:
In order to solve this problem we can start by building a free body diagram of the board and the pillars. (See attached picture).
a)
So in order to find the distance between the second pilar and the person x, we can do a summation of moments about the second pillar so we get the following:
[tex] \sum M_{P{2}}=0[/tex]
which will look like this:
[tex]Wx-P_{1}d=0[/tex]
we can now solve for x (the distance between the second pillar and the person) so we get:
[tex]Wx=P_{1}d[/tex]
[tex]x=\frac{P_{1}d}{W}[/tex]
We know that the weight of the person is given by mg so the equation can be rewritten like this:
[tex]x=\frac{P_{1}d}{mg}[/tex]
When substituting the respective data we get:
[tex]x=\frac{(810N)(3.3m)}{(75kg)(9.81m/s^{2})}[/tex]
which yields:
x=3.63m
b)
in order to find the magnitude of the upward force exerted by the second pillar we can do a sum of forces in the vertical direction so we get:
[tex]\sum F_{y}=0[/tex]
which yields:
[tex]-W+P_{2}-P_{1}=0[/tex]
which can be solved for [tex]P_{2}[/tex]:
[tex]P_{2}=P_{1}+mg[/tex]
When subsstituting the data we get:
[tex]P_{2}=810N+(75kg)(9.81m/s^{2})=1.55kN[/tex]
so the force exerted by the second pillar is 1.55kN.
Based on the data provided;
- the distance the person is standing from the end pillar 1 is 3.63 m
- magnitude of the upward force exerted by the second pillar is 1,545.75 N
What are moments?
Moments about a point is the product of force and the perpendicular distance from the lime of action.
- Moment = Force × perpendicular distance
The principle of moments states that the sum of clockwise moment about a point is equal to the sum of anticlockwise moments about that point
- Anticlockwise moments = clockwise moments
Calculating moments about the second pillar:
W × y = P1 × d
where;
- y is the distance the person is standing from the end of pillar 1
- W is weight of the man = 75 × 9.81 = 735.75
- P1 = 810 N
- d = 3.30 m
y = 810 × 3.30 / 735.75
y = 3.63 m
Therefore, the distance the person is standing from the end pillar 1 is 3.63 m
The magnitude of the upward force exerted by the second pillar is calculated as follows:
- Sum of forces in the vertical direction is equal to zero
-W + P2 - P1 = 0
P2 = W + P1
P2 = 735.75 + 810
P2 = 1,545.75 N
Therefore, magnitude of the upward force exerted by the second pillar is 1,545.75 N
Learn more about moments at: https://brainly.com/question/26117248