Question

question 8 of 29
the free - body diagram below represents the forces of several vehicles driving across a bridge. assume that the bridge is in static equilibrium and that it has zero weight, and solve for the unknown reaction force.
semi truck (150,000 n)
car (17,800 n)
small car (13,200 n)
reaction force (121,000 n)
reaction force (?)
a. 60,000 n
b. 13,200 n
c. 121,000 n
d. 80,200 n

Explanation:

Step1: Apply equilibrium condition

In static - equilibrium, the sum of the vertical forces is zero. Let the unknown reaction force be $F$. The downward forces are the weights of the vehicles: $150000N + 17800N+13200N$, and the upward forces are $121000N + F$. So, $\sum F_y=0$, which means $(150000 + 17800+13200)-(121000 + F)=0$.

Step2: Simplify the equation

First, calculate the sum of the downward forces: $150000+17800 + 13200=181000N$. Then the equation becomes $181000-121000 - F=0$.

Step3: Solve for $F$

$181000-121000=F$, so $F = 60000N$.

Answer:

A. 60,000 N