Question

1. a 9250 kg bridge going east - west is supported by two pillars. the bridge is 47.0 m long with a pillar 5.0 m from the west end and 10 meters from the east end. how much force is applied on each of the pillars?
2. a 1720 kg truck drives across the same bridge going east to west. how much force is applied on each pillar when the truck is 12 m across?

Explanation:

For Question 6:

Step1: Calculate bridge weight

First, find the weight of the bridge using $W = mg$.
$W_{bridge} = 9250\ \text{kg} \times 9.8\ \text{m/s}^2 = 90650\ \text{N}$

Step2: Set equilibrium equations

Let $F_A$ = force on west pillar, $F_B$ = force on east pillar.
Vertical equilibrium: $F_A + F_B = W_{bridge}$
Torque equilibrium about west pillar: $W_{bridge} \times \frac{47}{2}\ \text{m} = F_B \times (47 - 5 - 10)\ \text{m}$

Step3: Solve for $F_B$

Substitute values into torque equation:
$90650\ \text{N} \times 23.5\ \text{m} = F_B \times 32\ \text{m}$
$F_B = \frac{90650 \times 23.5}{32} = 6.64 \times 10^4\ \text{N}$

Step4: Solve for $F_A$

Use vertical equilibrium:
$F_A = 90650\ \text{N} - 6.64 \times 10^4\ \text{N} = 2.43 \times 10^4\ \text{N}$

Step1: Calculate truck weight

Find the weight of the truck using $W = mg$.
$W_{truck} = 1720\ \text{kg} \times 9.8\ \text{m/s}^2 = 16856\ \text{N}$

Step2: Set equilibrium equations

Let $F_A$ = force on west pillar, $F_B$ = force on east pillar.
Vertical equilibrium: $F_A + F_B = W_{bridge} + W_{truck} = 90650 + 16856 = 107506\ \text{N}$
Torque equilibrium about west pillar: $W_{bridge} \times 23.5\ \text{m} + W_{truck} \times 12\ \text{m} = F_B \times 32\ \text{m}$

Step3: Solve for $F_B$

Substitute values into torque equation:
$90650 \times 23.5 + 16856 \times 12 = F_B \times 32$
$2130275 + 202272 = 32F_B$
$F_B = \frac{2332547}{32} = 7.29 \times 10^4\ \text{N}$

Step4: Solve for $F_A$

Use vertical equilibrium:
$F_A = 107506\ \text{N} - 7.29 \times 10^4\ \text{N} = 3.46 \times 10^4\ \text{N}$

Answer:

Force on west pillar: $\boldsymbol{2.43 \times 10^4\ \text{N}}$, Force on east pillar: $\boldsymbol{6.64 \times 10^4\ \text{N}}$

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For Question 7: