Determine the vertical force exerted on the trailer by the support B. Express your answer to two significant figures and include the appropriate units.

Steps to Solve

1. Identify the Forces Acting on the Trailer

The vertical forces acting on the trailer include the weight of the trailer ($W$) exerted downward and the vertical force at support point B ($F_B$) exerted upward.

2. Calculate the Weight of the Trailer

The weight of the trailer is calculated using the mass and the acceleration due to gravity:

$$ W = m \cdot g $$

Here, (m = 2900 , \text{kg}) and (g = 9.81 , \text{m/s}^2).

3. Set Up the Equilibrium Equation

Since the system is in vertical equilibrium, the sum of the upward forces must equal the sum of the downward forces:

$$ F_B - W = 0 $$

This can be rearranged to solve for the vertical force at B:

$$ F_B = W $$

4. Substitute the Weight into the Equation

From step 2, we calculated (W):

$$ W = 2900 , \text{kg} \cdot 9.81 , \text{m/s}^2 \approx 28449 , \text{N} $$

Now substitute this value to find (F_B):

$$ F_B = 28449 , \text{N} $$

5. Express the Final Answer with Significant Figures

The answer should be expressed to two significant figures:

$$ F_B \approx 28000 , \text{N} $$