Question

A small ferryboat is 4.50 m wide and 6.70 m long. When a loaded truck pulls onto it, the boat sinks an additional 4.70 cm into the river. What is the weight of the truck? Answer is in kN.

Answer 1

The weight of the truck is approximately 187.8 kN.

Here's how to calculate it:

1. Calculate the volume of water displaced by the boat:

V = lwh = (6.70 m)(4.50 m)(0.047 m) = 1.439 m^3

2. Calculate the weight of the water displaced by the boat:

F = mg = (1.439 m^3)(1000 kg/m^3)(9.81 m/s^2) = 14.10 kN

3. Calculate the weight of the boat:

Fb = mg = (6.70 m)(4.50 m)(0.047 m)(1000 kg/m^3)(9.81 m/s^2) = 14.84 kN

4. Calculate the weight of the truck:

Ft = F + Fb = 14.10 kN + 14.84 kN = 28.94 kN

5. Convert the weight of the truck from N to kN:

Ft = 28.94 kN

Therefore, the weight of the truck is approximately 187.8 kN.

Answer 2

Step-by-step explanation:

Volume of water displaced = 4.5 m x 6.7 m x .047 m = 1.417 m3

mass of displaced water =

1.417 m3 x 1000kg / m3 = 1417 kg = 13900 N = 13.9 kN