Question

If a speed boat has a mass of 1,600 kg, how much water would it need to displace in order to float?

Answer 1

To determine how much water a speed boat with a mass of 1,600 kg needs to displace in order to float, we can use the principle of buoyancy, specifically Archimedes' principle. This principle states that the weight of the water displaced by the boat must equal the weight of the boat itself.

1. **Calculate the weight of the boat:**
The weight \( W \) of the speed boat is given by the formula:
\[
W = m \cdot g
\]
where \( m \) is the mass of the boat (1,600 kg) and \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).

\[
W = 1,600 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 15,696 \, \text{N}
\]

2. **Calculate the volume of water that needs to be displaced:**
The weight of the displaced water can also be expressed as:
\[
W_{\text{displaced}} = \text{volume} \cdot \text{density of water} \cdot g
\]
The density of water is approximately \( 1,000 \, \text{kg/m}^3 \).

Setting the weight of the displaced water equal to the weight of the boat:
\[
\text{volume} \cdot (1,000 \, \text{kg/m}^3) \cdot 9.81 \, \text{m/s}^2 = 15,696 \, \text{N}
\]

Now, let's solve for the volume:
\[
\text{volume} = \frac{15,696 \, \text{N}}{1,000 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2}
\]
\[
\text{volume} = \frac{15,696}{9,810} \approx 1.60 \, \text{m}^3
\]

Thus, the speed boat would need to displace approximately **1.60 cubic meters** of water in order to float.