what's the density of a box whose weight is 1648 newtons and whose volume is 2.8 cubic meters? Will it float in a liquid whose density is 600 kilograms per cubic meter?
Mass = Weight/g = 1678/9.8 = 171.22 kg.
Density ρ = m/V =171.22/2.8 =61.2 kg/m³.
The body is floating if
the buoyant force F acting on is greater than its weight
F =ρ1•V•g = 600•2.6•9.8 =15288 N.
F > Weight => the body will float
To calculate the density of the box, you need to divide its weight (force) by its volume.
1. Start with the given weight of the box, which is 1648 newtons.
2. Then, use the formula for density: density = weight/volume.
3. Divide the weight (1648 newtons) by the volume of the box (2.8 cubic meters).
Density = 1648 N / 2.8 m^3.
Now, let's determine if the box will float in the liquid with a density of 600 kg/m^3.
4. Compare the density of the box with the density of the liquid.
If the density of the box is less than the density of the liquid, it will float. Otherwise, it will sink.
To convert the density of the box from newtons per cubic meter (N/m^3) to kilograms per cubic meter (kg/m^3):
5. Note that 1N is equal to 1 kg·m/s^2.
6. Divide the density (calculated in step 3) by the acceleration due to gravity (approximately 9.8 m/s^2) to convert from N/m^3 to kg/m^3.
So, by following these steps, you can calculate the density of the box and determine if it will float in the liquid.