A solid aluminum ingot weighs 88.0 N in air.What is its volume?The ingot is suspended from a rope and totally immersed in water. What is the tension in the rope (the apparent weight of the ingot in water)?
To find the volume would i do density/specific gravity of aluminum?
For the volume, divide the mass (88.0 /9.81 = 8.97 kg or 8970 g) by the density of aluminum, which you should look up. Make sure you use units of
Use the volume to compute the buoyant force when totally submerged.
The weight MINUS the buoyant force will equal the cable tension.
To find the volume of the aluminum ingot, you'll need to use the concept of density. Density is defined as the mass of an object per unit volume. For aluminum, the density is typically known to be about 2,700 kg/m^3.
To calculate the volume, you can use the formula:
Volume = Mass / Density
However, only the weight of the ingot is given, which is 88.0 N. To convert this weight to mass, we need to use the formula:
Weight = Mass * Gravitational acceleration
In this case, the gravitational acceleration can be approximated as 9.8 m/s^2.
Rearranging the formula, we can calculate the mass:
Mass = Weight / Gravitational acceleration
Plugging in the given weight, we have:
Mass = 88.0 N / 9.8 m/s^2
Now that we have the mass, we can substitute it back into the volume formula to find the volume of the ingot.
Once you have the volume, you can move on to the second part of the question, which is calculating the tension in the rope when the ingot is immersed in water.
When the ingot is immersed in water, it experiences an upward buoyant force equal to the weight of the water displaced by the ingot. This buoyant force acts against the downward force of the ingot's weight. So, the tension in the rope (the apparent weight of the ingot in water) can be calculated by subtracting the buoyant force from the weight of the ingot.
The buoyant force can be calculated using Archimedes' principle:
Buoyant force = Density of water * Volume of the ingot * Gravitational acceleration
Substitute the known values, and then subtract the buoyant force from the weight of the ingot to find the tension in the rope.