An aluminum bar weighs 17 pounds in air. How much force is required to lift the bar while it is immersed in gasoline? The weight of aluminum is 170 pounds/ft3 and that of gasoline is 42 pounds/ft3.
I know that the answer is 12.8 pounds but how do I get to that answer? Thanks<3
I want to know the answer too :( Ashton Irwin, help us!!!!!!
To calculate the force required to lift the aluminum bar while immersed in gasoline, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Let's first find the volume of the aluminum bar. We know that the weight of aluminum is 170 pounds/ft^3, and the weight of the bar in air is 17 pounds. So, the volume of the aluminum bar can be calculated as:
Volume of aluminum bar = (Weight of bar in air) / (Weight of aluminum per unit volume)
= 17 pounds / 170 pounds/ft^3
= 0.1 ft^3
Next, let's calculate the weight of the displaced gasoline. Since the volume of the aluminum bar and the density of gasoline are given, we can calculate the weight of displaced gasoline as:
Weight of displaced gasoline = (Volume of aluminum bar) * (Density of gasoline)
= 0.1 ft^3 * 42 pounds/ft^3
= 4.2 pounds
According to Archimedes' principle, the force required to lift the aluminum bar while immersed in gasoline is equal to the weight of the displaced gasoline, which is 4.2 pounds. Therefore, the answer is 4.2 pounds, not 12.8 pounds.
Please double-check your calculations and data to ensure that there are no errors in the provided information.
To find the force required to lift the aluminum bar while immersed in gasoline, we need to calculate the buoyant force acting on the bar.
The buoyant force is equal to the weight of the fluid displaced by the object. In this case, the fluid is gasoline. The weight of the aluminum bar in air is its actual weight, and the weight of the displaced fluid (gasoline) is the weight it would have if submerged.
To calculate the weight of the aluminum bar in gasoline, we need to consider the loss of weight due to the buoyant force. The buoyant force is equal to the weight of the displaced fluid, which is the volume of the aluminum bar submerged in gasoline multiplied by the weight of one cubic foot of gasoline.
Let's go through the steps to find the force required to lift the bar:
1. Determine the volume of the aluminum bar submerged in gasoline:
Since we know the weight of aluminum is 170 pounds per cubic foot, we use this conversion factor to determine the volume of the aluminum bar submerged in gasoline.
Let V be the volume of the bar in cubic feet.
17 pounds (weight in air) * (1 ft^3 / 170 pounds) = V
Solving for V, we find that V ≈ 0.1 ft^3.
2. Calculate the weight of gasoline displaced by the aluminum bar:
The weight of gasoline is given as 42 pounds per cubic foot. We can use this to calculate the weight of the displaced gasoline.
W_gasoline = V * (weight of gasoline)
= 0.1 ft^3 * 42 pounds/ft^3
= 4.2 pounds.
3. Determine the buoyant force acting on the aluminum bar:
The buoyant force is equal to the weight of the displaced fluid.
Buoyant force = W_gasoline
= 4.2 pounds.
4. Compute the force required to lift the aluminum bar:
The force required to lift the aluminum bar while it is immersed in gasoline is equal to the buoyant force acting on it.
Force = buoyant force
= 4.2 pounds.
Therefore, the force required to lift the aluminum bar while it is immersed in gasoline is 4.2 pounds, not 12.8 pounds as mentioned in your question.