A partially filled bucket of water sits on a scale and its weight is 3.5 N. A piece of metal is suspended from a thread and completely immersed in the bucket (but does not touch the bottom). The scale now reads 7.5 N. Find the volume of the metal.
To find the volume of the metal, we need to use the principle of buoyancy. Buoyancy is the upward force exerted on an object immersed in a fluid, in this case, water. This force is equal to the weight of the fluid displaced by the object.
Here's how we can solve this problem step by step:
Step 1: Calculate the weight of the water in the bucket
Since the scale reads 3.5 N when the bucket is partially filled with water, the weight of the water alone is 3.5 N.
Step 2: Calculate the weight of the water and metal together
When the piece of metal is added to the bucket, the scale reads 7.5 N. Therefore, the weight of the water and metal combined is 7.5 N.
Step 3: Calculate the weight of the metal
The difference between the weight of the water and metal combined and the weight of the water alone is the weight of the metal.
Weight of the metal = weight of the water and metal - weight of the water = 7.5 N - 3.5 N = 4 N
Step 4: Calculate the volume of the metal
To calculate the volume of the metal, we can use the equation: weight of the metal = density of the metal * volume of the metal * acceleration due to gravity.
Since we are given the weight of the metal (4 N) and acceleration due to gravity (9.8 m/s^2), we can rearrange the equation to solve for the volume of the metal:
Volume of the metal = weight of the metal / (density of the metal * acceleration due to gravity)
Note: The density of the metal is typically given, or you can assume it to be a commonly known value (e.g., for iron, density is approximately 7,860 kg/m^3)
Let's assume the density of the metal is 7,860 kg/m^3:
Volume of the metal = 4 N / (7,860 kg/m^3 * 9.8 m/s^2)
After calculating this expression, you will get the volume of the metal in cubic meters.