When a container of water is placed on a laboratory scale, the scale reads 120 g. Now a 20-g piece of copper (of density 8.9 g/cm3) is suspended from a thread and lowered into the water, not touching the bottom of the container. What will the scale now read? The density of water is 1.0
g/cm3.
10
A) 138 g B) 120 g C) 140 g D) 122 g
122g
To find the new reading on the scale, we need to consider the buoyant force acting on the copper piece in water.
First, let's find the volume of the copper piece. The formula to calculate volume is:
Volume = mass / density
Given that the mass of the copper piece is 20 g and the density of copper is 8.9 g/cm3, we can calculate the volume as follows:
Volume = 20 g / 8.9 g/cm3 ≈ 2.247 cm3
Now, let's calculate the buoyant force acting on the copper piece in water. The formula for buoyant force is:
Buoyant force = density of fluid × volume × acceleration due to gravity
The density of water is 1.0 g/cm3, and the acceleration due to gravity is approximately 9.8 m/s2 or 980 cm/s2. Let's substitute the values and calculate the buoyant force:
Buoyant force = 1.0 g/cm3 × 2.247 cm3 × 980 cm/s2 ≈ 2199.36 g·cm/s2
The buoyant force acts in the upward direction. To balance this force, the scale needs to provide an equal and opposite force in the downward direction. This force is equal to the weight of the copper piece plus the weight of the water displaced by the copper piece.
The weight of the copper piece can be calculated using the formula:
Weight = mass × acceleration due to gravity
Weight = 20 g × 980 cm/s2 = 19600 g·cm/s2
The weight of the water displaced by the copper piece can be calculated using the formula:
Weight of water displaced = density of water × volume × acceleration due to gravity
Weight of water displaced = 1.0 g/cm3 × 2.247 cm3 × 980 cm/s2 ≈ 2199.36 g·cm/s2
Therefore, the total downward force exerted on the scale is the sum of the weight of the copper piece and the weight of the water displaced:
Total downward force = 19600 g·cm/s2 + 2199.36 g·cm/s2 ≈ 21799.36 g·cm/s2
Now let's calculate the new reading on the scale by subtracting the upward buoyant force from the total downward force:
New reading on the scale = 21799.36 g·cm/s2 - 2199.36 g·cm/s2 ≈ 19599 g·cm/s2
Converting this to grams:
New reading on the scale ≈ 19599 g
Therefore, the new reading on the scale will be approximately 19599 grams. The answer is not listed among the provided options.
To find out what the scale will read after the copper piece is lowered into the water, we need to consider the buoyant force acting on the copper.
The buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. In this case, the copper piece is suspended in the water, so it will displace an amount of water equal to its own volume.
To find the volume of the copper piece, we can use its mass and density. The formula for density is density = mass/volume, so we can rearrange this formula to solve for volume:
volume = mass/density
The mass of the copper piece is given as 20 g, and its density is 8.9 g/cm3. Plugging these values into the formula gives us:
volume = 20 g / 8.9 g/cm3 ≈ 2.24 cm3
Therefore, the copper piece will displace 2.24 cm3 of water.
Now, let's calculate the weight of the water displaced by the copper piece. The density of water is given as 1.0 g/cm3, so the weight of 2.24 cm3 of water is:
weight = volume x density = 2.24 cm3 x 1.0 g/cm3 = 2.24 g
This means that the buoyant force acting on the copper piece is 2.24 g. Since the copper piece is in equilibrium, the scale will read the sum of the weight of the water and the copper piece.
The initial weight of the water was 120 g, and the weight of the copper piece is 20 g, so the scale will read:
120 g + 20 g + 2.24 g = 142.24 g
Therefore, the correct answer is C) 140 g.