To determine the approximate mass of a small spherical shot of copper, the following experiment is performed. When 140 pieces of the shot are counted out and added to 8.6ml of water in a graduated cylinder, the total volume becomes 8.8ml . The density of copper is 8.92g/cm3.
Determine the approximate mass of a single piece of shot, assuming that all of the pieces are of the same dimensions.
The volume of water increased by 0.2 mL.
Mass = volume x density
That gives you mass of 140 pieces. You can determine the mass of 1 piece from that.
Sounds like small pieces to me. Could that have been 88 and 86 instead of 8.8 and 8.6?
still confused
nevermind i got it
To determine the mass of a single piece of copper shot, we need to calculate the mass of the 140 pieces of shot and then divide it by 140.
To do this, we first need to find the volume occupied by the 140 pieces of shot. We know that the total volume of the water and shot together is 8.8 ml, and the volume of the water alone is 8.6 ml. Therefore, the volume occupied by the shot is the difference between these two volumes.
Volume of shot = Total volume - Volume of water
Volume of shot = 8.8 ml - 8.6 ml
Volume of shot = 0.2 ml
Since the shot is small and spherical, we can approximate its volume using the formula for the volume of a sphere:
Volume of a sphere = (4/3) * π * r^3
We need to find the approximate radius of a single piece of shot to calculate its volume. The formula for the volume of a cylinder can help us.
Volume of a cylinder = π * r^2 * h
The height (h) of the cylinder is the difference between the total volume (8.8 ml) and the volume of shot (0.2 ml).
h = 8.8 ml - 0.2 ml
h = 8.6 ml
Substituting the values into the volume formula, we can solve for the radius (r) of a single piece of shot.
8.6 ml = π * r^2 * 8.6 ml
r^2 = (8.6 ml) / (π * 8.6 ml)
r^2 = 1 / π
r ≈ √(1/π)
Now that we have an approximation for the radius, we can substitute it into the formula for the volume of a sphere to determine the volume of a single piece of shot.
Volume of a single piece of shot = (4/3) * π * (r^3)
Next, we can calculate the mass of the shot using the density of copper.
Mass of shot = Volume of shot * Density of copper
Mass of shot = (Volume of a single piece of shot) * Density of copper
Finally, we can divide the mass of the shot by the number of pieces (140) to find the approximate mass of a single piece of shot.
Mass of a single piece of shot = Mass of shot / Number of pieces