To calculate the density of the brand new coin, we can use the formula:
Density = Mass / Volume
1. First, let's calculate the volume of the coin. Since the coin is an ideal cylinder, we can use the formula:
Volume = π * (diameter/2)^2 * thickness
Given that the diameter of the coin is 24.25 mm and the thickness is 1.73 mm, we can substitute these values into the formula:
Volume = π * (24.25/2)^2 * 1.73
2. Now, let's calculate the absolute and relative uncertainties for the diameter, thickness, volume, and mass of the coin.
For the diameter:
Absolute uncertainty = 0.01 mm (smallest scale division of the caliper)
Relative uncertainty = (0.01 mm / 24.25 mm) * 100
For the thickness:
Absolute uncertainty = 0.01 mm (smallest scale division of the caliper)
Relative uncertainty = (0.01 mm / 1.73 mm) * 100
For the volume:
To calculate the absolute and relative uncertainties for volume, we need to consider the uncertainties in diameter and thickness.
Absolute uncertainty in volume = Volume * √[(2 * (absolute uncertainty in diameter / diameter))^2 + (absolute uncertainty in thickness / thickness)^2]
Relative uncertainty in volume = (Absolute uncertainty in volume / Volume) * 100
For the mass:
Absolute uncertainty = 0.01 g (smallest scale division of the balance)
Relative uncertainty = (0.01 g / 2.15 g) * 100
3. Finally, let's calculate the absolute and relative uncertainties for the density of the coin.
Absolute uncertainty in density = Density * √[(2 * (absolute uncertainty in mass / mass))^2 + (absolute uncertainty in volume / volume)^2]
Relative uncertainty in density = (Absolute uncertainty in density / Density) * 100
By following these steps, you should be able to calculate the density of the coin and determine its absolute and relative uncertainties.