If ball 2: is 0.20 kg what amount of kg can I make ball 1 for it to be twice the size of ball 2 but still have the same mass
To make ball 1 twice the size of ball 2 but have the same mass, we need to consider the volumetric relationship between the two balls.
The volume of a sphere is given by the formula: V = (4/3) * π * r^3, where V is the volume and r is the radius.
Let's assume the radius of ball 2 is r2. Since ball 1 should be twice the size of ball 2, the radius of ball 1 should be 2r2.
Using the formula for volume, we have:
V1 = (4/3) * π * (2r2)^3
V2 = (4/3) * π * r2^3
To ensure that ball 1 has the same mass as ball 2, the density of both balls should be the same. Density is defined as mass divided by volume (ρ = m/V).
Let's assume the density is ρ. The mass of ball 2 is given as 0.20 kg, so we have:
m2 = 0.20 kg
For ball 1, we can set up the following equation:
m1/V1 = m2/V2
Substituting the equations for volume:
m1 / [(4/3) * π * (2r2)^3] = m2 / [(4/3) * π * r2^3]
Now we can solve for m1, the mass of ball 1, by multiplying both sides of the equation by [(4/3) * π * (2r2)^3]:
m1 = (0.20 kg) * [(4/3) * π * (2r2)^3] / [(4/3) * π * r2^3]
Simplifying the equation:
m1 = 0.20 kg * 8 * (r2^3) / (r2^3)
The terms r2^3 cancel out, resulting in:
m1 = 0.20 kg * 8
m1 = 1.6 kg
Therefore, to make ball 1 twice the size of ball 2 but still have the same mass, you would need to make ball 1 1.6 kg.