If ball 2: is 0.80 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 increase the mass of ball 1 such that the mass-to-size ratio remains constant.
Let's assume the size of ball 2 is represented by volume V.
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
Since we want ball 1 to be twice the size of ball 2, its volume should be 2V.
Now, let's assume the mass of ball 1 is represented by M1, and its size/radius by r1.
The mass-to-size ratio is the mass divided by the volume: M1/V = ρ1, where ρ1 is the density of ball 1.
Similarly, for ball 2: M2/V = ρ2, where ρ2 is the density of ball 2.
Since the mass of ball 2 is given as 0.80 kg, we have M2 = 0.80 kg.
To maintain the same mass-to-size ratio, we can set up the following equation:
M1/2V = ρ2
M1/V = 2ρ2
Substituting the values we know:
2ρ2 = 2(0.80 kg)
ρ2 = 0.80 kg
Therefore, the density/distribution of ball 2 is 0.80 kg/m^3.
Now, we can calculate the mass of ball 1 using ρ2 = M1/V:
0.80 kg = M1/2V
Since we want ball 1 to be twice the size of ball 2, which is 2V:
0.80 kg = M1/(2×2V)
1.60 kg = M1/4V
Multiplying both sides by 4V:
1.60 kg × 4V = M1
M1 = 6.4 kg
Thus, to make ball 1 twice the size of ball 2 but still have the same mass, you would need to make ball 1 have a mass of 6.4 kg.