Question

A standard baseball has a circumference of approximately 23 cm. if a baseball had the same mass per unit volume (see tables in section 1-5) as a neutron or a proton, about what would its mass be?

Answer 1

In order to determine the mass of a standard baseball if it had the same density (mass per unit volume) as a proton or neutron, we first determine the volume of the baseball. The formula to be used is V_sphere = (4/3)*pi*r^3. In this case, the radius r can be obtained from the circumference C, C = 2*pi*r. After plugging in C = 23 cm to the equation, we get r = 3.6066 cm. The volume of the baseball is then equal to 205.4625 cm^3.

Next, take note of these necessary information:

Mass of a neutron/proton = 10^-27 kg

Diameter of a neutron/proton = 10^-15 m

Radius of a neutron/proton = [(10^-15)/2]*100 = 5x10^-14 cm

Thus, the density, M/V of the neutron/proton is equal to 1.9099x10^12 kg/cm^3. Finally, the mass of the baseball if it was a neutron/proton can be determined by multiplying the density of the neutron/proton with the volume of the baseball. The final answer is then a large value of 3.9241x10^14 kg.

Answer 2

The mass of A standard baseball is 1.13.10¹⁵ kg

Further explanation

The ball is a 3-dimensional space constructed by many circles of the same diameter and has the same center point

Protons and neutrons are basic particles forming atoms of other than electrons

The mass of 1 proton is equal to the mass of 1 neutron, equal to 1 atomic mass unit and electrons have a mass smaller than both.

electron mass = 9.11.10 g

proton mass = 1.6726.10⁻²⁴ g

neutron mass = 1,675.10⁻²⁴ g

While

Because the diameter of the proton is unknown then we use it from sources on the internet obtained = 0.84.10⁻¹⁵ m

proton radius = 4.2.10⁻¹⁶ m

ball radius = 23 / 2π

ball radius = 3.6624 cm = 3.6624.10⁻² m

From the above question shows the density of the proton = density of the ball to find the mass of the ball,

so we can compare them (protons are considered like balls)

proton density = ball density

$\frac{m}{v}\:proton\:=\:\frac{m}{v}\:ball$

$\frac{1.6726.10^{-27}}{\frac{4}{3}\pi(4.2.10^{-16})^3 } \:=\: \frac{m\:ball}{\frac{4}{3}\pi(3.662.10^{-2})^3 }$

m ball = 1.13.10¹⁵ kg

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Keywords: protons, density, baseball, neutrons, mass, radius