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24 July, 14:56

Given that the mass of an average linebacker at Ursinus College is 250 lbs and the radius of a pea is 0.50 cm, calculate the number of linebackers that would be required to be stuffed into the volume of a pea in order to obtain the same density as an alpha particle.

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  1. 24 July, 17:54
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    1.544*10⁹ Linebackers would be required in order to obtain the same density as an alpha particle

    Step-by-step explanation:

    Assuming that the pea is spherical (with radius R = 0.5 cm = 0.005 m), then its volume is

    V = 4/3π*R³ = 4/3π*R³ = 4/3*π * (0.005 m) ³ = 5.236*10⁻⁷ m³

    the mass in that volume would be m = N*L (L = mass of linebackers=250Lbs = 113.398 Kg)

    The density of an alpha particle is ρa = 3.345*10¹⁷ kg/m³ and the density in the pea ρ will be

    ρ = m/V

    since both should be equal ρ=ρa, then

    ρa = m/V = N*L/V → N = ρa*V/L

    replacing values

    N = ρa*V/L = 3.345*10¹⁷ kg/m³ * 5.236*10⁻⁷ m³ / 113.398 Kg = 1.544*10⁹ Linebackers

    N=1.544*10⁹ Linebackers
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