4. The mass of the earth is 5.98times 10^wedge 24kg and the radius of the Earth is 3.68times 10^wedge 6 m. Use the law of Universal Gravitation to calculate the gravitational force between you and the Earth. 5. Convert your answer from #4 into pounds by multiplying the answer by 0.2245. How does this answer compare to your ORIGINAL weight. 6. Calculate the distance between two 75 kg masses that have a gravitational force of 8.34times 10^wedge -7N

4. To calculate the gravitational force between you and the Earth, we can use the law of Universal Gravitation, which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.<br /><br />The formula for the gravitational force is:<br /><br />F = G * (m1 * m2) / r^2<br /><br />Where:<br />F is the gravitational force<br />G is the gravitational constant (6.67430 × 10^-11 N⋅m^2/kg^2)<br />m1 and m2 are the masses of the two objects<br />r is the distance between the two objects<br /><br />Given information:<br />Mass of the Earth (m1) = 5.98 × 10^24 kg<br />Radius of the Earth (r) = 3.68 × 10^6 m<br /><br />Substituting the values into the formula:<br /><br />F = G * (m1 * m2) / r^2<br />F = (6.67430 × 10^-11 N⋅m^2/kg^2) * ((5.98 × 10^24 kg) * (1 kg)) / (3.68 × 10^6 m)^2<br />F = 9.81 N<br /><br />Therefore, the gravitational force between you and the Earth is 9.81 N.<br /><br />5. To convert the answer from question 4 into pounds, we can multiply the answer by 0.2245.<br /><br />Weight in pounds = 9.81 N * 0.2245 = 2.21 lbs<br /><br />The original weight is 9.81 N, and the converted weight in pounds is 2.21 lbs. The converted weight is significantly smaller than the original weight.<br /><br />6. To calculate the distance between two 75 kg masses that have a gravitational force of $8.34\times 10^{\wedge }-7N$, we can rearrange the formula for the gravitational force:<br /><br />F = G * (m1 * m2) / r^2<br />r^2 = G * (m1 * m2) / F<br />r = sqrt(G * (m1 * m2) / F)<br /><br />Given information:<br />Gravitational force (F) = $8.34\times 10^{\wedge }-7N$<br />Mass of each object (m1 and m2) = 75 kg<br /><br />Substituting the values into the formula:<br /><br />r = sqrt((6.67430 × 10^-11 N⋅m^2/kg^2) * ((75 kg) * (75 kg)) / ($8.34\times 10^{\wedge }-7N$))<br />r = 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000