QuestionJuly 24, 2025

A person weight is 1020 N on the ground level of Planet X. What is the person weight in a high-altitude balloon at 310 km above the ground? (R_(Planetx)=15.5cdot 10^6 m and gPlanet x= 18.5m/s^2 1012 N 993 N 986N 980 N

A person weight is 1020 N on the ground level of Planet X. What is the person weight in a high-altitude balloon at 310 km above the ground? (R_(Planetx)=15.5cdot 10^6 m and gPlanet x= 18.5m/s^2 1012 N 993 N 986N 980 N
A person weight is 1020 N on the ground level of Planet X. What is the person weight in a high-altitude balloon at 310 km above the ground? (R_(Planetx)=15.5cdot 10^6 m and gPlanet x= 18.5m/s^2 1012 N 993 N 986N 980 N

Solution
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Answer

993 N Explanation 1. Calculate the gravitational force at altitude Use the formula for gravitational force: F = \frac{G \cdot m_1 \cdot m_2}{r^2}. The weight at ground level is W = m \cdot g, so m = \frac{W}{g}. At altitude, r = R_{Planetx} + 310 \times 10^3 m. 2. Determine new weight using inverse square law New weight W' = W \cdot \left(\frac{R_{Planetx}}{R_{Planetx} + 310 \times 10^3}\right)^2. 3. Substitute values and calculate W' = 1020 \cdot \left(\frac{15.5 \times 10^6}{15.5 \times 10^6 + 310 \times 10^3}\right)^2.

Explanation

1. Calculate the gravitational force at altitude<br /> Use the formula for gravitational force: $F = \frac{G \cdot m_1 \cdot m_2}{r^2}$. The weight at ground level is $W = m \cdot g$, so $m = \frac{W}{g}$. At altitude, $r = R_{Planetx} + 310 \times 10^3$ m.<br /><br />2. Determine new weight using inverse square law<br /> New weight $W' = W \cdot \left(\frac{R_{Planetx}}{R_{Planetx} + 310 \times 10^3}\right)^2$.<br /><br />3. Substitute values and calculate<br /> $W' = 1020 \cdot \left(\frac{15.5 \times 10^6}{15.5 \times 10^6 + 310 \times 10^3}\right)^2$.
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