Question

1. suppose the astronaut from question #5 were to travel to a planet whose gravitational attraction has been reduced to 1/10 of that of earths gravitational attraction. what would be the weight of the astronaut on this planet? (show work) 7. a backpack weighs 8.2 newtons and has a mass of 5 kg on the moon. what is the acceleration due to gravity on the moon? (show work)

Explanation:

Step1: Recall weight - mass formula

The formula for weight is $W = mg$, where $W$ is weight, $m$ is mass and $g$ is the acceleration due to gravity.

Step2: Solve for $g$ on the moon

We know that $W = 8.2\ N$ and $m = 5\ kg$ on the moon. Rearranging the formula $g=\frac{W}{m}$. Substituting the given values, we get $g=\frac{8.2}{5}=1.64\ m/s^{2}$.

Step3: Solve for weight on the new planet

On Earth, the acceleration due to gravity is approximately $g_{E}=9.8\ m/s^{2}$. The gravitational attraction on the new planet is $\frac{1}{10}$ of Earth's, so $g_{p}=\frac{1}{10}\times9.8 = 0.98\ m/s^{2}$.
We assume the mass of the astronaut (from the backpack - mass concept) is $m = 5\ kg$. Using the weight formula $W=mg$, substituting $m = 5\ kg$ and $g = 0.98\ m/s^{2}$, we get $W=5\times0.98 = 4.9\ N$.

Answer:

The acceleration due to gravity on the moon is $1.64\ m/s^{2}$. The weight of the astronaut on the new planet is $4.9\ N$.