Question

mass & weight practice
w (weight) = m (mass) x g (acceleration due to gravity)
acceleration due to gravity on earth is 9.8 m/s² weight is measured in newtons (n)

1. what is mass?
2. what is weight?
3. describe what will happen to the mass of a textbook if you were to take it from earth to the moon?
4. describe what will happen to the weight of a textbook if you were to take it from earth to the moon?
5. what is the weight of a 60 kg astronaut on earth? (show work w = m x g)
6. suppose the astronaut from question #5 were to travel to a planet whose gravitational attraction has been reduced to 1/10 of that of earth’s 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 to gravity on the moon? (show work)

Explanation:

Step1: Identify the formula

The formula for weight is $W = m\times g$.

Step2: Find the new - gravitational acceleration

The gravitational attraction of the new planet is $\frac{1}{10}$ of Earth's. Earth's gravitational acceleration $g_{E}=9.8\ m/s^{2}$, so the gravitational acceleration of the new planet $g_{new}=\frac{1}{10}\times9.8\ m/s^{2}=0.98\ m/s^{2}$.

Step3: Calculate the weight on the new planet

The mass of the astronaut $m = 60\ kg$. Using the formula $W = m\times g$, we substitute $m = 60\ kg$ and $g = g_{new}=0.98\ m/s^{2}$. So $W=60\times0.98 = 58.8\ N$.

for question 7:

Step1: Rearrange the weight formula

We know $W = m\times g$, and we want to find $g$. Rearranging the formula gives $g=\frac{W}{m}$.

Step2: Substitute the given values

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

for question 3:
Mass is a measure of the amount of matter in an object. It is an intrinsic property and does not change with location. So, taking a textbook from Earth to the moon, the amount of matter in the textbook remains the same.

for question 4:
Weight is the force exerted on an object due to gravity, given by $W = m\times g$. The gravitational acceleration on the moon is about $\frac{1}{6}$ of that on Earth. Since the mass of the textbook $m$ is constant and $g$ (acceleration due to gravity) is smaller on the moon, the weight of the textbook on the moon will be less than its weight on Earth.

Answer:

The weight of the astronaut on this planet is $58.8\ N$.