Questionlass and Weight
1. The weight of an astronaut plus his space suit on the Moon is only 250 N . (a) How much does the suited astronaut weigh on Earth? (b) What is the mass on the Moon? On Earth?

Studdy Solution

STEP 1

1. The weight of the astronaut plus his space suit on the Moon is 250 N.
2. The acceleration due to gravity on the Moon is approximately $1.625 \, \text{m/s}^2$ .
3. The acceleration due to gravity on Earth is approximately $9.81 \, \text{m/s}^2$ .
4. Weight is the force due to gravity acting on a mass, calculated as $W = mg$ .
5. We need to find the weight of the suited astronaut on Earth and the mass on both the Moon and Earth.

STEP 2

1. Calculate the mass of the astronaut plus the space suit on the Moon.
2. Calculate the weight of the suited astronaut on Earth.
3. Verify that the mass is the same on both the Moon and Earth.

STEP 3

Calculate the mass of the astronaut plus the space suit on the Moon using the formula for weight:
$W_{\text{Moon}} = m \cdot g_{\text{Moon}}$
Given $W_{\text{Moon}} = 250 \, \text{N}$ and $g_{\text{Moon}} = 1.625 \, \text{m/s}^2$ , solve for $m$ :
$250 = m \cdot 1.625$
$m = \frac{250}{1.625}$
$m \approx 153.85 \, \text{kg}$

STEP 4

Calculate the weight of the suited astronaut on Earth using the mass found in Step 1:
$W_{\text{Earth}} = m \cdot g_{\text{Earth}}$
$W_{\text{Earth}} = 153.85 \cdot 9.81$
$W_{\text{Earth}} \approx 1509.28 \, \text{N}$

STEP 5

Verify that the mass is the same on both the Moon and Earth. Since mass is invariant, the mass remains:
$m = 153.85 \, \text{kg}$
The suited astronaut weighs approximately $1509.28 \, \text{N}$ on Earth, and the mass is $153.85 \, \text{kg}$ on both the Moon and Earth.

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