Question

The table shows the acceleration due to gravity on four different planets. What planet is a person standing on if the person has a mass of 85.0 kg and weighs 305 N?



a
Mars
b
Earth
c
Mercury
d
Venus

Answer 1

To determine which planet the person is standing on, we can use the formula for weight, which is given by:

\[ \text{Weight} = \text{mass} \times \text{acceleration due to gravity} \]

Given:
- Mass of the person = 85.0 kg
- Weight = 305 N

We can find the acceleration due to gravity on that planet by rearranging the formula:

\[ \text{acceleration due to gravity} = \frac{\text{Weight}}{\text{mass}} \]

Now, substituting the values:

\[ \text{acceleration due to gravity} = \frac{305 \, \text{N}}{85.0 \, \text{kg}} \approx 3.59 \, \text{m/s}^2 \]

Now, we can compare this value to the typical acceleration due to gravity on the different planets:

- Mars: approximately \(3.71 \, \text{m/s}^2\)
- Earth: approximately \(9.81 \, \text{m/s}^2\)
- Mercury: approximately \(3.7 \, \text{m/s}^2\)
- Venus: approximately \(8.87 \, \text{m/s}^2\)

Since \(3.59 \, \text{m/s}^2\) doesn't match those exactly but is quite close to Mars and Mercury, it suggests that the weight calculation may be influenced by rounding or variations.

However, the value \(3.59 \, \text{m/s}^2\) is closest to the acceleration due to gravity on Mars. Therefore, it is likely that the person is standing on:

**a. Mars**