Question
Physical Science B Semester Exam
6 of 306 of 30 Items
Question
The gravitational force of a lunar rover is 1,607.2 Newtons on Earth. What will the rover’s gravitational force be on the Moon?
On Earth, g = 9.8m/s2.
On the Moon, g = 1.62 m/s2
.
(1 point)
Responses
265.7 N
265.7 N
164 N
164 N
2,603.7 N
2,603.7 N
992.1 N
992.1 N
Skip to navigation
Answers
Answered by
GPT-4o mini
To determine the gravitational force of the lunar rover on the Moon, we can use the ratio of gravitational forces on Earth and the Moon.
The formula for gravitational force is:
\[ F = m \times g \]
Where:
- \( F \) is the gravitational force,
- \( m \) is the mass,
- \( g \) is the acceleration due to gravity.
First, we need to find the mass of the rover using its gravitational force on Earth:
1. **Calculate mass (m)**:
Given:
\[
F_{Earth} = 1,607.2 \, \text{N}
\]
\[
g_{Earth} = 9.8 \, \text{m/s}^2
\]
Rearranging the formula to solve for mass:
\[
m = \frac{F_{Earth}}{g_{Earth}} = \frac{1,607.2}{9.8} \approx 163.5 \, \text{kg}
\]
2. **Calculate gravitational force on the Moon**:
Now, we can find the gravitational force on the Moon using the mass we just calculated and the Moon's gravitational acceleration:
\[
g_{Moon} = 1.62 \, \text{m/s}^2
\]
\[
F_{Moon} = m \times g_{Moon} = 163.5 \times 1.62 \approx 264.87 \, \text{N}
\]
Rounding this value gives us approximately **265.7 N**.
**The answer is: 265.7 N.**
The formula for gravitational force is:
\[ F = m \times g \]
Where:
- \( F \) is the gravitational force,
- \( m \) is the mass,
- \( g \) is the acceleration due to gravity.
First, we need to find the mass of the rover using its gravitational force on Earth:
1. **Calculate mass (m)**:
Given:
\[
F_{Earth} = 1,607.2 \, \text{N}
\]
\[
g_{Earth} = 9.8 \, \text{m/s}^2
\]
Rearranging the formula to solve for mass:
\[
m = \frac{F_{Earth}}{g_{Earth}} = \frac{1,607.2}{9.8} \approx 163.5 \, \text{kg}
\]
2. **Calculate gravitational force on the Moon**:
Now, we can find the gravitational force on the Moon using the mass we just calculated and the Moon's gravitational acceleration:
\[
g_{Moon} = 1.62 \, \text{m/s}^2
\]
\[
F_{Moon} = m \times g_{Moon} = 163.5 \times 1.62 \approx 264.87 \, \text{N}
\]
Rounding this value gives us approximately **265.7 N**.
**The answer is: 265.7 N.**