How much would an 80.0kg person weigh on Mars, where the acceleration of gravity is 3.93m/s and in Earths moon, where the acceleration of gravity is 1.63m/s
The Correct Answer and Explanation is:
To calculate the weight of an 80.0 kg person on Mars and on the Moon, we use the formula for weight:
[
\text{Weight} = \text{Mass} \times \text{Acceleration due to gravity}
]
Where:
- Mass (m) = 80.0 kg (constant for the person)
- The acceleration due to gravity on Mars is ( 3.93 \, \text{m/s}^2 )
- The acceleration due to gravity on the Moon is ( 1.63 \, \text{m/s}^2 )
Weight on Mars:
The formula for weight on Mars is:
[
\text{Weight on Mars} = \text{Mass} \times \text{Gravity on Mars}
]
[
\text{Weight on Mars} = 80.0 \, \text{kg} \times 3.93 \, \text{m/s}^2
]
[
\text{Weight on Mars} = 314.4 \, \text{N}
]
So, the person’s weight on Mars would be 314.4 Newtons (N).
Weight on the Moon:
Similarly, the formula for weight on the Moon is:
[
\text{Weight on Moon} = \text{Mass} \times \text{Gravity on Moon}
]
[
\text{Weight on Moon} = 80.0 \, \text{kg} \times 1.63 \, \text{m/s}^2
]
[
\text{Weight on Moon} = 130.4 \, \text{N}
]
So, the person’s weight on the Moon would be 130.4 Newtons (N).
Explanation:
Weight is the force exerted on a body due to gravity, and it is dependent on both the mass of the object and the local gravitational field strength. The formula ( F = m \times g ) expresses this relationship, where:
- ( F ) is the weight (in Newtons),
- ( m ) is the mass (in kilograms),
- ( g ) is the acceleration due to gravity (in meters per second squared).
On Earth, gravity is approximately ( 9.81 \, \text{m/s}^2 ), but both Mars and the Moon have weaker gravitational fields than Earth. On Mars, the gravity is about ( 3.93 \, \text{m/s}^2 ), and on the Moon, it’s even weaker, at ( 1.63 \, \text{m/s}^2 ). Consequently, an object weighs less on both Mars and the Moon than on Earth because the gravitational pull is weaker.
In this case, the person’s mass remains constant at 80.0 kg, but the weight changes depending on the gravitational acceleration. Therefore, on Mars, the person weighs significantly less than on Earth, and on the Moon, the weight is even lower.