If a man weighs 600 N on the Earth, what would he weigh on Jupiter, where the free-fall acceleration is 25.9 m/s²?
The Correct Answer and Explanation is :
To calculate the weight of a man on Jupiter, we first need to understand the relationship between weight, mass, and gravitational acceleration. Weight is the force exerted by gravity on an object, and it can be calculated using the formula:
[
\text{Weight} (W) = \text{Mass} (m) \times \text{Gravitational Acceleration} (g)
]
Step 1: Find Mass on Earth
The man’s weight on Earth is given as 600 N. The acceleration due to gravity on Earth is approximately 9.81 m/s². We can rearrange the formula to find his mass:
[
m = \frac{W}{g}
]
Substituting the values for Earth:
[
m = \frac{600 \, \text{N}}{9.81 \, \text{m/s}^2} \approx 61.15 \, \text{kg}
]
Step 2: Calculate Weight on Jupiter
Now that we have the mass, we can find the weight of the man on Jupiter, where the gravitational acceleration is 25.9 m/s². We use the same weight formula:
[
W_{Jupiter} = m \times g_{Jupiter}
]
Substituting the values:
[
W_{Jupiter} = 61.15 \, \text{kg} \times 25.9 \, \text{m/s}^2 \approx 1586.44 \, \text{N}
]
Conclusion
Therefore, a man who weighs 600 N on Earth would weigh approximately 1586.44 N on Jupiter.
This significant increase in weight on Jupiter can be attributed to the planet’s much stronger gravitational pull compared to Earth. Jupiter’s gravitational acceleration is about 2.6 times greater than that of Earth’s. As a result, objects (and individuals) experience a proportionately greater force due to gravity, which is why a person weighing 600 N on Earth would feel much heavier on Jupiter. Understanding these calculations is essential in fields like physics and engineering, where gravitational effects play a crucial role in various applications.