Question

If a woman weighs \(130 \mathrm{lb}\) on Earth, will her weight on the moon be bigger, smaller, or the same?

Short answer

The woman's weight on the moon will be smaller.

Step-by-step solution

Understanding Weight on Different Celestial Bodies

Weight is the force exerted by gravity on an object. This force depends on the gravitational pull of the celestial body. Since the moon's gravity is weaker than Earth's gravity, an object will weigh less on the moon.

Gravitational Force Comparison

The gravitational force on the moon is approximately 1/6th of that on Earth. Therefore, if the gravitational acceleration on Earth is denoted by \( g \), then the gravitational acceleration on the moon is \( g/6 \).

Calculating Weight on the Moon

To calculate the weight on the moon, you take the weight on Earth and multiply it by the ratio of the moon's gravity to Earth's gravity. For a woman weighing \(130 \, \mathrm{lb}\) on Earth, her weight on the moon is \( \frac{130}{6} \approx 21.67 \, \mathrm{lb} \).

Conclusion

Based on the calculation, the woman's weight on the moon is 21.67 lb, which is significantly less than her weight of 130 lb on Earth.

Key concepts

Gravitational Force

Gravitational force is an invisible force that pulls objects toward each other. This force is the reason why we stay grounded on Earth and why planets orbit around stars. The strength of this force depends on the mass of the objects involved and the distance between them.
When we talk about weight, we are actually referring to the gravitational force exerted on an object by a planet, such as Earth. Thus, weight varies based on the planetary body you're on because each has different gravitational pull. Earth's gravitational force is stronger compared to the moon, primarily due to Earth's larger mass. Understanding these concepts helps us explain why our weight differs on other celestial bodies.

Moon Gravity

The moon's gravity is much weaker than Earth's. This is because the moon is smaller and has less mass compared to Earth. As a result, it exerts a weaker gravitational pull.
To offer a comparison, the gravitational force you experience on the moon is only about 1/6th of what you would feel on Earth. This means that if you weigh 130 pounds on Earth, gravity on the moon would make you feel much lighter.
It's interesting to note how significant the role of gravity is in determining our weight and how we perceive our physical presence on different planets or moons.

Calculate Weight on Different Planets

To calculate your weight on different planets, you need to understand the concept of gravitational acceleration. Each planet has its own unique gravitational acceleration, which affects how much you would weigh there.
To find your weight on any planet, use the formula:\[\text{Weight on planet} = \text{Weight on Earth} \times \left(\frac{\text{Gravitational acceleration on planet}}{\text{Gravitational acceleration on Earth}}\right)\]By plugging in the respective values of gravitational acceleration, you can calculate your new weight on other planets. For instance, knowing that gravity on the moon is 1/6th as strong as on Earth, we multiply 130 lb by 1/6 to find that the weight would be approximately 21.67 lb on the moon.

Gravitational Acceleration

Gravitational acceleration is a measure of how fast an object will accelerate when it is falling freely under the influence of gravity. On Earth, this acceleration is approximately 9.81 m/s², which is often simplified as "g".
For the moon, the gravitational acceleration is significantly lower, around 1.63 m/s². This difference in values is why the same object weighs differently on Earth compared to the moon. Gravitational acceleration helps explain why astronauts can jump much higher on the moon than on Earth. Knowing these numbers helps us understand and predict how objects will behave under different gravitational influences.