Response:
The question is not fully provided; here is the complete context:
Gravity's acceleration on the moon is 1.6 m/s², roughly one-sixth that of Earth's. What is the accurate description of an object's weight on the moon?
A. An object on the moon is lighter by a factor of 1/6 compared to Earth.
B. An object on the moon is heavier by a factor of 1/6 compared to Earth.
C. An object on the moon is six times lighter than on Earth.
D. An object on the moon is six times heavier than on Earth.
The correct choice is:
An object on the moon is six times lighter than on Earth. (C)
Explanation:
The acceleration resulting from gravity indicates how a gravitational force impacts an object, causing it to accelerate. This is a vectorial quantity because it possesses both magnitude and direction, measured in the unit of m/s². On Earth, this gravitational acceleration is represented by the letter g and its value is approximately 9.8m/s².
The larger size of the Earth in comparison to the moon causes its gravitational acceleration to be about six times greater than that of the moon, resulting in the moon's gravitational acceleration being approximately 1.6m/s².
Next, weight refers to the product of mass and gravity's acceleration. This reflects the gravitational pull acting upon a mass, which is also measured in Newtons, similar to force.
Weight = m × g (N)
From the weight formula, we can see that weight corresponds directly to mass and gravitational acceleration:
weight ∝ mass;
weight ∝ gravitational acceleration.
This implies that if gravitational acceleration increases, weight increases as well, and vice versa.
For instance, let's calculate the weights of a 10kg object on both Earth and the moon.
Gravitational acceleration on Earth (g₁) = 9.8m/s².
Gravitational acceleration on the moon (g₂) = 1.6m/s².
On Earth:
weight = m × g₁ = 10 × 9.8 = 98 N.
On the moon:
weight = m × g₂ = 10 × 1.6 = 16 N.
From the above example, since the acceleration due to gravity on the moon is 1/6 that of Earth, the weight of a 10kg object on the moon is approximately six times lighter (16 N) than its weight on Earth (98 N).
