An astronaut's pack weighs 17.5 N when she is on the earth but only 3.24 N when she is at the surface of a moon. (a) What is the acceleration due to gravity on this moon?

Verified step by step guidance

1. Identify the force of gravity acting on the pack on Earth and on the moon. On Earth, the force is 17.5 N, and on the moon, it is 3.24 N.
2. Recall the formula for weight, which is the force of gravity acting on an object: \( W = m \cdot g \), where \( W \) is the weight, \( m \) is the mass of the object, and \( g \) is the acceleration due to gravity.
3. Calculate the mass of the astronaut's pack using the weight on Earth and the acceleration due to gravity on Earth (\( g_{earth} = 9.81 \, m/s^2 \)). Use the formula rearranged to solve for mass: \( m = \frac{W}{g} \).
4. Use the mass calculated in the previous step to find the acceleration due to gravity on the moon. Rearrange the weight formula to solve for \( g_{moon} \): \( g_{moon} = \frac{W_{moon}}{m} \).
5. Substitute the mass and the weight on the moon into the equation to find the acceleration due to gravity on the moon.

Key Concepts

Weight and Gravity

Weight is the force exerted by gravity on an object, calculated as the product of mass and gravitational acceleration (W = mg). On Earth, the standard acceleration due to gravity is approximately 9.81 m/s². The weight of an object changes depending on the gravitational field strength of the celestial body it is on, which is crucial for understanding how weight varies between Earth and the moon.

Gravitational Acceleration

Gravitational acceleration is the acceleration experienced by an object due to the gravitational force of a celestial body. It varies depending on the mass of the body and the distance from its center. The formula to calculate gravitational acceleration (g) is derived from Newton's law of universal gravitation, and it can be determined by rearranging the weight equation to find g = W/m, where W is weight and m is mass.

Mass vs. Weight

Mass is a measure of the amount of matter in an object and remains constant regardless of location, while weight is the force that results from the gravitational pull on that mass. This distinction is important when analyzing how an object's weight changes in different gravitational fields, such as on the moon compared to Earth, as seen in the astronaut's pack example.