An astronaut's pack weighs 17.517.5 N when she is on the earth but only 3.243.24 N when she is at the surface of a moon. What is the acceleration due to gravity on this moon?

Ch 04: Newton's Laws of Motion

Young & Freedman Calc - University Physics 15th Edition

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Young & Freedman Calc 15th Edition

Ch 04: Newton's Laws of Motion

문제 16a

4장, 문제 16a

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. What is the acceleration due to gravity on this moon?

검증된 단계별 안내

Step 1: Recall the relationship between weight and gravitational force. Weight is given by the formula:

W = m g

, where

W

is the weight,

m

is the mass, and

g

is the acceleration due to gravity.

Step 2: Use the weight of the pack on Earth to calculate its mass. On Earth, the acceleration due to gravity is approximately

9.8 \, \(\text{m/s}\)^2

. Rearrange the formula to solve for mass:

m = $\frac{W}{g}$

. Substitute

= 17.5 \, \(\text{N}\)

and

= 9.8 \, \(\text{m/s}\)^2

Step 3: Once the mass is determined, use the weight of the pack on the moon to find the moon's gravitational acceleration. Rearrange the weight formula to solve for

g

g = $\frac{W}{m}$

. Substitute

= 3.24 \, \(\text{N}\)

and the mass calculated in Step 2.

Step 4: Perform the division to calculate the acceleration due to gravity on the moon. Ensure the units are consistent, and the result is expressed in

\(\text{m/s}\)^2

Step 5: Interpret the result. The calculated value represents the acceleration due to gravity on the moon's surface, which is significantly smaller than Earth's due to the moon's lower mass and size.

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주요 개념

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Weight and Gravitational Force

Weight is the force exerted by gravity on an object, calculated as the product of mass and the acceleration due to gravity (W = mg). On Earth, this acceleration is approximately 9.81 m/s², but it varies on different celestial bodies, affecting the weight of objects.

Acceleration due to Gravity

The acceleration due to gravity (g) is the rate at which an object accelerates towards a celestial body due to gravitational pull. It varies depending on the mass and radius of the body; for example, the moon has a lower g than Earth, resulting in lighter weights for the same mass.

Newton's Second Law of Motion

Newton's Second Law states that the force acting on an object is equal to the mass of that object multiplied by its acceleration (F = ma). This principle is essential for calculating the acceleration due to gravity on the moon by rearranging the weight equation to find g when the weight and mass are known.