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

Problem 16a

Chapter 4, Problem 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?

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Related Practice

Textbook Question

At the surface of Jupiter's moon Io, the acceleration due to gravity is $g equals 1.81$ m/s². A watermelon weighs $44.0$ N at the surface of the earth. What is the watermelon's mass on the earth's surface?

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Textbook Question

A $4.50$ -kg experimental cart undergoes an acceleration in a straight line (the $x$ -axis). The graph in Fig. E $4.13$ shows this acceleration as a function of time. During what times is the net force on the cart a constant?

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Textbook Question

A small $8.00$ -kg rocket burns fuel that exerts a time-varying upward force on the rocket (assume constant mass) as the rocket moves upward from the launch pad. This force obeys the equation $F = A + B t^{2}$ . Measurements show that at $t equals 0$ , the force is $100.0$ N, and at the end of the first $2.00$ s, it is $150.0$ N. Find the constants $A$ and $B$ , including their SI units.

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Textbook Question

A $4.50$ -kg experimental cart undergoes an acceleration in a straight line (the $x$ -axis). The graph in Fig. E $4.13$ shows this acceleration as a function of time. Find the maximum net force on this cart. When does this maximum force occur?

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Textbook Question

At the surface of Jupiter's moon Io, the acceleration due to gravity is $g = 1.81$ m/s². A watermelon weighs $44.0$ N at the surface of the earth. What would be its mass and weight on the surface of Io?

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Textbook Question

World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude $15$ m/s². How much horizontal force must a $55$ -kg sprinter exert on the starting blocks to produce this acceleration? Which body exerts the force that propels the sprinter: the blocks or the sprinter herself?

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