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

Welcome back everybody. We are told that the ratio of a weight of a person on Mars compared to the weight of that same person on Earth is 0.38. And we are asked to find what the gravitational acceleration on Mars is. Well, we know that the weight of an object on a given planet is equal to its mass times the gravitational acceleration of that planet. Well, the mass on both Earth and MARS is going to be constant, but here's what I'm gonna do. I'm gonna divide both sides by our gravitational acceleration and we're gonna get that the mass is equal, wait times the gravitational acceleration on a given planet. I'm actually gonna say this right side here is Earth, and since mass is constant, I can say that this is equal to the weight on MARS divided by the gravitational acceleration on MArs of this term is what we're looking for. So I'm gonna isolate that term and rearrange um these two equations here and we get that the gravitational acceleration of MArs equal to our ratio times the gravitational acceleration on Earth. So let's plug in our values. You know that the ratio is 0.8 that the gravitational acceleration on Earth is 9.8. When you plug this into your calculator, you get 3.7 m per second squared corresponding to our answer choice of D Thank you guys so much for watching this video helped. We will see you all in the next one

Ch 04: Newton's Laws of Motion

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th 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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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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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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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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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?

Verified video answer for a similar problem:

Key Concepts

Weight and Gravitational Force

Acceleration due to Gravity

Newton's Second Law of Motion

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?