Two objects attract each other with a gravitational force of magnitude 9.60 x 109 N when separated by 19.0 cm. If the total mass of the objects is 5.05 kg, what is the of each? heavier mass kg

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
icon
Related questions
icon
Concept explainers
Question
### Problem Statement

Two objects attract each other with a gravitational force of magnitude \(9.60 \times 10^{-9}\) N when separated by \(19.0\) cm. If the total mass of the objects is \(5.05\) kg, what is the mass of each?

- **Heavier mass:** \(\_\_\_\_) \text{ kg}\)
- **Lighter mass:** \(\_\_\_\_) \text{ kg}\)

### Explanation

This problem involves calculating the individual masses of two objects based on the gravitational force between them and the total combined mass. The problem provides the gravitational force, the separation distance, and the total mass. It requires applying the formula for gravitational force and solving for the individual masses.

### Key Concepts

- **Gravitational Force Formula:** 
  \[
  F = \frac{G \cdot m_1 \cdot m_2}{r^2}
  \]
  where \(F\) is the gravitational force, \(G\) is the gravitational constant \((6.674 \times 10^{-11} \, \text{N(m/kg)}^2)\), \(m_1\) and \(m_2\) are the masses of the objects, and \(r\) is the distance between the centers of the two masses.

- **Total Mass Equation:**
  \[
  m_1 + m_2 = 5.05 \text{ kg}
  \]

### Steps to Solve

1. Convert the separation distance from centimeters to meters.
2. Use the gravitational force formula to set up an equation.
3. Use the total mass to set up a system of equations.
4. Solve the system of equations to find the individual masses.
Transcribed Image Text:### Problem Statement Two objects attract each other with a gravitational force of magnitude \(9.60 \times 10^{-9}\) N when separated by \(19.0\) cm. If the total mass of the objects is \(5.05\) kg, what is the mass of each? - **Heavier mass:** \(\_\_\_\_) \text{ kg}\) - **Lighter mass:** \(\_\_\_\_) \text{ kg}\) ### Explanation This problem involves calculating the individual masses of two objects based on the gravitational force between them and the total combined mass. The problem provides the gravitational force, the separation distance, and the total mass. It requires applying the formula for gravitational force and solving for the individual masses. ### Key Concepts - **Gravitational Force Formula:** \[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \] where \(F\) is the gravitational force, \(G\) is the gravitational constant \((6.674 \times 10^{-11} \, \text{N(m/kg)}^2)\), \(m_1\) and \(m_2\) are the masses of the objects, and \(r\) is the distance between the centers of the two masses. - **Total Mass Equation:** \[ m_1 + m_2 = 5.05 \text{ kg} \] ### Steps to Solve 1. Convert the separation distance from centimeters to meters. 2. Use the gravitational force formula to set up an equation. 3. Use the total mass to set up a system of equations. 4. Solve the system of equations to find the individual masses.
Expert Solution
Step 1

Physics homework question answer, step 1, image 1

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Gravitational Force
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON