Two uniform spheres are positioned as shown. Determine the gravitational force F which the titanium sphere exerts on the copper sphere. The value of R is 40 mm. Assume a = 5.0,b=2.7,0=38⁰ aR R Titanium Ө Copper bR 1x

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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### Problem Statement

Two uniform spheres are positioned as shown. Determine the gravitational force \( F \) which the titanium sphere exerts on the copper sphere. The value of \( R \) is 40 mm.

Assume \( a = 5.0 \), \( b = 2.7 \), \( \theta = 38^\circ \).

![Diagram](image-link)

**Description of Diagram:**
The diagram depicts two spheres: one labeled "Titanium" with radius \( R \) and the other labeled "Copper" with radius \( bR \). Both spheres are positioned such that their centers form an angle \( \theta \) with the horizontal axis \( x \) and the vertical axis \( y \). The distance between the center of the titanium sphere and the copper sphere is represented as \( aR \).

---

### Part 1

#### Question:
Calculate the mass of each sphere.

Assume \( a = 5.0 \), \( b = 2.7 \), \( \theta = 38^\circ \).

![Diagram](image-link)

**Description of Diagram:**
The second diagram is identical to the first, showing the same two spheres with the same labels, distances, and angles.

#### Answers:
**Titanium Sphere**
\[ m_t = \text{[input box]} \, \text{kg} \]

---

*Note: The diagram is critical for visualizing the relative positions and distances between the spheres, which are essential for calculating the gravitational force and the masses.*

---
Transcribed Image Text:--- ### Problem Statement Two uniform spheres are positioned as shown. Determine the gravitational force \( F \) which the titanium sphere exerts on the copper sphere. The value of \( R \) is 40 mm. Assume \( a = 5.0 \), \( b = 2.7 \), \( \theta = 38^\circ \). ![Diagram](image-link) **Description of Diagram:** The diagram depicts two spheres: one labeled "Titanium" with radius \( R \) and the other labeled "Copper" with radius \( bR \). Both spheres are positioned such that their centers form an angle \( \theta \) with the horizontal axis \( x \) and the vertical axis \( y \). The distance between the center of the titanium sphere and the copper sphere is represented as \( aR \). --- ### Part 1 #### Question: Calculate the mass of each sphere. Assume \( a = 5.0 \), \( b = 2.7 \), \( \theta = 38^\circ \). ![Diagram](image-link) **Description of Diagram:** The second diagram is identical to the first, showing the same two spheres with the same labels, distances, and angles. #### Answers: **Titanium Sphere** \[ m_t = \text{[input box]} \, \text{kg} \] --- *Note: The diagram is critical for visualizing the relative positions and distances between the spheres, which are essential for calculating the gravitational force and the masses.* ---
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