Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To determine the force acting on object \(A\) due to object \(B\), we can use Coulomb's Law. Coulomb's Law states:
[tex]\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
where:
- \( F \) is the force between the charges,
- \( k \) is the constant of proportionality (Coulomb's constant), \( k = 9.0 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.
Given:
- The charge of object \(A\), \( q_A = -0.25 \, \text{C} \),
- The charge of object \(B\), \( q_B = 1 \, \text{C} \),
- The distance between the objects, \( r = 1.5 \, \text{m} \).
First, substitute these values into Coulomb's Law equation:
[tex]\[ F = 9.0 \times 10^9 \frac{|-0.25 \cdot 1|}{1.5^2} \][/tex]
Calculate the magnitude of the force:
[tex]\[ F = 9.0 \times 10^9 \frac{0.25}{2.25} \][/tex]
[tex]\[ F = 9.0 \times 10^9 \times \frac{0.25}{2.25} \][/tex]
[tex]\[ F = 9.0 \times 10^9 \times \frac{1}{9} \][/tex]
[tex]\[ F = 9.0 \times 10^9 \times 0.1111 \][/tex]
[tex]\[ F = 1.0 \times 10^9 \, \text{N} \][/tex]
Since the charges of objects \(A\) and \(B\) are opposite (one negative, one positive), the force between them will be attractive. An attractive force in this context implies that the force on \(A\) is directed towards \(B\), and we traditionally denote attractive forces as negative values.
Thus, the force on object \(A\) is:
[tex]\[ F = -1.0 \times 10^9 \, \text{N} \][/tex]
This matches one of the provided options. Therefore, the correct answer is:
[tex]\[ \boxed{-1.0 \times 10^9 \, \text{N}} \][/tex]
[tex]\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
where:
- \( F \) is the force between the charges,
- \( k \) is the constant of proportionality (Coulomb's constant), \( k = 9.0 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.
Given:
- The charge of object \(A\), \( q_A = -0.25 \, \text{C} \),
- The charge of object \(B\), \( q_B = 1 \, \text{C} \),
- The distance between the objects, \( r = 1.5 \, \text{m} \).
First, substitute these values into Coulomb's Law equation:
[tex]\[ F = 9.0 \times 10^9 \frac{|-0.25 \cdot 1|}{1.5^2} \][/tex]
Calculate the magnitude of the force:
[tex]\[ F = 9.0 \times 10^9 \frac{0.25}{2.25} \][/tex]
[tex]\[ F = 9.0 \times 10^9 \times \frac{0.25}{2.25} \][/tex]
[tex]\[ F = 9.0 \times 10^9 \times \frac{1}{9} \][/tex]
[tex]\[ F = 9.0 \times 10^9 \times 0.1111 \][/tex]
[tex]\[ F = 1.0 \times 10^9 \, \text{N} \][/tex]
Since the charges of objects \(A\) and \(B\) are opposite (one negative, one positive), the force between them will be attractive. An attractive force in this context implies that the force on \(A\) is directed towards \(B\), and we traditionally denote attractive forces as negative values.
Thus, the force on object \(A\) is:
[tex]\[ F = -1.0 \times 10^9 \, \text{N} \][/tex]
This matches one of the provided options. Therefore, the correct answer is:
[tex]\[ \boxed{-1.0 \times 10^9 \, \text{N}} \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.