Coulomb's Law (7 of 7) Force on Three Charges Arranged in a Right Triangle

Step by Step Science
15 Apr 201608:07
EducationalLearning
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TLDRIn this educational video, the presenter tackles a problem involving Coulomb's Law, focusing on determining the net force acting on a charge (Q3) within a triangular arrangement of three charges. The step-by-step explanation begins with establishing the direction of the forces based on the nature of the charges (attractive or repulsive), followed by calculating the magnitude of these forces. The video then delves into vector decomposition to find the X and Y components of the forces, and finally, uses trigonometry and the Pythagorean theorem to compute the resultant force's magnitude and direction. The presenter's methodical approach demystifies the complex physics concepts, making it accessible and understandable for viewers.

Takeaways
  • 📚 The problem involves calculating the net force on a charge (Q3) due to the presence of two other charges (Q1 and Q2) arranged in a triangular configuration.
  • 🔢 Q1 has a charge of -50 microcoulombs, Q2 has a charge of +75 microcoulombs, and Q3 has a charge of +65 microcoulombs.
  • 🧭 To find the direction of the force, opposite charges attract (Q1 and Q3) and like charges repel (Q2 and Q3). This determines the initial directionality of the forces.
  • 📐 The magnitude of the forces is calculated using Coulomb's Law, which states that the force (F) between two charges is given by k * (Q1 * Q2) / r², where k is the Coulomb's constant (9 * 10^9 N m²/C²) and r is the distance between the charges.
  • 🌟 The force from Q1 to Q3, F31, is in the negative y-direction with a magnitude of 214 Newtons after considering the conversion from microcoulombs to coulombs and squaring the distance.
  • 🔄 The force from Q2 to Q3, F32, is decomposed into X (F32x) and Y (F32y) components because it does not act along a principal axis. F32x is calculated using sine (sin) of the angle, and F32y using cosine (cos).
  • 📐 The X and Y components of the forces are then used to determine the total force in the X and Y directions, which are 69 Newtons and 174 Newtons respectively.
  • 🔢 The resultant force (the net force on Q3) is found by combining the X and Y components using vector addition, resulting in a force of 187 Newtons at an angle of 68° below the x-axis or 248° counterclockwise from the positive x-axis in the third quadrant.
  • 📊 The problem-solving process involves breaking down complex vector forces into their components, using trigonometric functions, and applying the Pythagorean theorem to find the magnitude of the resultant force.
  • 👍 The video provides a step-by-step guide on how to tackle such physics problems, emphasizing the importance of understanding the direction and magnitude of forces between charges.
  • 🎓 The video encourages viewers to practice these steps and apply them to similar problems for better understanding and mastery of the concepts.
Q & A

  • What is the main topic of the video?

    -The main topic of the video is to solve a problem involving Coulomb's Law with three charges arranged in a triangular formation, specifically focusing on finding the magnitude and direction of the force on Q3.

  • What are the values of the three charges mentioned in the problem?

    -The values of the three charges are Q3 = 65 microcoulombs, Q1 = -50 microcoulombs, and Q2 = 75 microcoulombs.

  • How does the presenter decide the direction of the force between Q1 and Q3?

    -The presenter decides the direction of the force between Q1 and Q3 by using the fact that opposite charges attract each other. Since Q1 is negative and Q3 is positive, the force on Q3 from Q1 will point in the negative y direction.

  • What is the significance of determining the direction of forces before calculating their magnitudes?

    -Determining the direction of forces before calculating their magnitudes helps in understanding how the forces interact with each other, whether they repel or attract, which is essential for the subsequent vector addition of forces to find the net force.

  • How does the video calculate the magnitude of the force between Q1 and Q3 using Coulomb's Law?

    -The video calculates the magnitude of the force between Q1 and Q3 using Coulomb's Law, which states that the force F is equal to the product of the charges (k * q1 * q2) divided by the square of the distance between them (r²). The constant k (Coulomb's constant) is 9 * 10^9 N m²/C². The video also converts microcoulombs to coulombs for consistency in units.

  • What is the resultant force on Q3 from the forces exerted by Q1 and Q2?

    -The resultant force on Q3 from Q1 is 214 Newtons and from Q2 is 80 Newtons. These forces are then broken down into their X and Y components to be added vectorially.

  • How does the video handle the vector decomposition of the force F32?

    -The video decomposes the force F32 into its X and Y components using trigonometric functions, considering the angle formed by the force and the coordinate axes. It uses sine for the Y component (opposite side) and cosine for the X component (adjacent side), given the known angle of 60°.

  • What are the X and Y components of the resultant force acting on Q3?

    -The X component of the resultant force is 69 Newtons, and the Y component is 174 Newtons. These components are derived from the vector addition of the individual forces considering their directions and magnitudes.

  • How is the net force acting on Q3 determined?

    -The net force acting on Q3 is determined by adding the X and Y components of the forces as vector quantities. This involves using the Pythagorean theorem to find the hypotenuse (magnitude of the resultant force) and the tangent function to find the angle of the force relative to the X-axis.

  • What is the magnitude and direction of the net force on Q3?

    -The magnitude of the net force on Q3 is 187 Newtons, and its direction is at an angle of 68° below the X-axis or 248° counterclockwise from the positive X-axis in the third quadrant.

  • What is the key takeaway from the video for solving similar problems?

    -The key takeaway is that by carefully analyzing the charges, their signs, and their arrangement, one can determine the direction and magnitude of the forces between them. Then, by applying vector addition and decomposition using trigonometric functions and Coulomb's Law, one can find the net force acting on a particular charge.

Outlines
00:00
📚 Introduction to Coulomb's Law and Force Calculation

The video begins with an introduction to a problem involving three charges arranged in a triangular formation. The objective is to determine the magnitude and direction of the total force acting on Q3, which has a charge of 65 microcoulombs. The other charges are -50 microcoulombs for Q1 and 75 microcoulombs for Q2. The explanation starts with a discussion on the direction of the forces based on the nature of the charges, highlighting that opposite charges attract and same charges repel. The force from Q1 to Q3 is directed towards the negative y-axis, while the force from Q2 to Q3 is explained to be along a line where positive charges repel each other. The video then transitions to calculating the magnitude of these forces using Coulomb's law, with an emphasis on converting the charges to the appropriate units and understanding the significance of the charges' signs in determining the direction of the force.

05:02
🔍 Calculating Magnitude and Direction of Forces

This paragraph delves into the calculation of the magnitude and direction of the forces acting on Q3 due to Q1 and Q2. Using Coulomb's law, the video demonstrates how to compute the force between two charges by considering the product of the charges and the inverse square of the distance between them. The force from Q1 to Q3 is calculated to be 214 Newtons, while the force from Q2 to Q3 is 80 Newtons. The video then explains the decomposition of the force vector F32 into its X and Y components using trigonometric functions, given the 30-60-90 right triangle formed by the forces. The X component (F32x) is found to be 69 Newtons, and the Y component (F32y) is 40 Newtons. The paragraph concludes with the summation of the forces in the X and Y directions to find the resultant force acting on Q3, which is a combination of the forces from Q1 and Q2. The direction of this resultant force is determined to be 68 degrees below the x-axis or 248 degrees from the positive side, counting counterclockwise in the third quadrant.

Mindmap
Keywords
💡Coulomb's Law
Coulomb's Law is a fundamental principle in physics that describes the electrostatic interaction between two charged particles. It states that the force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. In the video, Coulomb's Law is used to calculate the magnitude of the forces between the charges Q1, Q2, and Q3. The formula F = k * (q1 * q2) / r² is applied to find the force between each pair of charges, where F is the force, k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.
💡Charges
Charges refer to the quantity of electricity carried by an object or particle. In the context of the video, charges are represented by the symbols Q1, Q2, and Q3, with specific values given for each (e.g., -50 microcoulombs for Q1 and 75 microcoulombs for Q2). Charges can be positive or negative, and they play a crucial role in determining the nature of the force between particles—positive charges repel each other and attract negative charges, while negative charges repel each other and attract positive charges.
💡Force
In physics, force is any action that, when unopposed, will change the motion of an object. It can cause an object to accelerate, decelerate, change direction, or change shape. In the video, the force is the result of the interactions between the electric charges Q1, Q2, and Q3. The script describes calculating both the magnitude and the direction of the force on Q3 due to the other two charges, using both Coulomb's Law and vector addition.
💡Direction
Direction refers to the course along which something is moving or the orientation of an object in space. In the context of the video, direction is used to describe the line along which the force is acting on the charges. The direction is determined by the nature of the charges—opposite charges attract and their forces align, while like charges repel and their forces act in opposite directions. The final force on Q3 is determined by adding the vector components of the forces from Q1 and Q2.
💡Magnitude
Magnitude refers to the size or extent of something, often used in the context of measuring physical quantities. In the video, magnitude is used to describe the strength or intensity of the force acting on the charges. The magnitude of the force is calculated using Coulomb's Law and is measured in Newtons. The total force on Q3 is found by adding the magnitudes of the individual forces from Q1 and Q2 after considering their directions.
💡Vector
A vector is a quantity that has both magnitude and direction. In physics, vectors are used to represent physical quantities that have both size and direction, such as force, velocity, and acceleration. In the video, the force exerted on Q3 by Q1 and Q2 are vector quantities. The script discusses breaking down these forces into their X and Y components and then using trigonometric functions to find the resultant force, which is the vector sum of the individual forces.
💡Trigonometry
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right-angled triangles. In the video, trigonometry is used to decompose the forces into their X and Y components and to find the resultant force. Functions like sine and cosine are used to calculate these components, and the Pythagorean theorem is used to find the magnitude of the resultant force vector.
💡Resultant Force
Resultant Force is the single force that represents the combined effect of multiple forces acting on an object. It is found by vector addition of all the individual forces. In the context of the video, the resultant force is the net force experienced by Q3 due to the presence of Q1 and Q2. The script describes how to calculate this resultant force by adding the individual forces' components along the X and Y axes and then finding the hypotenuse of the right triangle formed by these components.
💡Angle
In geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex. In the context of the video, the angle is used to describe the direction of the resultant force. The angle is found using trigonometric relationships and is measured from the positive X-axis. The final direction of the force on Q3 is given as either 68 degrees below the negative X-axis or 248 degrees from the positive X-axis, counterclockwise in the third quadrant.
💡Pythagorean Theorem
The Pythagorean Theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the sum of the squares of the two shorter sides (a and b) is equal to the square of the longest side (c), or a² + b² = c². In the video, the Pythagorean Theorem is used to find the magnitude of the resultant force, where a and b are the X and Y components of the forces, and c is the resultant force.
Highlights

The problem involves calculating the force on a charge Q3 in a triangular arrangement of three charges using Coulomb's Law.

Q3 has a positive charge of 65 microcoulombs, Q1 has a negative charge of -50 microcoulombs, and Q2 has a positive charge of 75 microcoulombs.

The direction of the force on Q3 from Q1 is towards the negative y-direction due to the attraction between opposite charges.

The force on Q3 from Q2 is in the direction of the line connecting Q2 and Q3 because like charges repel each other.

Coulomb's Law is used to calculate the magnitude of the forces between the charges, with the formula k * q1 * q2 / r^2, where k is the Coulomb's constant.

The force on Q3 from Q1 (F31) is 214 Newtons, and from Q2 (F32) is 80 Newtons, with Q1 and Q2 being 73 meters apart.

The force vectors need to be decomposed into their X and Y components to determine their individual effects in those directions.

Trigonometric functions are used to calculate the components of the force vectors, with F31 having a y-component and F32 having both x and y components.

The total force in the X direction is 69 Newtons, resulting from the x-component of F32.

The total force in the Y direction is the difference between F31 and F32's y-components, resulting in 174 Newtons.

The resultant force on Q3 is found by combining the X and Y components using the Pythagorean theorem and trigonometric functions.

The direction of the resultant force is 68 degrees below the x-axis or 248 degrees from the positive direction, counted counterclockwise in the third quadrant.

The magnitude of the resultant force is 187 Newtons, calculated using the Pythagorean theorem for the combined X and Y components.

The step-by-step process of calculating the forces, decomposing them, and finding the resultant force is emphasized for clarity and understanding.

The video provides a comprehensive guide on how to solve complex problems involving multiple charges and their interactions.

The problem-solving approach is methodical, encouraging viewers to write down each step to ensure accuracy and understanding.

The video concludes with a call to action for viewers to subscribe, like, and comment, fostering engagement and support for the content creator.

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