4 Resultant force of two vectors at different angles

Simon Poliakoff
25 May 201703:21
EducationalLearning
32 Likes 10 Comments

TLDRIn the video, the presenter demonstrates how to calculate the resultant force of two forces using the parallelogram method. They establish a scale where 1 cm represents 50 Newtons and proceed to draw the forces, one of 250 Newtons at a 30° angle and another of 350 Newtons at a 40° angle. By starting both vectors from the same point, a parallelogram is formed. The presenter then calculates the resultant force by measuring the length of the diagonal of the parallelogram, which is approximately 10.3 cm, translating to 515 Newtons when scaled. Finally, they measure the angle of the resultant force, which is found to be approximately 11°. This step-by-step explanation provides a clear understanding of vector addition and its application in physics.

Takeaways
  • 📏 The speaker uses a scale where 1 cm represents 50 Newtons to visualize forces.
  • 📐 A 5 cm line is drawn at a 30° angle to represent a 250 Newton force.
  • 📏 A 7 cm line at a 40° angle is used to depict a 350 Newton force.
  • 📐 The parallelogram method is employed, starting both vectors from the same point.
  • 🔄 The angle between the 250 Newton force and the resultant force is 70°.
  • 📐 The angle in the parallelogram opposite to 70° is calculated to be 110° to complete the parallelogram.
  • 📏 The resultant force is drawn from the start to the end of the parallelogram.
  • 📐 The length of the resultant force line is measured to be approximately 10.3 cm.
  • 🔢 The resultant force is calculated as 10.3 cm times the scale factor of 50 Newtons/cm, equaling 515 Newtons.
  • 📐 The angle of the resultant force vector is measured to be approximately 11°.
  • 🟢 The final resultant vector is described as having a magnitude of 515 Newtons at an angle of 11°.
Q & A

  • What is the method used in the video to find the resultant force?

    -The parallelogram method is used to find the resultant force.

  • What scale is chosen for representing the forces in the video?

    -The scale chosen is 1 cm representing 50 Newtons.

  • How long are the two forces being represented in the video?

    -The two forces are represented as 5 cm and 7 cm long.

  • At what angle does the first force act in the video?

    -The first force acts at a 30° angle.

  • What is the magnitude of the first force?

    -The magnitude of the first force is 250 Newtons.

  • How is the second force's direction determined in the video?

    -The second force's direction is determined to be at a 40° angle.

  • What is the magnitude of the second force?

    -The magnitude of the second force is 350 Newtons.

  • How does the video ensure that both vectors start from the same place?

    -The video uses the parallelogram method, which inherently starts both vectors from the same point.

  • What is the angle between the two sides of the parallelogram that are not part of the original forces?

    -The angle between these sides of the parallelogram is 110°.

  • How is the resultant force's magnitude calculated in the video?

    -The resultant force's magnitude is calculated by measuring the length of the diagonal of the parallelogram, which is 10.3 cm. Multiplying this by the scale factor (50 Newtons/cm) gives a force of 515 Newtons.

  • What is the angle of the resultant force vector?

    -The angle of the resultant force vector is approximately 11°.

  • What is the final resultant vector described in the video?

    -The final resultant vector is described as having a magnitude of 515 Newtons at an angle of 11°.

Outlines
00:00
📐 Calculating Resultant Force Using the Parallelogram Method

The speaker begins by outlining their approach to finding the resultant force from two given forces using the parallelogram method. They decide on a scale where 1 cm represents 50 Newtons. The first force is drawn as a 5 cm line at a 30° angle, labeled as 250 Newtons. The second force is then drawn as a 7 cm line at a 40° angle, labeled as 350 Newtons. Both forces are drawn starting from the same point to form the parallelogram. The angles within the parallelogram are calculated to ensure they sum up to 180°. The resultant force is determined by drawing from the start to the end of the parallelogram, which measures approximately 10.3 cm. Multiplying this length by the scale factor (50 Newtons per cm) gives a resultant force of 515 Newtons. Finally, the angle of the resultant vector is measured to be approximately 11°, completing the calculation.

Mindmap
Keywords
💡Resultant Force
Resultant force is the single force that represents the combined effect of multiple forces acting on an object. In the video, the host aims to find the resultant force from two given forces using the parallelogram method. This concept is central to the video's theme as it is the end goal of the demonstration.
💡Parallelogram Method
The parallelogram method is a graphical technique used to determine the resultant force of two forces. It involves constructing a parallelogram where two adjacent sides represent the magnitudes and directions of the forces. In the script, the host uses this method to visually and geometrically combine the two forces and find the resultant force.
💡Scale
A scale in the context of physics problems is a ratio used to convert distances on a diagram into physical quantities such as force. The host establishes a scale where '1 cm represents 50 Newtons' to translate the diagrammatic representation into measurable forces.
💡Vector
A vector is a quantity that has both magnitude and direction. In the video, forces are represented as vectors, with their lengths corresponding to the magnitude of the force and the arrows indicating direction. The host draws vectors for the two forces and then combines them to find the resultant vector.
💡Angles
Angles are a fundamental aspect of vector addition, especially when using the parallelogram method. The host measures and uses angles such as 30° and 40° to draw the forces accurately and to calculate the angles within the parallelogram, which is crucial for determining the direction of the resultant force.
💡Newtons
Newtons is the unit of force in the International System of Units (SI). The video script mentions Newtons when quantifying the forces involved. For example, '250 Newtons' and '350 Newtons' are the magnitudes of the forces being combined, and '515 Newtons' is the magnitude of the resultant force found at the end.
💡Arrow Head
In the context of the video, an arrow head is used to indicate the direction of a force vector on the diagram. The host places arrow heads on the lines representing forces to show their direction, which is essential for the accurate representation of vectors.
💡Centimeters
Centimeters are used as units of length in the video to measure the components of the forces and the resultant force on the diagram. The host uses centimeters in conjunction with the established scale to convert the lengths into Newtons.
💡Protractor
A protractor is a tool used to measure angles. In the video, the host uses a protractor to measure the angles formed by the forces and the parallelogram, which is necessary to determine the direction of the resultant force accurately.
💡Graphical Representation
Graphical representation is a method of visually depicting physical quantities such as forces. The video uses a graphical approach to show the addition of forces and the determination of the resultant force. This method helps in visualizing the vector addition process and the final outcome.
💡Direction
The direction of a force is as important as its magnitude. In the script, the host carefully notes the direction of each force and the resultant force, measured in degrees, which is essential for understanding the overall effect of the forces acting on an object.
Highlights

Introducing the method of finding resultant force using the parallelogram method.

Setting a scale of 1 cm to 50 Newtons for measurement.

Drawing the first vector of 250 Newtons at 30° angle.

Labeling the first vector after measuring out 5 cm.

Drawing the second vector of 350 Newtons at 40° angle.

Labeling the second vector after measuring out 7 cm.

Establishing that the angle between vectors in the parallelogram is 70°.

Calculating the opposite angle in the parallelogram as 110°.

Drawing light lines from both vector ends to form a parallelogram.

Identifying the resultant force line from start to the opposite end of the parallelogram.

Measuring the resultant vector length as 10.3 cm.

Calculating the resultant force as 515 Newtons.

Determining the angle of the resultant force as 11°.

Completing the parallelogram to find the resultant vector accurately.

Highlighting the practical application of the parallelogram method in vector addition.

Transcripts

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PhysicsForce CalculationParallelogram MethodVector AnalysisScale DrawingNewtonsAnglesMathematical DemonstrationEducational ContentScience TutorialEngineeringProblem Solving