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Edexcel A Level Physics:复习笔记2.6 Finding the Resultant Vector

Category: A-level课程, 教材笔记, 福利干货 Date: 2022年9月30日 下午12:27

Adding Vectors

  • Vectors can be combined by?adding?or?subtracting?them to produce the resultant vector
    • The resultant vector is sometimes known as the ‘net’ vector (eg. the net force)

     

  • There are two methods that can be used to add vectors
    • Calculation?– if the vectors are perpendicular
    • Scale drawing?– if the vectors are not perpendicular

     

Combining Vectors Using a Scale Diagram

  • There are two methods that can be used to combine vectors using a scale diagram: the?triangle method?and the?parallelogram method
  • To combine vectors using the triangle method:
    • Step 1:?link the vectors head-to-tail
    • Step 2:?the resultant vector is formed by connecting the tail of the first vector to the head of the second vector

     

  • To combine vectors using the parallelogram method:
    • Step 1:?link the vectors tail-to-tail
    • Step 2:?complete the resulting parallelogram
    • Step 3:?the resultant vector is the diagonal of the parallelogram

     

Worked Example

Draw the vector c = a + b

1.3.2-Vector-addition

Worked Example

Draw the vector c = a – b

1.3.2-Vector-subtraction-11.3.2-Vector-subtraction-2

Combining Vectors by Calculating

  • Combining vectors by calculation is a two-step process
    • Finding the direction of the resultant using trigonometry
    • Finding the magnitude of the resultant using Pythagoras

 

Magntiude-of-Vectors

 

The magnitude of the resultant vector is found by using Pythagoras’ Theorem

 

 

  • The direction of the resultant vector is found from the angle it makes with the horizontal or vertical
    • The question should imply which angle it is referring to (ie. Calculate the angle from the x-axis)

     

  • Calculating the angle of this resultant vector from the horizontal or vertical can be done using?trigonometry
    • Either the sine, cosine or tangent formula can be used depending on which vector magnitudes are calculated

     

Direction-of-Vectors

The direction of vectors is found by using trigonometry

 

Worked Example

A swimmer is crossing a river by swimming due north at 2 m s?1. The current flows east at 5 m s?1.

Determine the resultant velocity of the swimmer's motion.

Step 1: Sketch a diagram, including all known values

 

Step 2: Calculate the magnitude of the resultant using Pythagoras

= 5.4

Step 3: Calculate the angle using trigonometry

θ?= 21.8

Step 4: Write the answer in full giving both magnitude and direction of the velocity and all units

The swimmer's velocity is 5.4 ms-1?at 22o?to the horizontal direction

 

 

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