Edexcel A Level Physics:复习笔记2.6 Finding the Resultant Vector
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
Worked Example
Draw the vector c = a – b
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
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
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
转载自savemyexams
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