Section 1 review
Vectors are quantities that specify direction as well as amount. Adding vectors is necessary in order to determine the resultant, or net, force on an object (the force that appears in Newton’s second law). Vectors can be added graphically using the “head-to-tail” method. Vectors can be expressed in terms of components; they also can be expressed in terms of magnitude and angle. To add two vectors mathematically, first add their x-components to obtain the x-component of the vector sum; then repeat this procedure with y (and, in the case of three dimensions, z as well). A free-body diagram can help you identify all of the forces acting on an object of interest. Read the text aloud
vector, vector diagram, magnitude, scalar, resultant vector, component force, component, resolution of forces, sine, cosine, tangent, radian (rad)

F =( F x , F y , F z )
F x =Fcosθ F y =Fsinθ
F= F x 2 + F y 2
θ= tan 1 ( F y F x )

Review problems and questions

Calculate the sum of these two force vectors
  1. Using each force vector’s x- and y-components, calculate the sum F1 + F2 indicated here. Use component arithmetic and the graphical “head-to-tail” method. Express your sum graphically and with numbers. Read the text aloud Show
  1. Calculate the magnitude of the vector F1 + F2 from the previous problem. Read the text aloud Show
Add these two force vectors
  1. Using each force vector’s x- and y-components, calculate the sum F1 + F2 indicated here. Use component arithmetic and the graphical “head to tail” method. Express your sum graphically and with numbers. Read the text aloud Show
  1. Calculate the magnitude of the vector F1 + F2 from the previous problem. Read the text aloud Show
  1. Calculate the magnitude of F1 from the first problem in this review. Next, calculate the magnitude of F2. Finally, calculate the magnitude of the sum F1 + F2. Does the magnitude of the vector sum equal the sum of the two individual vectors’ magnitudes? Explain. Read the text aloud Show

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