Resolving Vectors

• What can two vectors be represented by?

  A single resultant vector
• What is resolving a vector?

  It is the opposite of adding vectors
• What can a single resultant vector be resolved into?

  Two vectors with the same effect
• What are the parts of a resolved vector called?

  Components

  
• How can a force vector of magnitude F and angle θ be represented?

  As a resultant force at angle θ

  
• How can the resultant force F be split?

  Into horizontal and vertical components
• What is the formula for the horizontal component of force F?

  F = F cos θ
• What is the formula for the vertical component of force F?

  F = F sin θ
• What is an inclined plane?

  A flat surface tilted at an angle
• How should forces on an inclined plane be considered?

  As parallel or perpendicular to the slope
• What direction does the weight of an object act?

  Vertically downwards
• What is the normal force R?

  It acts vertically up from the object
• How can the weight W be split on an inclined plane?

  Into W cos(θ) and W sin(θ)
• What does the force W sin(θ) cause?

  It causes the object to move down the slope
• What is the normal force R when there is no movement perpendicular to the slope?

  R = W cos(θ)
• What can the weight vector of an object on an inclined plane be split into?

  Components parallel and perpendicular to the slope

  
• What are the steps to resolve the lift force of a helicopter?

  1. Draw a vector triangle of the forces
  2. Calculate vertical component: Vertical = 250 × cos(15)
  3. Calculate horizontal component: Horizontal = 250 × sin(15)

  
• What is the vertical component of the lift force if the lift is 250 kN at 15º?

  242 kN

  
• What is the horizontal component of the lift force if the lift is 250 kN at 15º?

  64.7 kN

  
• What indicates that forces are in equilibrium?

  • Object is at rest
  • Object is moving at constant velocity
  • Represented by closed vector triangles
• What are the common forces on objects in equilibrium?

  Weight, normal reaction force, tension, friction
• How are coplanar forces represented in equilibrium?

  • By vector triangles
  • Form a closed path when joined
• What does a weight hanging in equilibrium from a cable indicate?

  It shows the tensions in the cables
• What should you have handy for drawing diagrams in exam questions?

  A ruler