5.1.3 Forces as Vectors

• What is a force?

  A force is a push or pull that can cause an object to accelerate, change direction, or change shape.
• How is force measured?

  Force is measured in Newtons (N).
• What is a vector?

  A vector is a quantity that has both magnitude and direction.
• Why are forces considered vector quantities?

  Forces are vector quantities because they have both magnitude and direction.
• How would you represent a force of 10 N pushing to the right in a diagram?

  You would draw an arrow pointing to the right with a length corresponding to 10 N.
• How are forces represented graphically?

  • Forces are represented as arrows in diagrams.
  • The length of the arrow represents the magnitude of the force.
  • The direction of the arrow shows the direction in which the force is acting.
• What is the resultant force when multiple forces act on an object?

  The resultant force is the vector sum of all the individual forces acting on the object.
• What happens when two forces act in the same direction?

  Their magnitudes add up to create a larger resultant force.
• If two forces of 3 N and 4 N act to the right, what is the resultant force?

  The resultant force is 7 N to the right.
• What occurs when two forces act in opposite directions?

  Their magnitudes subtract to determine the resultant force.
• If a force of 5 N acts to the right and a force of 3 N acts to the left, what is the resultant force?

  The resultant force is 2 N to the right.
• How do you find the resultant force when forces act at an angle to each other?

  You can use vector addition, often using the parallelogram method or breaking the forces into components.
• How would you calculate the resultant force of a 4 N force acting east and a 3 N force acting north?

  You would calculate it using the Pythagorean theorem.
• What is the process of resolving a force?

  • Breaking down a force into its horizontal and vertical components.
  • Useful for analyzing situations where forces act at angles.
• If a force of 10 N acts at an angle of 30° to the horizontal, how do you find its horizontal component?

  The horizontal component is calculated as 10 N × cos(30°).
• What is the formula for the vertical component of a force acting at an angle?

  The vertical component is calculated as F × sin(θ).
• What does it mean for an object to be in equilibrium?

  An object is in equilibrium if the resultant force acting on it is zero.
• If two forces of 5 N act on an object in opposite directions, what can be said about the object?

  The object is in equilibrium because the forces cancel each other out.
• What are the key points to remember about forces?

  • Forces are vectors: They have both magnitude and direction.
  • Resultant force: The overall force acting on an object after all forces are combined.
  • Resolving forces: Breaking down a force into perpendicular components helps in analyzing situations where forces act at angles.
  • Equilibrium: When forces are balanced, and there is no net force on an object.
• What is the resultant force when two forces of 7 N and 5 N act in the same direction?

  The resultant force is 12 N in that direction.
• How do you find the resultant of two forces acting at right angles to each other?

  You use the Pythagorean theorem: Resultant force = √(F₁² + F₂²).
• If a force of 10 N acts at a 45° angle to the horizontal, what are its horizontal and vertical components?

  The horizontal component = 10 N × cos(45°), Vertical component = 10 N × sin(45°).
• What are the practical applications of understanding forces as vectors?

  • Essential in mechanics for predicting object movement.
  • Crucial for solving problems involving structures, vehicles, or any scenario where forces interact.