Force, energy and momentum

• What is the difference between a scalar and a vector?

  Scalars describe only a magnitude, while vectors describe both magnitude and direction
• What are some examples of scalar quantities?

  Distance, speed, mass, temperature
• What are some examples of vector quantities?

  Displacement, velocity, force/weight, acceleration
• When should you use the calculation method to add vectors?

  When the two vectors are perpendicular
• How do you use Pythagoras' theorem to find the resultant of two perpendicular vectors?

  $R =$$\sqrt{F_1^2 + F_2^2}$
• How do you use trigonometry to find the direction of the resultant of two perpendicular vectors?

  $\theta =$$\tan^{-1}\left(\frac{F_1}{F_2}\right)$
• How do you add vectors using a scale drawing?

  • Draw a scale diagram using a ruler and protractor
  • Measure the magnitude of the resultant vector from the scale diagram
  • Measure the angle of the resultant vector to find the direction
• What is the opposite of adding vectors called?

  Resolving vectors
• How do you resolve a vector into its components using trigonometry?

  x = V cos θ, y = V sin θ

  
• How do you remember the formulas for resolving a vector into its components?

  If moving through the angle θ, use cos. If moving away from θ, use sin.

  
• What are the vertical and horizontal components of a velocity of 10 m/s at an angle of 30° from the horizontal?

  Horizontal: $10 \cos 30^\circ =$$8.7 \text{ m/s}$, Vertical: $10 \sin 30^\circ =$$5 \text{ m/s}$

  
• What are the vertical and horizontal components of a 50 N weight acting on a block on a 15° inclined plane?

  Parallel component: $50 \sin 15^\circ =$$12.9 \text{ N}$, Perpendicular component: $50 \cos 15^\circ =$$48.3 \text{ N}$

  
• What is the condition for an object to be in equilibrium?

  The sum of all the forces acting on it must be zero
• How can you show an object is in equilibrium?

  • Add the horizontal and vertical components of the forces acting on it, showing they equal zero
  • Draw a scale diagram of the forces, if it forms a closed triangle then the object is in equilibrium
• What is the definition of the moment of a force about a point?

  The force multiplied by the perpendicular distance from the line of action of the force to the point
• What is the definition of a couple?

  A pair of coplanar forces that are equal in magnitude but act in opposite directions
• How do you find the moment of a couple?

  Multiply one of the forces by the perpendicular distance between the lines of action of the forces
• What is the principle of moments?

  For an object in equilibrium, the sum of anticlockwise moments about a pivot is equal to the sum of clockwise moments
• How can you use the principle of moments to find an unknown force?

  Take moments about a pivot point and set the sum of clockwise and anticlockwise moments equal
• What is the definition of the center of mass of an object?

  The point at which an object's mass acts
• What is the difference between speed and velocity?

  Speed is a scalar quantity describing how quickly an object is travelling, while velocity is a vector quantity describing the rate of change of displacement
• What is the difference between instantaneous velocity and average velocity?

  Instantaneous velocity is the velocity at a specific point in time, while average velocity is the velocity over a specified time frame
• What is the definition of uniform acceleration?

  Acceleration of an object that is constant

  
• What information can you get from different types of motion graphs?

  • Acceleration-time graph: The area under the graph is the change in velocity
  • Velocity-time graph: The gradient is the acceleration, and the area under the graph is the displacement
  • Displacement-time graph: The gradient is the velocity

  
• What are the kinematic equations for an object moving with uniform acceleration?

  v = u + at

  s = (u + v)t/2

  s = ut + at^2/2

  v^2 = u^2 + 2as
• How would you solve a problem involving a stone dropped from a bridge?

  1. Note the given information: s = 50 m, u = 0 m/s, a = -9.81 m/s^2
  2. Use the kinematic equations to find the final velocity v and time t:

  v^2 = u^2 + 2as

  v = sqrt(2 * 9.81 * 50) = 31.3 m/s

  s = ut + 0.5at^2

  t = sqrt(2 * 50 / 9.81) = 3.19 s
• What is the difference between free fall and projectile motion?

  Free fall is where an object experiences an acceleration of g, while projectile motion involves an object experiencing independent horizontal and vertical motion
• How would you solve a problem involving a projectile launched at an angle?

  1. Resolve the initial velocity into horizontal and vertical components
  2. Use the kinematic equations to find the maximum height and time of flight separately for the vertical motion
  3. The horizontal distance travelled is the horizontal component of velocity multiplied by the time of flight
• What are the main forces acting on an object in projectile motion?

  • Gravity (acting downwards)
  • Air resistance/drag (acting opposite to the direction of motion)
  • Lift (acting perpendicular to the direction of motion)

  
• What is terminal speed/velocity?

  The speed/velocity at which the frictional/drag forces acting on an object balance the driving forces, so there is no net acceleration
• How does an object reach terminal velocity?

  • As the object accelerates, the frictional/drag forces increase
  • Eventually the frictional/drag forces balance the driving forces
  • At this point, the net force on the object is zero and it travels at a constant terminal velocity
• What is an example of an object reaching terminal velocity?

  A skydiver falling through the air
• What is the time for the journey to reach the maximum height?

  3.5 s
• What is free fall?

  An object experiences an acceleration of g
• What is friction?

  A force that opposes the motion of an object
• How does friction affect an object's motion?

  Friction converts kinetic energy into other forms like heat and sound
• How does the magnitude of air resistance change as an object's speed increases?

  The magnitude of air resistance increases as the speed increases
• What is lift?

  An upward force acting on objects travelling in a fluid
• What is terminal speed/velocity?

  The speed where the frictional forces and driving forces are equal
• How does air resistance affect the motion of a projectile?

  It decreases the maximum height and the horizontal and vertical distances travelled