IB DP Physics: SL复习笔记2.1.8 Terminal Speed

Fluid Resistance & Terminal Speed

Fluid Resistance

  • When an object moves through a fluid (a gas or a liquid) then there are resistive forces for that movement.
    • These forces are known as drag forces
  • Examples of drag forces are friction and air resistance
  • Drags forces:
    • Are always in the opposite direction to the motion of the object
    • Never speed an object up or start them moving
    • Slow down an object or keep them moving at a constant speed
    • Convert kinetic energy into heat and sound
  • Lift is an upwards force on an object moving through a fluid. It is perpendicular to the fluid flow
    • For example, as an aeroplane moves through the air, it pushes down on the air to change its direction
    • This causes an equal and opposite reaction upwards on the wings (lift) due to Newton's third law

Lift-Force

Drag forces are always in the opposite direction to the thrust (direction of motion). Lift is always in the opposite direction to the weight

  • A key component of drag forces is it increases with the speed of the object
  • This is shown in the diagram below:

3.1.2.1-Drag-force-increases-with-speed

Frictional forces on a car increase with speed

Air Resistance & Projectile Motion

  • Air resistance decreases the horizontal component of the velocity of a projectile
    • This means both its range and maximum height is decreased compared to no air resistance

Projectile-Motion-Air-ResistanceA projectile with air resistance travels a smaller distance and has a lower maximum height than one without air resistance

  • The angle and speed of release of a projectile is varied to produce either a longer flight path or cover a larger distance, depending on the situation
    • For sports such as the long jump or javelin, an optimum angle against air resistance is used to produce the greatest distance
    • For gymnastics or a ski jumper, the initial vertical velocity is made as large as possible to reach a greater height and longer flight path

Terminal Velocity

  • For a body in free fall, the only force acting is its weight and its acceleration g is only due to gravity.
  • The drag force increases as the body accelerates
    • This increase in velocity means the drag force also increases
  • Due to Newton’s Second Law, this means the resultant force and therefore acceleration decreases (recall F = ma)
  • When the drag force is equal to the gravitational pull on the body, the body will no longer accelerate and will fall at a constant velocity
    • This velocity is called the terminal velocity
  • Terminal velocity can occur for objects falling through a gas or a liquid

3.1.2.3-Terminal-Velocity-diagram-1

3.1.2.3-Terminal-Velocity-diagram-2

3.1.2.3-Terminal-Velocity-diagram-3

A skydiver in freefall reaching terminal velocity

  • The graph shows how the velocity of the skydiver varies with time
  • Since the acceleration is equal to the gradient of a velocity-time graph, the acceleration decreases and eventually becomes zero when terminal velocity is reached
  • After the skydiver deploys their parachute, they decelerate to a lower terminal velocity to reduce the impact on landing
  • This is demonstrated by the graph below:

terminal-velocity-graph

A graph showing the changes in speed of the skydiver throughout their entire journey in freefall

Worked Example

Skydivers jump out of a plane at intervals of a few seconds.

Skydivers A and B want to join up as they fall.

WE-Terminal-velocity-question-image

If A is heavier than B, who should jump first?

  • Skydiver B should jump first since he will take longer to reach terminal velocity
  • This is because skydiver A has a higher mass, and hence, weight
  • More weight means higher acceleration and hence higher speed, therefore, A will reach terminal velocity faster than B

Exam Tip

A common misconception is that skydivers move upwards when their parachutes are deployed - however, this is not the case, they are in fact decelerating to a lower terminal velocityIf a question considers air resistance to be ‘negligible’ this means in that question, air resistance is taken to be so small it will not make a difference to the motion of the body. You can take this to mean there are no drag forces acting on the body.

 

 

 

 

 

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