Forces, acceleration and Newton's laws

• Terminal velocity is the maximum speed of an object, reached when the forces moving the object are balanced by its frictional forces
• Near the surface of the Earth, any object falling freely will have an acceleration of about 9.8 metres per second squared (m/s^2)
• Objects falling through a fluid eventually reach terminal velocity
• At terminal velocity, the object moves at a steady speed in a constant direction because the resultant force acting on it is zero
• Three stages of falling through a fluid:

  • At the start, the object accelerates downwards due to the force of gravity
  • As the object's speed increases, frictional forces such as air resistance or drag increase
  • At terminal velocity, the weight of the object due to gravity is balanced by the frictional forces, and the resultant force is zero
• Velocity-time graphs for falling objects:

  • Between A and B: The object accelerates at first because of the force of gravity. Its speed increases.
  • Between B and C: The object is still accelerating but its acceleration decreases as time goes by. Its speed still increases but by a smaller amount.
  • Between C and D: The object is not accelerating anymore. It has reached its terminal velocity and is falling at a steady speed. The resultant force is zero because the frictional force acting against it is now the same as the weight of the object
• Newton's First Law of motion states that an object remains in the same state of motion unless a resultant force acts on it
• If the resultant force on an object is zero:

  • A stationary object stays stationary
  • A moving object continues to move at the same velocity (at the same speed and in the same direction)
• Inertia is the tendency of an object to continue in its current state (at rest or in uniform motion) unless acted on by a resultant force
• Examples of objects with uniform motion:

  • When a car travels at a constant speed, the driving force is balanced by resistive forces like air resistance and friction in the car's moving parts
  • A runner at their top speed experiences the same air resistance as their thrust
  • An object falling at terminal velocity experiences the same air resistance as its weight
• Examples of objects with non-uniform motion:

  • When a car accelerates, the driving force from the engine is greater than the resistive forces, resulting in a non-zero resultant force
  • At the start of their run, a runner experiences less air resistance than their thrust, so they accelerate
  • An object that begins to fall experiences less air resistance than its weight, so it accelerates
• Forces on a submarine:

  • Horizontal forces do not affect vertical movement and vice versa
  • Balanced horizontal forces result in no horizontal acceleration
  • Balanced vertical forces result in no vertical acceleration
  • The submarine will continue with the same motion, either remaining stationary or moving at a constant speed
• Newton's Second Law of motion can be described by this equation: resultant force = mass × acceleration
• The acceleration of an object is:

  • Proportional to the resultant force on the object
  • Inversely proportional to the mass of the object
• Inertial mass is a measure of how difficult it is to change the velocity of an object
• The ratio of force over acceleration is called inertial mass
• Example:

  • Calculate the force needed to accelerate a 22 kg cheetah at 15 m/s²
  • Calculation: F = 22 × 15 = 330 N
• Estimations:

  • The symbol ~ is used to indicate that a value or answer is an approximate one
  • It is important to be able to estimate speeds, accelerations, and forces involved in road vehicles
• Estimate the force needed to accelerate a family car to its top speed on a single carriageway

  • Using values of ~1,600 kg and ~3 m/s², and F = m × a: 1,600 × 3 = ~4,800 N
• Estimate the force needed to accelerate a lorry to its top speed on a single carriageway

  • Using values of ~36,000 kg and ~0.4 m/s², and F = m × a: Force (F) is ~14,400 N
• Falling objects eventually reach terminal velocity where their resultant force is zero
• Stopping distances depend on speed, mass, road surface, and reaction time
• To investigate the effect of varying the force on the acceleration of an object, it is important to:

  • Make and record measurements of length, mass, and time accurately
  • Measure and observe the effect of force
  • Use appropriate apparatus and methods to measure motion
• Apparatus for the experiment includes:

  • Air track
  • Bench pulley
  • Two light gates
  • Interrupt card attached to an air track glider
  • Hanging mass connected by a string
  • Data logging software
• Method:

  • Position the air track on a bench with a bench pulley at one end and two light gates above the track
  • Cut an interrupt card to a known length and attach it to the air track glider
  • Connect the glider to a hanging mass by a string passing over the bench pulley
  • Ensure the air track is level and the card will pass through both gates before the mass strikes the floor
  • Set the data logging software to calculate acceleration
  • Add 5 × 20 g slotted masses (0.98 N of force) to the end of the string
  • Release the glider, then record the weight and acceleration
• Results should be recorded in a table showing force, run 1 acceleration, run 2 acceleration, run 3 acceleration, and mean acceleration
• Analysis:

  1. Plot a line graph with acceleration on the vertical axis and force on the horizontal axis, drawing a line of best fit

  2. Describe the results regarding the effect of increasing force on acceleration
• Evaluation:

  Acceleration is directly proportional to the force exerted on the object. Consider if the results show this relationship and identify any anomalous points
• Hazards and control measures:

  • Hazard: Electrical appliance

  Consequence: Electrical fault - fire/shock

  Control measures: Check mains cable and plug before use

  • Hazard: Masses and/or glider falling to the floor

  Consequence: Objects falling on feet - bruise/fracture

  Control measures: Use relatively small masses, step back after releasing the glider
• Falling objects eventually reach terminal velocity where their resultant force is zero
• Stopping distances depend on speed, mass, road surface, and reaction time
• To investigate the effect of varying the mass of an object on the acceleration produced by a constant force:
• Add increasing numbers of slotted masses to the glider
• Record the total mass of the glider and hanging masses combined
• Acceleration is inversely proportional to the mass of the object
• A graph of acceleration against 1/mass should produce a straight line passing through the origin
• Newton's Third Law of motion states that whenever two objects interact, they exert equal and opposite forces on each other
• Hazard: Electrical appliance, Consequence: Electrical fault - fire/shock, Control measures: Check mains cable and plug before use
• Hazard: Masses and/or glider falling to floor, Consequence: Objects falling on feet - bruise/fracture, Control measures: Use relatively small masses, Step back after releasing glider
• Examples of force pairs:

  • Pushing a pram:
  • Contact forces between the person and the pram
  • The person pushes the pram forwards, and the pram pushes the person backwards
  • Car tyre on a road:
  • Contact forces between the tyre and the road
  • The tyre pushes the road backwards, and the road pushes the tyre forwards
  • A satellite in Earth orbit:
  • Non-contact gravitational forces between Earth and the satellite
  • The Earth pulls the satellite, and the satellite pulls the Earth