Free fall under gravity

What free fall means

• An object is in free fall when the only force acting on it is its weight.
• Air resistance is ignored at Level 2 unless a question specifically raises it.
• Every object in free fall has the same acceleration, called the acceleration due to gravity:

$$g = 9.8 \text{ m s}^{-2} \text{ downward}$$

• This value is given in the assessment specification and printed on the resource sheet. Use $9.8$, not $10$.
• Free fall covers more than dropping:
  • an object released from rest,
  • an object thrown upward — it is in free fall from the moment it leaves the hand,
  • an object thrown downward,
  • a projectile's vertical motion.

Why mass makes no difference

• A heavier object has a larger weight, $F = mg$, pulling it down.
• It also has a larger mass, so it is harder to accelerate.
• The two effects cancel exactly:

$$a = \frac{F}{m} = \frac{mg}{m} = g$$

• The mass divides out, so the acceleration is the same for every object.
• In air, a feather falls slowly not because it is light but because air resistance is large compared with its small weight. Drop the same feather in a vacuum and it falls at $9.8$ m s⁻² like everything else.

Free fall is just the equations of motion with $a = g$

• Use the same four equations, with the acceleration fixed at $9.8$ m s⁻².
• Choose a positive direction and stay with it. Most students take down as positive for dropping problems and up as positive for throwing problems.
• Taking down as positive for an object dropped from rest:
  • $$v_f = gt$$
  • $$d = \tfrac{1}{2}gt^2$$
  • $$v_f^2 = 2gd$$

Objects thrown upward

Taking up as positive, so $a = -9.8$ m s⁻²:

• On the way up the velocity is positive and decreasing.
• At the highest point the velocity is zero — but the acceleration is still $-9.8$ m s⁻², because weight still acts.
• On the way down the velocity is negative and growing in size.
• Two useful consequences of the symmetry:
  • The time up equals the time down (for equal heights).
  • The object returns to its launch height at the same speed it left, in the opposite direction.
• To find the maximum height, set $v_f = 0$ and solve for $d$.
• To find the total time of flight back to the launch height, set $d = 0$ and solve for $t$ — or simply double the time to the top.

What air resistance actually changes

• Air resistance is a friction force that opposes motion and grows with speed.
• For a real falling object, the net downward force is $mg - F_{\text{air}}$, so the acceleration is less than $9.8$ m s⁻² and it decreases as the object speeds up.
• Consequences worth stating in an explanation question:
  • a real object lands slower than the free-fall calculation predicts,
  • a real object takes longer to fall than predicted,
  • an object thrown up takes longer coming down than going up, because air resistance opposes the motion in both phases.