Question

If I toss an apple in the air at what point will the net force on the apple be balanced during its trajectory?
What does this mean for the velocity and acceleration of the apple?

Answer 1

Short answer: In the idealized case with no air resistance, there is no point where the net force is balanced (zero) — gravity acts the whole time, so the net force is always mg downward. In the real world with air resistance the net force is zero only when the drag equals the weight (that is, when the apple happens to be at its terminal speed).

What that means for velocity and acceleration
- Ideal case (no air resistance): acceleration is constant downward, a = −g (≈ −9.8 m/s²). The apple’s upward velocity decreases at rate g, becomes zero instantaneously at the apex, then increases downward. The velocity can be zero at the top, but the net force and acceleration are not zero.
- With air resistance: if speed reaches the terminal speed v_t so drag = mg, net force = 0, acceleration = 0 and the apple moves at constant velocity v_t. Otherwise acceleration = (sum of forces)/m and need not equal −g; its magnitude and sign change depending on the speed and direction relative to the air.