Forces and motion, Year 11: falling and terminal velocity

9.8

HintIt is the same number as the Earth's gravitational field strength in N/kg.

The whyAny object falling freely near the Earth, with nothing but gravity acting, gains about 9.8 m/s of velocity every second. It is no accident that this matches g = 9.8 N/kg: weight = m g, and dividing that force by the mass gives the acceleration.

14 m/s

HintThe stone starts from rest, so one term in the equation is zero; the last step is a square root.

The whyIn symbols the equation is v² − u² = 2 a s. With u = 0, v² = 2 × 9.8 × 10 = 196, so v = √196. AQA gives this equation on the Physics equation sheet, so pupils need to apply it, not recall it.

12

HintShe ends at rest, and a deceleration goes into the equation as a negative acceleration.

The whyHere v = 0, u = 6 m/s and a = −1.5 m/s². So 0² − 6² = 2 × (−1.5) × s, which gives −36 = −3 s and s = 12. The two minus signs cancel, leaving a positive distance. The equation is on the Physics equation sheet.

Motion with uniform (constant) acceleration

HintThink about which of the four quantities must not change while the object moves.

The whyThe equation assumes the velocity changes at a steady rate over the whole distance s. Free fall with no air resistance and steady braking fit that; a car whose driver keeps changing the pressure on the pedal does not.

Neither — they land together

HintThe acceleration of free fall near the Earth is one value for every object.

The whyAny object falling freely near the Earth's surface accelerates at about 9.8 m/s², whatever its mass. Gravity pulls harder on the heavy ball, but that ball also has more mass to speed up, and the two effects cancel exactly.

Terminal velocity

HintA skydiver reaches it after falling for several seconds.

The whyAt this point the resultant force on the object is zero, so by Newton's first law it stops speeding up and carries on falling at a constant velocity. It applies to anything falling through a fluid — a gas or a liquid.

Her weight is greater than the air resistance on her

HintCompare the size of the downward force with the upward one at the start.

The whyAt the start she is moving slowly, so the air resistance is small while gravity pulls her down with her full weight. The resultant force is downwards, so she accelerates. Anything dropped into a gas or a liquid starts by speeding up, because gravity is the only large force on it.

increases

HintThink of how the wind feels on your face as a bike goes faster.

The whyThe faster an object moves through a fluid, the more fluid it has to push aside each second, so the resistive force grows. The weight stays the same, so the resultant force gets smaller and smaller until it reaches zero.

No — the resultant force on her is zero

HintUse Newton's first law on a faller whose forces balance.

The whyAt terminal velocity the upward air resistance equals her downward weight, so the forces are balanced. With no resultant force her velocity cannot change, so she falls at a constant speed in a straight line. She is still moving fast — just not getting any faster.

In the oil — its resistance is much larger, so it balances the weight at a lower speed

HintAsk how fast each ball must go before the upward force is big enough.

The whyBoth balls have the same weight to balance. Thick oil resists motion far more strongly than air does, so the resistive force reaches the size of the weight while the ball is still moving slowly. In air the ball must be going much faster before the forces balance.