Singapore GCE
O Level Physics /5058 2010 Paper 1 Q 3.
Question: At which point in Fig.1 A, B, C or D
is the parachute fully open?
From the
moment that the skydiver steps out from the plane, as his weight is the only
downward force acting on him, his start to accelerate. As his speed increases,
the air resistance increases. The air resistance or drag is proportional to v2
and the perpendicular area of a moving object.
D α v2.A,
where area, A, is constant because he does not use any parachute.
This
results in a decreasing downward resultant force. Hence, by Newton’s Second
Law, the acceleration is also decreasing as his speed increase. This continues
until air resistance reaches the same value of his weight.
At this
point the forces are balanced, hence he continues to fall at a constant speed,
it reaches terminal velocity (A') in Fig. 2.
From A’ to
B, he continues to fall at terminal velocity.
A Point B
At point B,
he pulls his parachute.
The air
resistance or drag is proportional to v2 and the perpendicular area
of a moving object.
D α v2.A
At B, the
gradient of the speed-time graph is negative and constant from the points of
speeds of 40 m/s to 25 m/s.
This
suggests that the deceleration at point B is constant. Hence, there must be a
constant upward resultant force present according to Newton’s 2nd
Law of motion, F=ma.
Immediately
after point B, when the parachutist continues to decent, its speed continues to
decreases.
According to the formula for D α v2.A, air resistance will
decrease when speed decreases. To maintain a constant air
resistance, area, A, must increase to compensate the decrease of air resistance due to
decrease in speed.
The above
means that the area of the parachute is not constant, but increases. This
suggests the parachute is in the process of opening from point B. Hence, at
point B, the parachute cannot be fully opened.
Point C
At point C,
supposed that the parachute is opened fully, the area, A is constant in the
drag force equation D α v2.A.
The air
resistance will decrease as the speed continues to decrease, since area, A, is
constant. From point C, the upward air resistance is still greater than the
weight of the parachutist. As the air
resistance decreases, the upward resultant force decreases. Hence the
deceleration of the parachutist is decreasing, which is evident from the
gradient of the speed-time graph from point C, this happens until it reaches
another terminal velocity (C’), where the air resistance equals to the weight
of the parachutist.
The above suggests that at point C in Fig. 1, the pareachute is fully open, not point B as the answer provided by Cambridge Marker's Report for the paper.
He continues to fall at the terminal velocity
until he reaches the ground.
For a better visualisation, please watch the video below
Skydiving Modelling using Tracker. The duration of parachute opening is modelled and parameterized in the model.
