Question

The strings of a parachute can bear a maximum tension of 72 kg-weight. By what minimum acceleration can a person of 96 kg descend by means of this parachute?

Answer 1

Person with a parachute descending downward is accelerated downward by acceleration due to gravity. As a person is with a parachute hence it will descend slowly but the net acceleration will only be downward. Balancing the forces keeping net acceleration a variable in downward direction will give the answer.

Complete step by step solution:
Imagine the body falling slowly with a parachute will generate tension in the strings of the parachute. Tension in string acts upward that slows down the fall of the body. There will be only gravitational pull in the body that will pull the body or accelerate the body in falling.
As the body is accelerating downward (because of which fall is possible) with a net acceleration which is obtained by equating tension and gravitational acceleration.
Let that net acceleration of body be $'a'\,m{s^{ - 2}}$
Drawing free body diagram:

Tension and weight both act opposite to each other and the body is accelerating downward so weight is dominant over tension hence, their evaluation will give net force (F) acting downward on the body.
$F = mg - T$
Net force will be product of mass with net acceleration i.e.
$F = ma$
Equating both equations;
$ma = mg - T$
Putting values of mass (m), accelerating due to gravity (g), and tension force (T);
$96 \times a = (96 \times 9.8) - (72 \times 9.8)$
$a = 2.45\,m\,{s^{ - 2}}$

Note: It is important to notice that the strength of tension is mentioned in terms of $kgw/{\text{kilogram}}\,{\text{weight}}$ i.e. we cannot directly keep this value as 76 defines only mass term of force. To use this in terms of force we need to produce it with acceleration due to gravity $(g = 9.8)$ . In order to resolve it we have to neglect several factors like air resistance etc.