Andrew B. answered • 12/18/21
Bachelor of Science in Physics
At the instant the parachute deploys, a free body diagram would show a 600N force downward from gravity Fg, and a 2000N force upwards from the parachute drag Fd. Since we are given forces and are looking for acceleration, we want an equation that relates these two quantities, which is Newton's Second Law ΣF=ma.
So first we solve the left-hand side of the equation which is to find the net force ΣF:
ΣF=Fg+Fd.
Now we know that these forces are pointing in opposite directions so one should be negative. I will choose to define up to be positive but the choice is arbitrary as long as you are consistent.
ΣF=Fg+Fd=(-600N)+(2000N)=1400N⇒ΣF=1400N
Now to solve the right side of Newton's Second Law we need the mass of the diver. We are given the diver's weight of 600N which is defined as the gravitation force acting on the diver Fg=mg. With this we can easily solve for m:
Fg/g = m ⇒(600N)/(9.81m/s2)= m = 61.162kg (60kg if you use g=10m/s2)
Now we solve for acceleration in Newton's Second Law:
ΣF=ma ⇒ΣF/m=a ⇒(1400N)/(61.162kg)= 22.89m/s2 upwards (remember we defined positive values to mean upwards)
This answer makes sense because the drag force is over 3 times greater than the gravitational force, so the diver ought to be accelerating upwards. But it's important to note that this does not mean they will be moving upwards. Drag forces are typically dependant on velocity, meaning that the slower you move, the weaker the force. The diver has a negative velocity (moving downwards) and the upwards acceleration will cause that velocity to approach 0. As the velocity decreases, Fd will approach Fg and keep the diver in static equilibrium at a terminal velocity until the diver safely reaches the ground. The whole system is dependent on the velocity dependence of Fd which regulates the equilibrium of the forces, preventing the diver from plummetting into the ground or being suspended in mid-air.
