Question

a parachutist weighs 1000N. when she opens her parachute, it pulls upwards on her with a force of 2000N. (a) draw a diagram to show forces acting on the parachutist. (b) calculate the resultant forces acting on the parachutist. (c) what effect will this force have on her ?​

Answer 1

(a) See attached figure

There are only two forces acting on the parachutist:

- Its weight, downward, of magnitude 1000 N, indicated with (mg) in the diagram (where m = mass and g = acceleration of gravity)

- The air resistance on the parachute, upward, of magnitude 2000 N, indicated with R in the diagram

The magnitude of the air resistance is twice that of the weight, therefore in the diagram is shown with an arrow approximately twice as long as the arrow representing the weight.

(b) +1000 N

Taking upward as positive direction, the two forces can be written as:

R = +2000 N

mg = -1000 N

Since the two forces are along the same line, we can find their resultant by simply calculating their algebraic sum:

`F=R+mg=+2000+(-1000)=+1000 N`

And the positive sign indicates that the direction is upward.

(c) The parachutist will slow down (accelerates upward)

Since there is a net force acting on the parachutist, there is also an acceleration, which can be calculated using Newton's second law:

`F=ma \rightarrow a=(F)/(m)`

where

F = +1000 N is the net force

m is the mass of th parachutist

The mass can be found from the weight:

`m=(mg)/(g)=(1000)/(9.8)=102 kg`

Therefore, the acceleration is

`a=(+1000)/(102)=+9.8 m/s^2`

And the direction of the acceleration is upward, while the direction of motion of the parachutist is downward: therefore, the parachutist will slow down.