Question

An 80 kg person is parachuting and experiencing a downward acceleration of $\mathbf{2}\mathbf{.}\mathbf{5}\raisebox{1ex}{$\mathbf{}\mathbf{m}$}\!\left/ \!\raisebox{-1ex}{${\mathbf{s}}^{\mathbf{2}}$}\right.$ . The mass of the parachute is 5.0 kg. (a) What is the upward force on the open parachute from the air? (b) What is the downward force on the parachute from the person?

Short answer

(a)The upward force on the open parachute from the air is 620 N

(b)The downward force on the parachute from the person is 584 N

Step-by-step solution

Given information

It is given that,

$$\begin{gathered} massofperson\left(M\right)=80kg \\ massofparachute\left(M\right)=5kg \\ a=2.5m/s^2 \end{gathered}$$

Determining the concept

The problem is based on Newton’s second law of motion which states that the rate of change of momentum of a body is equal in both magnitude and direction of the force acting on it. Thus, using the free body diagramfor parachute and system of parachute and person, the force can be calculated.

Formula:

According to the Newton’s second law of motion,

$F_{net}=\underset{}{\sum Ma}$

where, is the net force, Mis mass and a is an acceleration.

(a) Determining the upward force on the open parachute from the air

From first FBD:

W - F = ( M +m ) x a

(M + m )g - F = (M +m) x a

(85 x 9.8) - F = 85 x 2.5

By solving for F

F = 620 N

Hence, The upward force on the open parachute from the air is 620 N

(b) Determining the downward force on the parachute from the person

From second FBD:

$$\begin{gathered} W-F_p=Ma \\ (80x9.8)-F_p=80x2.5 \\ Hence, \\ {F}_p=584N. \\ Hence,Thedownwardforceontheparachutefromthepersonis584N \end{gathered}$$