Answer to Question #262836 in Physics for Mex

Question

An 85 kg person is parachuting and experiencing a downward acceleration of 4.5 m/s2. The

mass of the parachute is 4.0 kg.

a) (10%) Draw free body diagram.

b) (10%) What is the upward force on the open parachute from the air?

C)

(10%) What is the downward force on the parachute from the person?

Answer 1

(a) Let's draw a free body diagram for both parts of the question:

(b) Let's consider the parachute and the person as a single object with mass $M$. Let's also take the downward as the positive direction. Then, applying the Newton's Second Law of Motion, we can find the upward force on the open parachute from the air:

$$Mg-F_{up}=Ma,$$ $$F_{up}=Mg-Ma=M(g-a)=(m_1+m_2)(g-a),$$ $$F_{up}=(85\ kg+4\ kg)\times(9.8\ \dfrac{m}{s^2}-4.5\ \dfrac{m}{s^2})=472\ N.$$

(c) Let's consider the parachute only and take the downward as the positive direction. Then, applying the Newton's Second Law of Motion, we can find the downward force on the parachute from the person:

$$F_{down}+m_2g-F_{up}=m_2a,$$ $$F_{down}=F_{up}+m_2(a-g),$$ $$F_{down}=472\ N+4\ kg\times(4.5\ \dfrac{m}{s^2}-9.8\ \dfrac{m}{s^2})=451\ N.$$