Why did the envelope lose the race with the cardboard box? (math worksheet all problems answer)

Air resistance is greater for envelope than cardboard box. See explanation

Step-by-step explanation:

- If an envelope and a cardbox is dropped from any height we need to realize that they are two forces acting on both objects.

- The force of gravity acts downward on both objects. Assuming the mass of both objects m to be constant then the force of gravity Fg is also constant:

Fg = m*g

- The second force that acts on both the objects is air resistance also called viscous drag. It is a function of the surface area the object. The viscous drag force on both object differs because the surface area of the envelope is larger than the surface area of the cardbox box.

- The drag force acts upwards for both object and larger for envelop. The net acceleration for both objects can be determined from newton's law of motion.

F_net = m*a

For envelop Fg - Fd1 = m*a1

Where, Fd is the drag force acting on envelope.

For cardboard box Fg - Fd2 = m*a2

- From the explanation above we determined that with the fact that viscous drag Fd is proportional to Area of the object. Then we have:

Fd1 > Fd2

Then we can conclude:

a1 < a2

Hence, the envelope has drops slower in air than compared to cardbox owing fundamentally to the difference in surface areas causing larger upward drag force (air resistance) on envelope as compared to cardbox.