Question

A box with its contents has a total mass of 36 kg. It is dropped from a very high building. (a) After reaching terminal speed, what is the magnitude of the air resistance force acting upward on the falling box? (b) The box survived the fall and is returned to the top of the building. More objects are put into the box, and the box with its contents now has a total mass of 71 kg. The box is dropped, and it reaches a higher terminal speed than before. After reaching terminal speed, what is the magnitude of the air resistance force acting upward on the falling box? (The fact that the heavier object reaches a higher terminal speed shows that the air resistance force increases with increasing speed.)

Short answer

1. The magnitude of the air resistance of the box is 352.8 N.
2. The magnitude of the magnitude of the air resistance force acting upward on the falling box of mass 71 kg is 696 N .

Step-by-step solution

Identification of given data

The given data can be listed below,

• The mass of the box is, m=36 kg .
• The new mass of the box is, ${\mathrm{m}}_{\mathrm{N}}=71\mathrm{kg}$.

Concept/Significance of air resistance

Any movement in the air encounters air resistance. The collision of a moving item with air molecules causes this effect.

(a) Determination of the magnitude of the air resistance force acting upward on the falling box

When box is falling at terminal velocity, acceleration on the falling box is zero. net force is given by,

${\mathrm{F}}_{\mathrm{net}}=0$

The air resistance force is equal to the gravitational force which is given by,

role="math" localid="1657800089151" $F_r=F_g$

So, the air resistance of the box is given by,

$F_r=mg$

Here, m is the total mass of the box and g is the acceleration due to gravity.

Substitute all the values in the above,

$$\begin{gathered} {\mathrm{F}}_{\mathrm{r}}=\left(36\mathrm{kg}\right)\left(9.8\mathrm{m}/{\mathrm{s}}^2\right)\left(\frac{1\mathrm{N}}{1\mathrm{kg}.\mathrm{m}/{\mathrm{s}}^2}\right) \\ =352.8\mathrm{N} \end{gathered}$$

Thus, the magnitude of the air resistance of the box is =352.8 N.

(b) Determination of the magnitude of the air resistance force acting upward on the falling box

The magnitude of the air resistance force is given by,

$F_{net}=0$

Here, m is the new mass of the box and gis the acceleration due to gravity.

$F_r=F_g$

Substitute all the values in the above,

$F_r=mg$

$$\begin{gathered} {\mathrm{F}}_{\mathrm{r}}=\left(71\mathrm{kg}\right)\left(9.8\mathrm{m}/{\mathrm{s}}^2\right)\left(\frac{1\mathrm{N}}{1\mathrm{kg}.\mathrm{m}/{\mathrm{s}}^2}\right) \\ =696\mathrm{N} \end{gathered}$$

Thus, the magnitude of the magnitude of the air resistance force acting upward on the falling box of mass 71 kg is 696 N .