Chapter 6, Problem 54A

Suzy Skydiver, who has mass m, steps from the basket of a high-flying balloon of mass M and does a sky dive.

a. What is the net force on Suzy at the moment she steps from the basket?

b. What is the net force on her when air resistance builds up to equal half her weight?

c. What is the net force on her when she reaches terminal speed v?

d. What is the net force on her after she opens her parachute and reaches a new terminal speed 0.1 v?

To determine

The net force on S at the moment she steps from the basket.

Answer to Problem 54A

The net force on S at the moment she steps from the basket is $mg$ .

Explanation of Solution

Given:

The mass of the skydiver is $m$ .

Formula used:

The expression for force as follows:

  $F=mg$

Here, $m$ is the mass and $g$ is the acceleration due to gravity.

Calculation:

The net force on S at the instant when she steps from the basket as follows:

  $\begin{array}{l}{F}_{\text{net}}=F_{\text{g}}\\ F_{\text{net}}=mg\end{array}$

Conclusion:

Thus, the force on S at the instant when she steps from the basket is $mg$ .

To determine

The net force on S when air resistance builds up to equal half of weight.

Answer to Problem 54A

  $\frac{mg}{2}$

Explanation of Solution

Given:

The mass of the skydiver is $m$ .

Formula used:

The expression for force as follows:

  $F=mg$

Here, $m$ is the mass and $g$ is the acceleration due to gravity.

Calculation:

The net force on S when air resistance builds up to equal half of weight as follows:

  $\begin{array}{l}{F}_{\text{net}}=F_{\text{g}}-F_{\text{air}}\\ F_{\text{net}}=mg-\frac{mg}{2}\\ F_{\text{net}}=\frac{mg}{2}\end{array}$

Conclusion:

Thus, the net force on S when air resistance builds up to equal half of weight is $\frac{mg}{2}$ .

To determine

The net force on S when she reaches terminal speed $v$ .

Answer to Problem 54A

  $0$

Explanation of Solution

Introduction:

Terminal speed is defined as the speed at which the acceleration is zero for the falling object, because friction balances the weight. Zero acceleration does not refer to zero velocity.

Zero acceleration refers that the velocity will maintain for the object, neither increasing the speed nor slowing down or changing direction.

The expression for force as follows:

  $F=ma$

Here, $m$ is the mass and $a$ is the acceleration.

At terminal speed $v$ the acceleration of the diver to be zero.

Find the net force on S she reaches terminal speed $v$ as follows:

  $\begin{array}{l}{F}_{\text{net}}=ma\\ F_{\text{net}}=m\left(0\right)\\ F_{\text{net}}=0\end{array}$

Conclusion:

Thus, the net force on S when she reaches terminal speed $v$ is $0$ .

To determine

The net force on S after she opens her parachute and a new reaches terminal speed $0.1v$ .

Answer to Problem 54A

  $0$

Explanation of Solution

Introduction:

Terminal speed is defined as the speed at which the acceleration is zero for the falling object, because friction balances the weight. Zero acceleration does not refer to zero velocity.

Zero acceleration refers that the velocity will maintain for the object, neither increasing the speed nor slowing down or changing direction.

The expression for force as follows:

  $F=ma$

Here, $m$ is the mass and $a$ is the acceleration.

At any terminal velocity, the acceleration of the diver to be zero.

Find the net force on S she reaches terminal speed $v$ as follows:

  $\begin{array}{l}{F}_{\text{net}}=ma\\ F_{\text{net}}=m\left(0\right)\\ F_{\text{net}}=0\end{array}$

Conclusion:

Thus, the net force on S after she opens her parachute and a new reaches terminal speed $0.1v$ is $0$ .