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Chapter 4: Problem 38

Refer to Problem \(36 .\) Consider the skydiver and parachute to be a single system. What are the external forces acting on this system?

Short Answer

Expert verified
Answer: The two main external forces acting on the skydiver and parachute system are the gravitational force (weight) pulling the system downward and the air resistance (drag) acting against the motion of the system. The gravitational force causes the system to accelerate towards the Earth, while the air resistance opposes this motion and slows the system down.

Step by step solution

01

Identify the system and external forces

The given problem considers the skydiver and parachute as a single system. Our task is to identify the external forces acting on this system. Several forces act on the system, including the gravitational force (weight) pulling the system downwards and air resistance acting against the motion of the system.
02

Gravitational force (weight)

The gravitational force, also known as the weight of the system, acts on the skydiver and the parachute. This force pulls the system downward towards the Earth's surface. The gravitational force acting on the system is given by \(\textbf{W} = m\textbf{g}\), where \(m\) is the total mass of the skydiver and the parachute, and \(\textbf{g}\) is the acceleration due to gravity (\(9.8\,\text{m/s^2}\)).
03

Air resistance

The other significant external force on the skydiver and parachute system is the air resistance (drag). This force acts in the opposite direction to the system's motion, slowing it down. The air resistance depends on the system's speed, the air density, and the shape and size of the skydiver and parachute. The drag force is given by \(\textbf{F}_{\textbf{D}}=0.5\,C_{\textbf{D}}\,\rho\,A\,v^2\), where \(C_{\textbf{D}}\) is the drag coefficient, \(\rho\) is the air density, \(A\) is the frontal area of the skydiver and the parachute, and \(v\) is their velocity relative to the air.
04

Conclusion

There are two main external forces acting on the skydiver and parachute system: the gravitational force (weight) pulling the system downward and the air resistance (drag) acting against the motion of the system. Understanding these forces is crucial for analyzing the motion of the skydiver and parachute as they fall towards the Earth.

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