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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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Most popular questions from this chapter

A woman who weighs \(600 \mathrm{N}\) sits on a chair with her feet on the floor and her arms resting on the chair's armrests. The chair weighs $100 \mathrm{N}\(. Each armrest exerts an upward force of \)25 \mathrm{N}$ on her arms. The seat of the chair exerts an upward force of \(500 \mathrm{N}\). (a) What force does the floor exert on her feet? (b) What force does the floor exert on the chair? (c) Consider the woman and the chair to be a single system. Draw an FBD for this system that includes all of the external forces acting on it.
A large wooden crate is pushed along a smooth, frictionless surface by a force of \(100 \mathrm{N}\). The acceleration of the crate is measured to be $2.5 \mathrm{m} / \mathrm{s}^{2} .$ What is the mass of the crate?
By what percentage does the weight of an object change when it is moved from the equator at sea level, where the effective value of \(g\) is $9.784 \mathrm{N} / \mathrm{kg},\( to the North Pole where \)g=9.832$ N/kg?
The mass of the Moon is 0.0123 times that of the Earth. A spaceship is traveling along a line connecting the centers of the Earth and the Moon. At what distance from the Earth does the spaceship find the gravitational pull of the Earth equal in magnitude to that of the Moon? Express your answer as a percentage of the distance between the centers of the two bodies.
(a) What is the magnitude of the gravitational force that the Earth exerts on the Moon? (b) What is the magnitude of the gravitational force that the Moon exerts on the Earth? See the inside front and back covers for necessary information.
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