Physics
Resistive Force
Resistive force is a force that opposes the motion of an object through a fluid or a gas. It is also known as drag force and is proportional to the velocity of the object. Resistive force can be calculated using the equation F = bv, where b is the drag coefficient and v is the velocity of the object.
Written by Perlego with AI-assistance
Related key terms
1 of 5
4 Key excerpts on "Resistive Force"
- Raymond Serway, John Jewett(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
This direction may or may not be in the direction opposite the object’s velocity according to the observer. For example, if a marble is dropped into a bottle of shampoo, the marble moves downward and the resis- tive force is upward, resisting the falling of the marble. In contrast, imagine the moment at which there is no wind and you are looking at a flag hanging limply on a flagpole. When a breeze begins to blow toward the right, the flag moves toward the right. In this case, the drag force on the flag from the moving air is to the right and the motion of the flag in response is also to the right, the same direction as the drag force. Because the air moves toward the right with respect to the flag, the Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 6.4 Motion in the Presence of Resistive Forces 139 flag moves to the left relative to the air. Therefore, the direction of the drag force is indeed opposite to the direction of the motion of the flag with respect to the air! The magnitude of the Resistive Force can depend on speed in a complex way, and here we consider only two simplified models. In the first model, we assume the Resistive Force is proportional to the velocity of the moving object; this model is valid for objects falling slowly through a liquid and for very small objects, such as dust particles, moving through air. In the second model, we assume a Resistive Force that is proportional to the square of the speed of the moving object; large objects, such as skydivers moving through air in free fall, experience such a force.
eBook - PDF- Patrick Hamill(Author)
- 2022(Publication Date)
- Cambridge University Press(Publisher)
For objects moving at higher speeds (but less than the speed of sound) it is more realistic to assume the Resistive Force is proportional to the speed squared. That is, F = −Dv 2 . The equation of motion can then be written in the form m dv dt = −Dv 2 . The proportionality constant D depends on the size and shape of the body and the density of the fluid through which it is moving. A reasonable formula for calculating D is D = 1 2 C D Aρ, where the “drag coefficient” C D is a unitless parameter of the order unity which depends on the shape of the body. In practical applications the value C D = 0.2 is often used. A is the cross- sectional area of the object and ρ is the air density and depends on both the altitude and the temperature. (You can appreciate that air resistance problems can be very complicated, but here we are only going to concentrate on the method for solving them and assume D is a known constant.) If you apply this law to a body falling through air under the action of the force of gravity, the Resistive Force is upwards and the gravitational force is downwards, so the equation of motion becomes m dv dt = +Dv 2 − mg. In applying this last equation you will have to be very careful with the signs. If the body is rising, then both gravity and the force of air resistance are acting downwards. Worked Example 3.4 A body of mass m is acted upon by the gravitational force (−mg) and the retarding force of air resistance given by Dv 2 . It is dropped from rest at an initial height x 0 . Obtain expressions for its velocity and position as a function of time. Solution In problems such as this one, it is often convenient to express relations in terms of the “terminal velocity” which is the speed when the two forces are equal and opposite and the object is no longer accelerating. In this problem the net force is F = Dv 2 − mg. The terminal velocity is obtained by setting F = 0, so v T = mg/D.
eBook - PDF- Philip Dyke, Roger Whitworth(Authors)
- 2017(Publication Date)
- Red Globe Press(Publisher)
CHAPTER 2 Forces 2.1 Force as a vector We now introduce the concept of force. When forces are studied alone, the study is called statics . When they are studies in conjunction with kinematics, then the area of study is called dynamics . If a body changes its velocity, we conclude that a force acts upon it. Consider the motion of parachutists falling from an airplane: 1 At first, they fall vertically downwards as a result of the force acting on them in that direction (Figure 2.1(a)). Their speed increases as they move downwards. The vertical force involved is principally the weight , which is the force of the Earth's attraction acting on the parachutist. In addition, there are resistance forces . Resistance forces will always oppose motion when they occur. 2 After the parachute opens (Figure 2.1(b)), the parachutist's speed will eventually reach a stage when it stops increasing. In this case, the velocity is no longer changing and all the forces acting on the body must cancel out. In fact, the magnitude of the resistance force is then equal to the magnitude of the weight (see Chapter 5). In the case of a body in a state of equilibrium , that is, at rest, the total force acting on the body must also be zero. Consider the following cases of a body P in equilibrium: Resistance Resistance Weight Weight (b) (a) Figure 2.1 Parachutists 27 Tension Weight (a) Reaction Reaction Weight Weight (c) Thrust Weight (b) (d) (e) Normal reaction Friction Push Normal reaction Friction Weight Weight (f) Figure 2.2 Bodies in equilibrium 1 When the body is suspended by a string to hang freely (Figure 2.2(a)), the weight is supported by an upward force in the string, the tension . 2 When the body is supported on a spring from below (Figure 2.2(b)), the weight is supported by an upward force in the spring, the thrust . 3 When the body is resting on a horizontal surface, the weight is supported by an upward force supplied by the surface, the reaction or normal reaction (Figure 2.2(c)).
eBook - PDF- Stephen Lee(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
Forces and Newton’s laws of motion Nature to him was an open book. He stands before us, strong, certain and alone. Einstein on Newton 2.1 Force diagrams The picture shows a crate of medical supplies being dropped into a remote area by parachute. What forces are acting on the crate of supplies and the parachute? One force which acts on every object near the earth’s surface is its own weight . This is the force of gravity pulling it towards the centre of the earth. The weight of the crate acts on the crate and the weight of the parachute acts on the parachute. The parachute is designed to make use of air resistance . A resistance force is present whenever a solid object moves through a liquid or gas. It acts in the opposite direction to the motion and depends on the speed of the object. The crate also experiences air resistance, but to a lesser extent than the parachute. Other forces are the tensions in the guy lines attaching the crate to the parachute. These pull upwards on the crate and downwards on the parachute. All these forces can be shown most clearly if you draw force diagrams for the crate and the parachute. 2 Figure 2.1: Forces acting on the crate Figure 2.2: Forces acting on the parachute Force diagrams are essential for the understanding of most mechanical situations. A force is a vector: it has a magnitude, or size, and a direction. It also has a line of action . This line often passes through a point of particular interest. Any force diagram should show clearly ● the direction of the force ● the magnitude of the force ● the line of action. In figures 2.1 and 2.2 each force is shown by an arrow along its line of action. The air resistance has been depicted by a lot of separate arrows but this is not very satisfactory. It is much better if the combined effect can be shown by one arrow. When you have learned more about vectors, you will see how the tensions in the guy lines can also be combined into one force if you wish.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
