The second image has background info used to help solve the practice problem. Page 136 Practice Problem 5.13:An average-sized cat of 4.5kg falls with a terminal velocity of approximately 27m/s. What is the value of the proportionality constant D for the cat? Answer:0.062 kg/m. EXAMPLE 5.13 Fluid frictionIn this example we are going to take a look at a different type of friction, one that is not described by Equa-tions 5.1 and 5.2. When an object moves through a fluid (such as water or air), it exerts a force on the fluidto push it out of the way. By Newton's third law, the fluid pushes back on the object, in a direction oppositeto the object's velocity relative to the fluid, always opposing the object's motion and usually increasing withspeed. In high-speed motion through air, the resisting force is approximately proportional to the square ofthe object's speed u; it's called a drag force, or simply drag. We can represent its magnitude Fp byFD = Du²where D is a proportionality constant that depends on the shape and size of the object and the density of air.When an object falls vertically through air, the drag force opposing the object's motion increases andthe downward acceleration decreases. Eventually, the object reaches a terminal velocity: Its accelerationapproaches zero and the velocity becomes nearly constant. Derive an expression for the terminal-velocitymagnitude UT in terms of D and the weight mg of the object.ones as special cases. We employ this strategy throughout the t-starting with a simpleIn this chapter, we started willmore and more general situations. Note that our most gscenario and applying it to several situations.SOLUTIONSET UP As shown in Figure 5.20, we take the positive y direction tobe downward, and we ignore any force associated with buoyancy in thefluid. The net vertical component of force is mg - Dv².SOLVE Newton's second law givesmg - Du = may.When the object has reached terminal velocity UT, the acceleration ayis zero andmg - Du 0UT =REFLECT For a skydiver in the spread-eagle position, the value of theconstant D is found experimentally to be about 0.25 kg/m. (Does thisnumber have the correct units?) If the skydiver's mass is 80 kg, theterminal-velocity magnitude ismgor UT = VDmg (80 kg) (9.8 m/s²)0.25 kg/mVDThis magnitude is about 125 mi/h. Does that seem reasonable?QUANTITATIVE= 56 m/s.Before terminalvelocity: Objectaccelerating; dragforce less thanweightilliØ回饋街口0ZX%Dv² < mgde Amgugh)Video Tutor SolutionDv² = mgmgAt terminal velocity:Object in equilibrium;drag force equalsweightA FIGURE 5.20 An object falling through air, before and after itreaches its terminal velocity.Practice Problem: An average-sized cat of 4.5 kg falls with a terminalvelocity of approximately 27 m/s. What is the value of the proportion-ality constant D for the cat? Answer: 0.062 kg/m.squarecompar5.4 EIn Secare apthe usmagrLshowto arposicomstreobfarextuofWistC

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Page 136 Practice Problem 5.13: An average-sized cat of 4.5kg falls with a terminal velocity of approximately 27 m/s. What is the value of the proportionality constant D for the cat? Answer: 0.062 kg/m.

Page 136 Practice Problem 5.13: An average-sized cat of 4.5kg falls with a terminal velocity of approximately 27 m/s. What is the value of the proportionality constant D for the cat? Answer: 0.062 kg/m.

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter5: The Laws Of Motion

Section: Chapter Questions

Problem 5P: Two forces, F1=(6.00i4.00j)N and F2=(3.00i+7.00j)N, act on a particle of mass 2.00 kg that is...

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