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Chapter 5: Problem 4
Why do airplanes bank when turning?
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Riders on the "Great American Revolution" loop-the-loop roller coaster of Example \(5.7\) wear seatbelts as the roller coaster negotiates its \(6.7-\mathrm{m}\)-radius loop at \(9.5 \mathrm{~m} / \mathrm{s}\). At the top of the loop, what are the magnitude and direction of the force exerted on a \(55-\mathrm{kg}\) rider (a) by the roller-coaster seat and (b) by the seatbelt? (c) What would happen if the rider unbuckled at this point?
Disc brakes are becoming increasingly popular on bicycles of all types, in part because the brake dise can tolerate large forces that would damage the wheel rim in a rim-brake system. In a typical disc brake, the force of the brake pads against the brake disc is \(3.5 \mathrm{kN}\). (a) If the coefficient of friction is \(0.51\), what's the frictional force on the disc? (b) Compare with the frictional force associated with rim brakes, where the force of the brakes against the rim is \(870 \mathrm{~N}\) and the frictional coefficient is \(0.39\). (This isn't the whole story, though, as you'll learn when you study torque in Chapter \(10 .\) )
Moving through a liquid, an object of mass \(m\) experiences a resisCH tive drag force proportional to its velocity, \(F_{\text {frag }}=-b v\), where \(b\) is a constant. (a) Find an expression for the object's speed as a function of time, when it starts from rest and falls vertically through the liquid. (b) Show that it reaches a terminal velocity \(m g / b\).
A \(2.1-\mathrm{kg}\) mass is connected to a spring with spring constant \(k=150 \mathrm{~N} / \mathrm{m}\) and unstretched length \(18 \mathrm{~cm}\). The two are mounted on a frictionless air table, with the free end of the spring attached to a frictionless pivot. The mass is set into circular motion at \(1.4 \mathrm{~m} / \mathrm{s}\). Find the radius of its path.
A jet plane flies at constant speed in a vertical circular loop. At what point in the loop does the seat exert the greatest force on the pilot? The least force?
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