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Chapter 6: Problem 6
Does your car's kinetic energy change if you drive at constant speed for 1 hour?
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You"re an engineer for a company that makes bungee-jump cords, and you're asked to develep a formula for the work involved in stretching cords to double their length. Your cords have forcedistance relations described by \(F=-\left(k x+b x^{2}+c x^{3}+d x^{4}\right)\), where \(k, b, c\), and \(d\) are constants. (a) Given a cord with un stretched length \(L_{0}\). what's your formula? (b) Evaluate the work done in doubling the stretch of a 10 -m cord with \(k=420 \mathrm{~N} / \mathrm{m}\), \(b=-86 \mathrm{~N} / \mathrm{m}^{2}, c=12 \mathrm{~N} / \mathrm{m}^{3}\), and \(d=-0.50 \mathrm{~N} / \mathrm{m}^{4} .\)
A truck is moving northward at \(55 \mathrm{mi} / \mathrm{h}\). Later, it's moving eastward at the same speed. Has its kinetic energy changed? Has work been done on the truck? Has a force acted on the truck? Explain.
You and your cycling partner are capable of producing 955 W of power. What's the fastest you can pedal up a \(4.40^{\circ}\) slope if the combined mass of your tandem bicycle and both riders is \(152 \mathrm{~kg}\) and you face a \(14.5-\mathrm{N}\) force from air resistance?
To push a stalled car, you apply a \(470-\mathrm{N}\) force at \(17^{\circ}\) to the car's motion, doing \(860 \mathrm{~J}\) of work in the process. How far do you push the car?
Example 6.9: You're an aircraft designer charged with determining the maximum speed for a new aircraft when it's climbing at a \(15.4^{\circ}\) angle. The total mass of the plane is \(138,000 \mathrm{~kg}\), and its total engine power is \(105 \mathrm{MW}\). While climbing it encounters a force of \(193 \mathrm{kN}\) from air resistance. What do you report for the maximum speed while climbing?
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