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Chapter 12: Problem 5
Is a ladder more likely to slip when you stand near the top or the bottom? Explain.
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A portion of a roller-coaster track is described by the equation \(h=0.65 x-1.3 \times 10^{-2} x^{2}\), where \(h\) and \(x\) are the height and horizontal position in meters. (a) Find a point where the rollercoaster car could be in static equilibrium on this track. (b) Is this equilibrium stable or unstable?
The potential energy associated with a particle at position \(x\) is given by \(U=2 x^{3}-2 x^{2}-7 x+10\), with \(x\) in meters and \(U\) in joules. Find the positions of any stable and unstable equilibria.
Give an example of an object on which the net force is zero, but that isn't in static equilibrium.
If you take the pivot point at the application point of one force in a static- equilibrium problem, that force doesn't enter the torque equation. Does that make the force irrelevant to the problem? Explain.
You're investigating ladder safety for the Consumer Product Safety Commission. Your test case is a uniform ladder of mass \(m\) leaning against a frictionless vertical wall with which it makes an angle \(\theta\). The coefficient of static friction at the floor is \(\mu\). Your job is to find an expression for the maximum mass of a person who can climb to the top of the ladder without its slipping. With that result, you're to show that anyone can climb to the top if \(\mu \geq \tan \theta\) but that no one can if \(\mu<\frac{1}{2} \tan \theta\).
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