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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.

Short Answer

Expert verified
A ladder is more likely to slip when a person stands near the top as opposed to the bottom.

Step by step solution

01

Understanding the Ladder's Stability

It's important to understand that the stability of the ladder is largely determined by the friction between the ladder's base and the ground. When this frictional force is exceeded by the force exerted by a person climbing the ladder, the ladder will slip.
02

Analyzing Forces and Torque When Standing at the Top

When standing near the top of the ladder, your weight acts downwards from a position that is far from the ground. If we consider the point where the ladder contacts the ground as a pivot, the torque caused by your weight is significant (since torque equals force times distance from the pivot). This large torque tends to rotate the ladder, which in turn decreases the normal force between the ladder's base and the ground thereby decreasing the friction. Hence, there is a higher likelihood for the ladder to slip.
03

Analyzing Forces and Torque When Standing at the Bottom

Contrarily, when standing near the bottom of the ladder, the weight acts at a position much closer to the ground. This results in a smaller torque on the ladder. Therefore, the normal force between the ladder's base and the ground remains relatively high, maintaining high friction. This decreases the likelihood of the ladder slipping.

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Most popular questions from this chapter

A 4.00-m, 6.47-kg ladder rests against a wall, inclined at \(70.0^{\circ}\) to the horizontal. The wall is frictionless, while the coefficient of friction between the bottom of the ladder and the ground is \(0.265\). How far up the ladder can a person with mass \(68.8 \mathrm{~kg}\) climb before the ladder starts to slip?

A \(2.0-\mathrm{m}\)-long rod has density \(\lambda\) in kilograms per meter of length described by \(\lambda=a+b x\), where \(a=1.0 \mathrm{~kg} / \mathrm{m}, b=2.0 \mathrm{~kg} / \mathrm{m}^{2}\), and \(x\) is the distance from the left end of the rod. The rod rests horizontally with each end supported by a scale. What do the two scales read?

If you secure the boom at a fixed angle and lower the sampling apparatus at constant speed, the boom rope tension will a. increase. b. decrease. c. remain the same. d. increase only if the sampling apparatus is more massive than the boom.

Why does an acrobat in a circus carry a long pole in his hands while walking on a tightrope?

When the boom rope is horizontal, it can't exert any vertical force. Therefore, a. it's impossible to hold the boom with the boom rope horizontal. b. the boom rope tension becomes infinite. c. the pivot supplies the necessary vertical force. d. the boom rope exerts no torque.
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