Conceptual Questions
12.1 Conditions for Static Equilibrium
Under what conditions can a rotating body be in equilibrium? Give an example.
Mechanics sometimes put a length of pipe over the handle of a wrench when trying to remove a very tight bolt. How does this help?
For the next four problems, evaluate the statement as either true or false and explain your answer.
If there is only one external force (or torque) acting on an object, it cannot be in equilibrium.
If an object is in equilibrium there must be an even number of forces acting on it.
A body moving in a circle with a constant speed is in rotational equilibrium.
12.2 Examples of Static Equilibrium
Is it possible to rest a ladder against a rough wall when the floor is frictionless?
Show how a spring scale and a simple fulcrum can be used to weigh an object whose weight is larger than the maximum reading on the scale.
A painter climbs a ladder. Is the ladder more likely to slip when the painter is near the bottom or near the top?
12.3 Stress, Strain, and Elastic Modulus
Note: Unless stated otherwise, the weights of the wires, rods, and other elements are assumed to be negligible. Elastic moduli of selected materials are given in Table 12.1.
Why can a squirrel jump from a tree branch to the ground and run away undamaged, while a human could break a bone in such a fall?
When a glass bottle full of vinegar warms up, both the vinegar and the glass expand, but the vinegar expands significantly more with temperature than does the glass. The bottle will break if it is filled up to its very tight cap. Explain why and how a pocket of air above the vinegar prevents the bottle from breaking.
A thin wire strung between two nails in the wall is used to support a large picture. Is the wire likely to snap if it is strung tightly or if it is strung so that it sags considerably?
Review the relationship between stress and strain. Can you find any similarities between the two quantities?
What type of stress are you applying when you press on the ends of a wooden rod? When you pull on its ends?
Can compressive stress be applied to a rubber band?
If a hypothetical material has a negative bulk modulus, what happens when you squeeze a piece of it?
Discuss how you might measure the bulk modulus of a liquid.
12.4 Elasticity and Plasticity
Note: Unless stated otherwise, the weights of the wires, rods, and other elements are assumed to be negligible. Elastic moduli of selected materials are given in Table 12.1.
What is meant when a fishing line is designated as “a 10-lb test?”