The above dependence of air drag upon velocity does not hold if the object is small, slow, or dense.
The drag force is proportional to the speed.
Where is the object's radius, is the fluid's viscosity, and is the object's velocity.
The object's radius is 5.25, the fluid's viscosity is 5.25, and the object's velocity is 5.25.
Good examples of this law are provided by the organisms.
Many of these objects travel at a constant terminal velocity because they are so small.
The terminal velocities forbacteria can be about.
The flagella are powered by little motors embedded in the cell and are used to move at a greater speed.
It can take days to reach the bottom of the lake after being deposited on the surface because the lake can move at a greater terminal velocity.
drag has influenced evolution if we compare animals living on land with those in water.
In order to reduce drag forces, fish, dolphins, and whales are streamlined.
Birds that fly large distances have certain features such as long necks.
One example of streamlining is the shape of sperm, which needs to be efficient in their use of energy.
This shape reduces drag and energy consumption for individual birds, and also allows them a better way to communicate.
The Tower of Pisa is said to have been dropped by Galileo.
The time it took each to reach the ground was measured.
We no longer consider forces that affect the motion of an object, but those that affect the object's shape.
The car will not move if a bulldozer pushes it into a wall.
Some forces are known to cause some damage.
Two important characteristics are observed for small deformations.
Hooke's law is obeyed if the size of the deformation is proportional to the force.
The force is a function of the deformation, not a constant force.
The straight line region in which Hooke's law pertains is much larger for metals and springs.
The bones are brittle and the elastic region is small.
A large amount of stress will cause the material to break.
There is a graph of applied force and deformation.
Hooke's law is obeyed in the straight segment.
The straight region has a slope.
The elastic graph will return to zero if the force is removed.
The object is permanently damaged until it finally breaks.
The shape of the curve depends on how the force is applied.
The slope increases just before the fracture, indicating that a small increase is producing a large increase.
There are a number of factors that affect the proportionality constant.
A guitar string made of nylon stretches when it is tightened and is proportional to the force applied.
When the force is removed, the nylon and steel strings return to their normal lengths, implying that they have a larger.
Most materials will behave in this way if the deformation is less than 1%.
The shaded segments show the different deformations produced by the same force applied to three different guitar strings of the same length.
The string on the left is thin nylon, the one in the middle is thicker nylon, and the one on the right is steel.
Changes in length, tension and compression, sideways shear and changes in volume are three different types of deformations.
Unless otherwise stated, all deformations are assumed to be small.
When a force is applied to a wire or rod parallel to its length, a change in length can be produced.
When a force is applied parallel to the rod's length, it is stretched a length.
The rod is compressed by the same force in the opposite direction.
The magnitude of tension or compression is the same for very small deformations and uniform materials.
As the rod is stretched or compressed, the cross-sectional area changes.
Experiments show that the change in length depends on a few variables.
The force is proportional to the substance from which the object is made.
The change in length is proportional to the original length and the cross-sectional area of the wire.
A long guitar string will stretch more than a short one, and a thick string will stretch less than a thin one.
The table shows the values of several materials, which are said to have a large tensile stiffness because they don't deform as much for a given tension or compression.
The moduli cannot be stretched or compressed in only one direction.
There are two applied forces of magnitude acting in opposite directions because of the assumption that the object does not accelerate.
Ski resorts use suspension cables to carry gondolas.
The maximum tension that the cable can endure is assumed to be.
The Gala Yuzawa ski resort in Japan has gondolas.
The force is the same as the tension.
All quantities are known.
Young's moduli for tension and compression are averaged here.
Young's moduli for tension and compression is different for Bone.
This is a stretch, but only a small one.
The effects of temperature on length might be important.
Tension or compression do not cause bones to break.
They break due to sideways impact or bending, resulting in bone shearing or snapping.
The load the bones can carry is determined by the behavior of bones under tension and compression.
Columns in buildings and trees are classified as weight-bearing structures.
Columns in a building have steel reinforcing rods, while trees and bones are not.
Different parts of the body have different bones that are prone to different stresses.
The bone in the top of the femur is arranged in thin sheets separated by marrow, while in other places the bones can be cylindrical and filled with marrow or just solid.
Overweight people have a tendency to have compressions in their bones.
There is a biological example of Hooke's law.
When a force is applied, the tissue connecting the muscle to the bone needs to be stretched quickly, but it also needs to be restored for a greater strain.
There is relatively little strain, or length change, for some tendons with high collagen content, while others can change length up to 10%.
Since the slope of the line changes in different regions, this stress-strain curve is not linear.
The first part of the stretch called the toe region is called uncrimping because the fibers in the tendon begin to align in the direction of the stress.
Individual fibers begin to break in the failure region as the fibrils are stretched in the linear region.
A model of this relationship can be seen by springs in parallel.
The problems at the end of the chapter give examples of this.
Similarities exist between tissue connecting bone to bone.
Three regions are shown.
The arteries and lungs need to be very stretchable, unlike bones and tendons, which need to be strong as well as elastic.
The arteries have elastic properties.
When the blood is pumped out of the heart, the pressure in the arteries increases.
When the valve is shut, the pressure in the arteries drops and the walls of the arteries relax.
The elastic behavior of the arteries as the blood gushes through with each pump of the heart is what you feel when you feel your pulse.
You wouldn't feel a pulse if the arteries were inflexible.
The heart has special elastic properties.
The lungs expand when we breathe in but relax when we breathe out.
Our skins are very elastic.
A young person can go from 100 kilo to 60 kilo with no visible skin wrinkling.
Reduction in elasticity starts in the early 20s.
Assume the upper leg bone is equivalent to a uniform rod that is 40.0 cm long and 2.00 cm in radius, and that a 70.0 kilogram man supports 62.0 kilogram of his mass on it.
The change in length can be found using the equation.
The quantities are known.
The value of Young's modulus for bone must be used here.
Our experience is that bones are rigid, so this small change in length seems reasonable.
Even the large forces encountered during strenuous physical activity do not cause bones to be compressed or bend.
Although bone is rigid compared with fat or muscle, several of the substances listed in Table 5.3 have larger values of Young's modulus.
They are more rigid.
The equation is similar to Hooke's law in that it has stress and strain.
The general idea is that force is proportional for small changes in length, sideways bending, and volume.
Stress is measured in N/m2 and is defined as the ratio of force to area.
The strain is the ratio of the change in length to length.
The deformation is called and it is not parallel as with tension and compression.
Similar equations can be used to describe shear deformation.
For example, it is easier to bend a long thin pencil than a short thin one, and both are more easily bent than similar steel rods.
The shear modulus is the force applied parallel to the cross-sectional area.
Shearing forces are applied parallel to the area.
In addition to the two shearing forces, there must be supporting forces to keep the object from rotating.
The effects of these supporting forces are not taken into account in this treatment.
The object's weight is not shown since it is usually negligible compared with forces large enough to cause significant deformations.
For most materials, shear moduli are less than Young's moduli.
It is a remarkable exception.
Its shear modulus is larger than that of steel.
The reason bones are so rigid is because of this.
The main support for the head and upper part of the body is provided by the spine column.
Increased shearing forces on the lower vertebrae can be caused by the increased curvature of the spine.
Discs hold compressional forces better than shear forces.
The weight of the upper body exerts some of the weight on the spine.
Increasing the shear component of the stress is one of the reasons pregnant women and people with large abdomens need to move their shoulders back to maintain balance.
Shear forces along the plane increase due to an increased angle.
The risk of back injury is increased by higher shear forces.
The lumbosacral disc is at risk because of its location.
The shear moduli for brick are too variable to be listed.
Modern structures were made possible with steel and steel-reinforced concrete.
Liquids and gases flow in response to shearing forces.
Because of the shear effect of the supported weight, the nail flexes slightly.
The upward force of the wall on the nail is shown to show that there are equal and opposite forces applied across the cross sections of the nail.
The weight of the picture is the force on the nail.
The mass of the picture is just if we can find it.
The equation can be solved.
Table 5.3 has S in it.
The figure shows the value for.
This is a large picture, and it is impressive that the nail only flexes a small amount to the untrained eye.
If inward forces are applied evenly on all the surfaces of the object, it will be easy to compress gases and difficult to compress liquids.
When a wine bottle is corked, the air in it is compressed.
If you want to cork a full bottle, you have to remove some of the cork.
The reason for the different compressibilities is that atoms and Molecules are packed close together in liquids and Solids.
The atoms and molecules of a gas must be closer together in order for it to be compressed.
There are very strong electromagnetic forces in liquids andsolids that oppose compression.
The cube is compressed by an inward force.
The force per unit area and original volume are related to the compressibility of the substance.
The object can be described with an equation.
The ratio of force to area on all surfaces is known as the force applied evenly.
No bulk moduli are given for gases.
One example is the manufacture of industrial grade diamonds by using a very large force per unit area.
The more tightly packed pattern of diamonds is rearranged by the carbon atoms.
In nature, a similar process occurs deep underground, where large forces result from the weight of overlying material.
The weight of water in deep parts of the oceans is a natural source of large compressive forces.
Water exerts an inward force on all the surfaces of a submerged object.
The following example shows how water is compressed at great depths.
The correct physical relationship is Equation.
The quantities in the equation are known.
The force per unit area is about 500 atmospheres, so this is not a significant decrease in volume.
It is difficult to compress liquid and solid objects.
Liquids and Solids are compressed to less than their normal volume when they try to expand, because they are constrained from doing so.
Since most materials expand when their temperature increases, this occurs when a contained material warms up.
The container can be broken if the materials are tightly constrained.
When water freezes, it is a very common example.
Water, unlike most materials, expands when it's cold, and it can break a boulder, break a biological cell, or crack an engine block if it gets in its way.
The tension, shear, and bulk deformations are considered here.
Friction is a contact force between systems.
The Hooke's law is given by the systems together.
The length is the applied force, and is a magnitude of static friction between systems constant that depends on the shape and composition of stationary relative to one another is given by the object and the direction of the force.
The relationship between the applied and the applied is dependent on both the materials and the coefficients of static friction.
The where of Young's modulus is the most important factor in determining the force between systems moving relative to one another.
Stress is measured in N/m2 and is defined as the ratio of force to area.
The motion is the ratio of the change in length to length.
A strain is a unitless quantity for larger objects.
The drag force is given by how fast the air moves, where the object is facing the fluid, and the shear modulus.
The glue on the tape exerts force.
Examine different types of shoes, including sports shoes, which screeches because it rapidly alternates.
The bottom of the board can either slip or stick to it.
Would you expect your height to be different?
Two expressions were used to describe the drag force experienced when a moving object is hit into hard materials.
One used pliers to hold the center of the nail.
If the road bottle is not filled, oil and gasoline will break as cars travel.
A steel cylinder can be further caused by increased frictional forces.
The damage and pain are normal.
A team of eight dogs pull a sled with wood on it to show how to solve a Problem-Solving Runner on wet snow.
The dogs have good strategies.
If an object is to rest on an incline without slipping, the mass is more than 200 lbs.
The force of 185 N on the snow is required.
You can use the result of the problem.
This isn't a large force for such a large system.
Railroads are very energy efficient because of their small Rolling Friction.
The force is parallel to her legs.
Assume little force by her arms.
The terminal velocity of a person falling in air is determined by the weight and area of the person facing the fluid.
Two skydivers jump from an airplane at an altitude of 6000 m, both falling in a headfirst position.
Take their frontal areas into account and calculate their terminal velocities.
All values should be accurate to three significant digits.
To verify that the units are stiff to a solid cylinder of 4.00 cm in diameter, use the Stokes' law.
Find the terminal velocity of a spherical bacterium.
The diameter is falling in the water.
Each new section of drill pipe terminal velocity is when an oil well is drilled.
Take the density of the bacterium to support its own weight and the pipe and drill bit to support it.
The law states that the particles in the steel pipe can be used to measure the viscosity of the liquids in the pipe.
Liquids achieve terminal velocity quickly.
It is possible to measure the time it takes for a particle to fall by comparing it to a solid cylinder.
Find the distance between the vertebra and the oil.
One performer swings upside down shearing force of 600 N while hanging from a trapeze holding another.
Three times her weight, how much and 4.00 cm in diameter is what the disk is equivalent to.
You can assume each is equivalent to a uniform rod 35.0 cm 6.00 N at a distance of 2.00 cm from the hardwood long and 1.80 cm in radius by using a pencil eraser.
Her body mass is 60.0 kilograms.
A wrestler briefly held at an angle of to the horizontal during a wrestling match.
A uniform rod of 38.0 cm in length data can be used to represent the effect of wires hung on poles.
A farmer fills a glass bottle with grape juice consistent with what you have seen when using brim and caps it tightly.
Water can exert itself on a container if it poles in straight parts of the line.
There is a telephone pole near a power line.
A guy wire is attached to the pole at a certain angle.