Explain Hooke's law using graphical representation.
Determine the change in mass, length and radius.
The four basic forces discussed in the previous chapter are not included in the categorization of forces.
The motion, position, and shape of an object are affected by a net force.
There are some interesting and common forces that will provide further applications of the laws of motion.
The forces of air or liquid drag are what we have in mind.
While a common force, the behavior of friction is not completely understood.
We have to rely heavily on observations.
We can still understand the circumstances in which it behaves and deal with its more elementary general characteristics.
Friction is a force that affects relative motion.
One of the simpler characteristics of friction is that it is parallel to the contact surface between the surfaces and always in a different direction than the motion of the systems relative to each other.
A hockey puck sliding on ice is an example.
If two surfaces are moving relative to one another, then they are in contact with each other.
You can push harder and harder on the crate if you want to slide it across the concrete floor.
It increases to be equal to and in the opposite direction of what you do.
The crate starts to move if you push hard enough.
It is easier to keep it in motion than it is to start it.
If you put a box on top of the crate, you need to push harder to get it started and keep it moving.
Figure 5.2 is a representation of how the two objects interact.
These surfaces are shown to be rough.
When you push to get an object moving, you must raise the object until it can skip along with just the tips of the surface hitting, break off the points, or do both.
A force can be resisted with no apparent motion.
The harder the surfaces are pushed together, the more force is needed to move them.
The bonds between the surface molecule of the two objects explain the dependence on the nature of the substances.
Adhesion is a complicated aspect of surface physics.
Less force is needed to keep the object moving because there are fewer points of contact.
Friction is almost independent of speed at small speeds.
Frictional forces always oppose motion between surfaces.
The expanded view shows the roughness of the surfaces in contact.
The object must rise in order for it to move.
A force is needed to set the object in motion.
A force to maintain motion is required for some of the peaks to be broken off.
There are attractive forces between the two objects that make up the surface so that it is not friction-free.
For example, rubber-soled shoes slip less than those with leather soles because of the substances the surfaces are made of.
The magnitude of the force is divided into two forms, one for static and one for motion.
The symbol implies that static friction can have a minimum and maximum value.
A responsive force that increases to be equal and opposite to whatever force is used, is called static friction.
The object will move when the force exceeds.
A system that behaves simply is described as a system.
The coefficients of kinetic friction are less than their static counterparts.
The values in Table 5.1 are stated in one or two digits, which is an indication of the approximate description of the above two equations.
The normal force and the dependence of friction on materials are included in the earlier equations.
The direction of motion is parallel to the surface between objects, and the same as the normal force.
If you try to push a crate with a force parallel to the floor, the normal force would be equal to the weight of the crate.
You would have to exert a force parallel to the floor greater than you would to move the crate.
When there is motion, the force of only 290 N is enough to keep it moving at a constant speed.
The coefficients are less than they would be without lubrication.
It is a unit less quantity with a magnitude between 0 and 1.0.
The two surfaces that are in contact have an effect on the coefficient of the friction.
If you want to slide a small plastic object on a kitchen table, you need to give it a gentle tap.
A light shower of rain is what you'll get if you spray water on the table.
Give the same tap if you add a few drops of vegetable or olive oil to the water.
After a light rain shower, this latter situation is important for drivers to note.
The slipperiness of walking on ice has been experienced by many people.
Many parts of the body have smaller coefficients of friction than ice.
A joint is formed by the ends of two bones.
The lower leg bone and thighbone form the knee joint.
The hip has a ball at the end of the femur and a part of the pelvis.
Cartilage covers the ends of the bones in the joint, making it a smooth, almost glassy surface.
The fluid produced by the joints reduces wear.
An artificial joint can be used to replace a damaged or arthritic joint.
These replacements can be made of metal or plastic with small coefficients of friction.
Artificial knee replacement has been done for more than 20 years.
The figure shows the post-op Xrays of the knee replacement.
Other natural lubricants include saliva produced in our mouths to aid in the swallowing process, and the slippery mucus found between organs in the body, allowing them to move freely past each other during heartbeats, during breathing, and when a person moves.
Hospitals and doctor's clinics have artificial lubricants.
The gel that couples the transducer to the skin lubricates the surface between the transducer and the skin, which reduces the coefficient of friction between the two surfaces.
The transducer can move over the skin.
A skier is sliding down a snowy slope.
If the friction is known to be 45.0 N, you can find the coefficients for the skier.
If we can find the normal force of the skier on a slope, we can find the magnitude of kinetic friction.
The skier's weight should be equal to the normal force on the slope since there is no motion on the surface.
The motion of the skier is parallel to the slope and so it is most convenient to project all forces onto a coordinate system where one axis is parallel to the slope.
There is acceleration down the slope because it is less than in magnitude.
The result is a little smaller than the one listed in Table 5.1, but it is still reasonable since the coefficients of friction can vary greatly.
All objects will slide down a slope.
There is proof left for the Problems and Exercises.
If the net force on the object is zero, the object will slide down the inclined plane.
This fact can be used to measure the coefficient of friction between objects.
The acceleration is zero when the forces act in opposite directions.
Put a coin on a book and tilt it so that the coin slides down the book.
To get the coin to move, you might need to lightly tap the book.
The coin won't slide until the angle is greater than the coefficient of static friction.
Discuss how this may affect the value.
When an object rests on a horizontal surface, there is a force that is equal in magnitude to the object's weight.
It is always proportional to the force.
The small aspects of friction have been dealt with so far.
Over the past several decades, great strides have been made in the atomic-scale explanation of friction.
The atomic nature of friction seems to have several fundamental characteristics.
These characteristics hold the potential for the development of nearly friction-free environments that could save hundreds of billions of dollars in energy which is currently being converted to heat.
Figure 5.5 shows a characteristic of friction that is explained by small-scale research.
It has been noted that the area in contact is not proportional to the normal force.
When two rough surfaces are in contact, the actual contact area is a tiny fraction of the total area.
The contact area increases when a greater normal force is applied.
The total area of two rough surfaces is larger than the actual contact area.
As a result of a greater applied force, the area of actual contact increases.
The atomic-scale view promises to explain more than the simpler features.
The mechanism for generating heat is being determined.
lattices are formed when atoms are linked.
Sound waves are created when surface atoms adhere and cause atomic lattices to vibrate.
The sound waves diminish with distance.
There can be chemical reactions between atoms and molecule on the surface.
The force needed to drag the tip can be measured and found to be related to shear stress, which will be discussed later in this chapter.