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Chapter 4 -- Part 1
In Chapter 3, it was stated that most natural movements of animals are linear and angular.
In this chapter, we will look at some aspects of the movement of animals.
The basic equations used in this chapter are reviewed in Appendix A.
The simplest motion is one in which the body moves along a curved path at a constant speed.
The problem here is to determine the effect on the motion of the object.
The maximum speed at which an automobile can round a curve without skidding is a common problem solved in basic physics texts.
This problem will be solved because it leads to an analysis of running.
The car needs a centripetal force between the road and the tires to stay on the curved path.
When the force is greater than the force on the curve, the car skids.
Banking the road along the curve may increase the safe speed on a curved path.
Skidding can be prevented if the road is properly banked.
The weight of the car is supported by this force.
A runner on a track is subject to the same type of forces as a car.
The runner leans toward the center of the curve.
An analysis of the forces acting on the runner can be used to understand the reason for this position.
This is a 4-min.
angle for a speed of 6.7 m/sec.
No effort is required to lean into the curve.
The body is balanced at the proper angle.
There are four exercises that look at other aspects of the force.
The swinging motion of animals is basically a straight line because the limbs are pivoted at the joints.
When the swing is through 120* (60* in each direction), the period is only 7% longer than predicted.
There is constant interchange between poten tial and kinetic energy as the pendulum swings.
The pendulum is temporarily stationary at the extreme of the swing.
Potential energy is what it is here.
The force of gravity causes the pendulum to start returning to the center.
When the pendulum begins to return toward the center, the acceleration is at a maximum.
The potential energy is converted to kinetic energy when the pendulum is accelerated toward the center.
When the pendulum moves to the center position, it's at its maximum speed.
The simple motion of a pendulum can be used to analyze some aspects of walking.
The motion of one foot in each step is considered to be a half-cycle of a simple motion.
Assume that a person walks at a rate of 120 steps/min and that each step is 90 cm long.
Each foot rests on the ground for a short time and then swings forward 180 cm and comes to rest 90 cm ahead of the other foot.
The full period of the motion is one second.
This is 3.6 times the force of gravity.
The leg is seen as a physical pendulum with a moment of inertia of a thin rod pivoted at one end.
The period is 1.6 seconds for a 90- cm leg.
The number of steps per second is simply the inverse of the half period because each step in the act of walking can be regarded as a half-swing of a simple motion.
It is tiring to walk faster or slower.
The effect of the walker's size on the speed of walking is now known.
The speed of walking is determined by the number of steps taken and the length of the step.
The size of the step is related to the size of the bibliography.
The square root of a person's legs increases the speed of his/her walk.
The walk of a small animal is slower than that of a large animal.
When a person runs at full speed, the situation is different.
In a fast run the swing Torque is mostly produced by the muscles, whereas in a natural walk it is mostly produced by gravity.
We can show that similar built animals can run at the same maximum speed, even if they have different leg sizes.
If one animal has a leg twice as long as another, the area of its muscle is four times larger and the mass of its leg is eight times larger.
A pendulum swinging under the force of gravity is an example of a pendulum swinging under the expression in the equation.
The maximum speed of running is determined by the leg size, which is in line with observation: A fox can run at about the same speed as a horse.
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