SEHS Topic 4.3 The Fundamentals of Biomechanics (Part I)

Intro Intro• The mathematical quantities that are used to

describe the motion of objects can be divided into two categories. The quantity is either a vector or a scalar. These two categories can be distinguished from one another by their distinct definitions:

• Scalars

• Vectors

Check for Understanding• Consider the following quantities listed below. Categorize each

quantity as being either a vector or a scalar. Click the button to see the answer.

• Quantity Category

• a. 5 m _________________• b. 30 m/sec, East _________________• c. 5 mi., North _________________• d. 20 degrees Celsius _________________ • e. 256 bytes _________________• f. 4000 Calories _________________

Define the following terms

• Force –

• In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or a flexible object to deform.

• A force has both magnitude and direction, making it a vector quantity. • It is measured in the SI unit of newtons and represented by the symbol F

•

Cont’d• Speed : is a scalar quantity that refers to "how fast an

object is moving." – Speed can be thought of as the rate at which an object covers

distance. A fast-moving object has a high speed and covers a relatively large distance in a short amount of time. Contrast this to a slow-moving object that has a low speed; it covers a relatively small amount of distance in the same amount of time. An object with no movement at all has a zero speed.

– http://www.physicsclassroom.com/mmedia/kinema/trip.cfm

• Velocity- is a vector measurement of the rate and direction of motion or, in other terms, the rate and direction of the change in the position of an object

Speed vs. Velocity cont’d• Imagine a person moving rapidly - one step forward and one step back -

always returning to the original starting position. While this might result in a frenzy of activity, it would result in a zero velocity.

• Why?

• Because the person always returns to the original position, the motion would never result in a change in position. IF a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position.

• Remember: velocity is direction aware.

• It would not be enough to say that an object has a velocity of 55 mi/hr. One must include direction information in order to fully describe the velocity of the object. For instance, you must describe an object's velocity as being 55 mi/hr, east.

Speed vs. Velocity cont’d• The average speed during the course of a motion is

often computed using the following formula:

• In contrast, the average velocity is often computed using this formula

Check for understanding

• While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed?

• Displacement –

Cont’d• To test your understanding of this distinction, consider the motion

depicted in the diagram below. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

• Even though the physics teacher has walked a total distance of 12 meters, her displacement is 0 meters. During the course of her motion, she has "covered 12 meters of ground" (distance = 12 m). Yet when she is finished walking, she is not "out of place" - i.e., there is no displacement for her motion (displacement = 0 m). Displacement, being a vector quantity, must give attention to direction. The 4 meters east cancels the 4 meters west; and the 2 meters south cancels the 2 meters north. Vector quantities such as displacement are direction aware. Scalar quantities such as distance are ignorant of direction. In determining the overall distance traveled by the physics teachers, the various directions of motion can be ignored

Cont’d

The diagram below shows the position of a cross-country skier at various times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D.

Use the diagram to determine the resulting displacement and the distance traveled by the skier during these three minutes.

Check your understanding

• 1. What is the displacement of the cross-country team if they begin at the school, run 10 miles and finish back at the school?

• 2. What is the distance and the displacement of the race car drivers in the Indy 500?

Cont’d

• Remember our physics teacher? What was his average speed if he walked the perimeter in 24 seconds? And what was his velocity?

Definitions/Concepts Cont’d

• Momentum – is a vector describing a "quantity of motion" or in mathematical terms p (momentum) = mass (m) X velocity (v). – As momentum is the product of mass and the velocity, you can increase momentum by

increase either of these elements. Ex… using a heavier bat or racquet or increasing running speed or hand speed.

• Acceleration –

• A person can be moving very fast and still not be accelerating. Acceleration has to do with changing how fast an object is moving. If an object is not changing its velocity, then the object is not accelerating. The data at the right are representative of a northward-moving accelerating object. The velocity is changing over the course of time.

•

• http://www.physicsclassroom.com/mmedia/kinema/acceln.cfm

• Impulse –

Cont’d• Fastball Egg Toss.

PROCEDUREHold a flat bed sheet at each of the four corners to provide a large target for the pitcher. Make a "pocket" in the bottom of the sheet by holding it up slightly. (You want to prevent the egg from rolling out of the sheet.)

• Throw an egg into the sheet as fast and hard as you can. The object is to break the egg by throwing it into the sheet. (You may want to place the egg in a plastic sandwich bag, just in case.)

• An egg cannot be thrown hard enough into a sheet to break the shell because the sheet, which "gives," transfers the momentum of the egg over a long period of time, greatly decreasing the force on the egg shell.

• Compare what happens when momentum is transferred abruptly. Drop the raw egg (in the plastic bag) on a solid surface. Now, time is very short, making the force much greater.

Analyze velocity-time; distance-time; and force-time graphs of sporting actions

Final term/concept for Part I• Center of mass/Center of gravity -

Explain that a change in body position during sporting activities can change the position of the center of

mass• The center of gravity is the theoretical point where all the body

weight is concentrated or the theoretical point about which the body weight is evenly distributed.

• If a body is of uniform density and has a symmetrical shape the center of gravity is in the geometric center.

• If the object is not symmetrical and does not have uniform density, it is more difficult to describe the location of its center of gravity.

Cont’d• In addition to the shifting of the center of gravity caused by body

movements, external loads alter the position of the center of gravity. When an external load is added, the concern is the combined center of gravity of the load and the person. When the person lifts or carries a load, the combined center of balance must be kept over the base to be in balance. The greater the external load, the greater the distance the load is held from the person's body, the farther the combined center of gravity will be from the person's center of gravity.