0.11 Phy1080: motion -- variable velocity and acceleration  (Page 3/19)

According to this author , there is no universally accepted name for the rate of change of jerk.

The algebraic sign of acceleration

When the velocity of a moving object increases, that is viewed as positive acceleration. When the velocity of the object decreases, that is viewed asnegative acceleration.

Uniform or variable acceleration

Acceleration may be uniform or variable. It is uniform only if equal changes in velocity occur in equal intervals of time.

A vector quantity

Acceleration has both direction and magnitude. Therefore, acceleration is a vector quantity.

The units for acceleration

The above definition for acceleration leads to some interesting units for acceleration. For example, consider a situation in whichthe velocity of an object changes by 5 feet/second in a one-second time interval. Writing this as an algebraic expression gives us

(5 feet/second)/second

Multiplying the numerator and the denominator of the fraction by 1/second gives us

5 feet/(second*second)

This is often written as

5 feet/second^2

which is pronounced five feet per second squared.

The acceleration of gravity

The exercises in the remainder of this module are based on the following two assumptions:

• For practical purposes, the effect of the acceleration of gravity is the same regardless of the height of an object above the surface of the earth,provided that the distance above the surface of the earth is small relative to the radius of the earth.
• In the absence of an atmosphere, all objects fall toward the earth with the same acceleration regardless of their masses.

Let's examine the validity of these two assumptions.

Newton's law of universal gravitation

This law states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. (Separately ithas been shown that large spherically symmetrical masses attract and are attracted as if all their mass were concentrated at their centers.)

Effect of gravity versus altitude

An object at the surface of the earth is approximately 3963 miles from the center of the earth. An object that is six miles above the surface of the earth(typical flying altitude for a passenger plane) is approximately 3969 miles from the center of the earth.

Therefore, (if I didn't make an arithmetic error) the gravitational attraction between the earth and that object changes by less than 0.5 percentwhen the object is transported from the surface of the earth to a position that is six miles above the surface of the earth.

For practical purposes, therefore, we can assume that the acceleration of gravity is constant up to at least 32000 feet above the surface of the earth.

Acceleration is independent of mass

Newton's law, as applied to the gravitational attraction of the earth, expressed in algebraic terms, looks something like the following :

f =E*m/d^2

where

• f is the attractive force between the earth and another object
• E is the mass of the earth
• m is the mass of the other object
• d is the distance between the center of mass of the earth and the center of mass of the other object