1. Velocity, Acceleration, Force, and PressureIt is quite common in
everyday conversation to hear the terms force and pressure used
interchangeably, just as velocity and speed are often considered
synonymous. In the language of science, however, intermixing these terms
can lead to great confusion. Let us look briefly at how they differ and
their connection to a related concept, acceleration.Velocity, Speed,
and AccelerationAny object that moves has a particular speed, defined as
the distance traveled per unit of time. Speed is related to, but not
the same as, velocity. Velocity incorporates direction as well as speed.
Think, for example, of two cars traveling at 20 meters per second [44
mph) but moving in opposite directions. Though they have the same speed,
their velocities are not equal because of their different directions.
This distinction is crucial for understanding our next quantity,
acceleration, the change in velocity(not speed) with respect to
time.Because velocity includes both speed and direction, a change in
either speed or direction is an acceleration. Consider a car that at one
moment in time travels at 20 m/sec; one second later, the same car has a
speed of 19 m/sec; one second later, the speed is 18 m/sec, and so on.
As each second goes by, the car’s speed decreases 1 m/sec (note that
acceleration can be either positive or—as in this example—negative). An
acceleration can also occur as a change in direction with respect to
time, even for an object whose speed does not change. A car traveling at
a constant speed but gradually turning undergoes an acceleration, just
like a car whose speed is changing.In meteorology there is one
particular acceleration of utmost importance—gravity (g). This
acceleration, 9.8 m/sec2 (32.1 ft/sec2), is nearly constant across the
globe. It describes the acceleration an object would experience if
gravity were the only force affecting its movement. There is a slight
decrease in g from equator to pole, and also a very small difference in g
from the surface to the upper atmosphere. For most applications,
however, these variations in g are so slight they can be ignored.Force
and PressureOne of the most important tenets of physical science is
Newton’s Second Law, which relates the concept of force (denoted F) to
mass (m) and acceleration (a). Specifically, Newton’s Second Law tells
us that the acceleration of an object is proportional to the force
acting on it and inversely proportional to its mass. Symbolically, this
is expressed as...Imagine that a fully loaded 18-wheeler truck is
stopped at a traffic light next to a bicycle. Suppose that when the
light turns green, both begin to accelerate at the same rate and
therefore remain next to each other. For them to accelerate at the same
rate, it is easy to see that the much more massive truck requires a
larger force (and more powerful “engine”). Likewise, if two bodies with
equal mass are subjected to different forces, the one subjected to the
greater force will undergo a greater acceleration.Keep in mind that F in
the equation above is the net force acting on the object. If various
forces are acting simultaneously, they must all be considered together
to determine the acceleration; we must account for both the magnitude
and direction of each. As we will see with regard to falling raindrops
(Chapter 7), forces acting in opposite directions reduce the net force
and resulting acceleration, sometimes to zero.Let’s apply Newton’s
Second Law to our atmosphere. The mass of the atmosphere is S.14 × 1018
kg. (To get an idea of what 5.14 × 1018 kg weighs, picture a million
boxcars, each containing a billion elephants) Multiplying the mass of
the atmosphere by the acceleration of gravity, we determine that the
force exerted on the atmosphere is about 5.0 × 1019 newtons (a newton
[N] is the unit of force it takes to accelerate 1 kg one meter per
second every second).Force divided by the area on which it is exerted
equals pressure. So dividing this force of 5.0 × 1019 newtons by the
surface area of Earth gives us the average force per unit area, or
average surface pressure of about 10.132 newtons per square
centimeter.This is equivalent to 1013.2 mb, or about 14.7 pounds per
square inch.Having made the distinction between force and pressure, we
now should address the question of how this distinction applies to the
atmosphere. The answer is that despite the nearly constant total force
of the atmosphere, its gases are not uniformly distributed across the
planet. Consider a particular area at Earth’s surface with an imaginary
column extending upward to the top of the atmosphere, as shown in the
top right of Figure 4-1-1, Greater surface pressures exist at the bases
of atmospheric columns that contain a greater number of molecules, and
lower surface pressures are found where less air occupies the column.
Just how these differences in pressure arise is considered later in this
chapter; for the time being, the important point is that surface
pressure reflects the mass of atmosphere within the column, as shown in
Figure 4-1-1.FIGURE 4-1-1 Gravity, Mass, and Pressure. The downward
force of the atmosphere is equal to the mass of the entire atmosphere
times the acceleration of gravity. Because the amount of mass and the
acceleration of gravity are constant through time, the total force of
the entire atmosphere does not change. Pressure is defined as the amount
of force exerted per unit of area. Thus, the shaded area in the figure
experiences a certain amount of pressure Pressure varies because the
mass of overlying air varies from place to place and time to
time....What is the difference between force and pressure? Get solution
2. Velocity, Acceleration, Force, and PressureIt is quite common in everyday conversation to hear the terms force and pressure used interchangeably, just as velocity and speed are often considered synonymous. In the language of science, however, intermixing these terms can lead to great confusion. Let us look briefly at how they differ and their connection to a related concept, acceleration.Velocity, Speed, and AccelerationAny object that moves has a particular speed, defined as the distance traveled per unit of time. Speed is related to, but not the same as, velocity. Velocity incorporates direction as well as speed. Think, for example, of two cars traveling at 20 meters per second [44 mph) but moving in opposite directions. Though they have the same speed, their velocities are not equal because of their different directions. This distinction is crucial for understanding our next quantity, acceleration, the change in velocity(not speed) with respect to time.Because velocity includes both speed and direction, a change in either speed or direction is an acceleration. Consider a car that at one moment in time travels at 20 m/sec; one second later, the same car has a speed of 19 m/sec; one second later, the speed is 18 m/sec, and so on. As each second goes by, the car’s speed decreases 1 m/sec (note that acceleration can be either positive or—as in this example—negative). An acceleration can also occur as a change in direction with respect to time, even for an object whose speed does not change. A car traveling at a constant speed but gradually turning undergoes an acceleration, just like a car whose speed is changing.In meteorology there is one particular acceleration of utmost importance—gravity (g). This acceleration, 9.8 m/sec2 (32.1 ft/sec2), is nearly constant across the globe. It describes the acceleration an object would experience if gravity were the only force affecting its movement. There is a slight decrease in g from equator to pole, and also a very small difference in g from the surface to the upper atmosphere. For most applications, however, these variations in g are so slight they can be ignored.Force and PressureOne of the most important tenets of physical science is Newton’s Second Law, which relates the concept of force (denoted F) to mass (m) and acceleration (a). Specifically, Newton’s Second Law tells us that the acceleration of an object is proportional to the force acting on it and inversely proportional to its mass. Symbolically, this is expressed as...Imagine that a fully loaded 18-wheeler truck is stopped at a traffic light next to a bicycle. Suppose that when the light turns green, both begin to accelerate at the same rate and therefore remain next to each other. For them to accelerate at the same rate, it is easy to see that the much more massive truck requires a larger force (and more powerful “engine”). Likewise, if two bodies with equal mass are subjected to different forces, the one subjected to the greater force will undergo a greater acceleration.Keep in mind that F in the equation above is the net force acting on the object. If various forces are acting simultaneously, they must all be considered together to determine the acceleration; we must account for both the magnitude and direction of each. As we will see with regard to falling raindrops (Chapter 7), forces acting in opposite directions reduce the net force and resulting acceleration, sometimes to zero.Let’s apply Newton’s Second Law to our atmosphere. The mass of the atmosphere is S.14 × 1018 kg. (To get an idea of what 5.14 × 1018 kg weighs, picture a million boxcars, each containing a billion elephants) Multiplying the mass of the atmosphere by the acceleration of gravity, we determine that the force exerted on the atmosphere is about 5.0 × 1019 newtons (a newton [N] is the unit of force it takes to accelerate 1 kg one meter per second every second).Force divided by the area on which it is exerted equals pressure. So dividing this force of 5.0 × 1019 newtons by the surface area of Earth gives us the average force per unit area, or average surface pressure of about 10.132 newtons per square centimeter.This is equivalent to 1013.2 mb, or about 14.7 pounds per square inch.Having made the distinction between force and pressure, we now should address the question of how this distinction applies to the atmosphere. The answer is that despite the nearly constant total force of the atmosphere, its gases are not uniformly distributed across the planet. Consider a particular area at Earth’s surface with an imaginary column extending upward to the top of the atmosphere, as shown in the top right of Figure 4-1-1, Greater surface pressures exist at the bases of atmospheric columns that contain a greater number of molecules, and lower surface pressures are found where less air occupies the column. Just how these differences in pressure arise is considered later in this chapter; for the time being, the important point is that surface pressure reflects the mass of atmosphere within the column, as shown in Figure 4-1-1.FIGURE 4-1-1 Gravity, Mass, and Pressure. The downward force of the atmosphere is equal to the mass of the entire atmosphere times the acceleration of gravity. Because the amount of mass and the acceleration of gravity are constant through time, the total force of the entire atmosphere does not change. Pressure is defined as the amount of force exerted per unit of area. Thus, the shaded area in the figure experiences a certain amount of pressure Pressure varies because the mass of overlying air varies from place to place and time to time....If the acceleration of gravity were to double with no change in the atmosphere’s mass, what would happen to air pressure? Get solution
2. Velocity, Acceleration, Force, and PressureIt is quite common in everyday conversation to hear the terms force and pressure used interchangeably, just as velocity and speed are often considered synonymous. In the language of science, however, intermixing these terms can lead to great confusion. Let us look briefly at how they differ and their connection to a related concept, acceleration.Velocity, Speed, and AccelerationAny object that moves has a particular speed, defined as the distance traveled per unit of time. Speed is related to, but not the same as, velocity. Velocity incorporates direction as well as speed. Think, for example, of two cars traveling at 20 meters per second [44 mph) but moving in opposite directions. Though they have the same speed, their velocities are not equal because of their different directions. This distinction is crucial for understanding our next quantity, acceleration, the change in velocity(not speed) with respect to time.Because velocity includes both speed and direction, a change in either speed or direction is an acceleration. Consider a car that at one moment in time travels at 20 m/sec; one second later, the same car has a speed of 19 m/sec; one second later, the speed is 18 m/sec, and so on. As each second goes by, the car’s speed decreases 1 m/sec (note that acceleration can be either positive or—as in this example—negative). An acceleration can also occur as a change in direction with respect to time, even for an object whose speed does not change. A car traveling at a constant speed but gradually turning undergoes an acceleration, just like a car whose speed is changing.In meteorology there is one particular acceleration of utmost importance—gravity (g). This acceleration, 9.8 m/sec2 (32.1 ft/sec2), is nearly constant across the globe. It describes the acceleration an object would experience if gravity were the only force affecting its movement. There is a slight decrease in g from equator to pole, and also a very small difference in g from the surface to the upper atmosphere. For most applications, however, these variations in g are so slight they can be ignored.Force and PressureOne of the most important tenets of physical science is Newton’s Second Law, which relates the concept of force (denoted F) to mass (m) and acceleration (a). Specifically, Newton’s Second Law tells us that the acceleration of an object is proportional to the force acting on it and inversely proportional to its mass. Symbolically, this is expressed as...Imagine that a fully loaded 18-wheeler truck is stopped at a traffic light next to a bicycle. Suppose that when the light turns green, both begin to accelerate at the same rate and therefore remain next to each other. For them to accelerate at the same rate, it is easy to see that the much more massive truck requires a larger force (and more powerful “engine”). Likewise, if two bodies with equal mass are subjected to different forces, the one subjected to the greater force will undergo a greater acceleration.Keep in mind that F in the equation above is the net force acting on the object. If various forces are acting simultaneously, they must all be considered together to determine the acceleration; we must account for both the magnitude and direction of each. As we will see with regard to falling raindrops (Chapter 7), forces acting in opposite directions reduce the net force and resulting acceleration, sometimes to zero.Let’s apply Newton’s Second Law to our atmosphere. The mass of the atmosphere is S.14 × 1018 kg. (To get an idea of what 5.14 × 1018 kg weighs, picture a million boxcars, each containing a billion elephants) Multiplying the mass of the atmosphere by the acceleration of gravity, we determine that the force exerted on the atmosphere is about 5.0 × 1019 newtons (a newton [N] is the unit of force it takes to accelerate 1 kg one meter per second every second).Force divided by the area on which it is exerted equals pressure. So dividing this force of 5.0 × 1019 newtons by the surface area of Earth gives us the average force per unit area, or average surface pressure of about 10.132 newtons per square centimeter.This is equivalent to 1013.2 mb, or about 14.7 pounds per square inch.Having made the distinction between force and pressure, we now should address the question of how this distinction applies to the atmosphere. The answer is that despite the nearly constant total force of the atmosphere, its gases are not uniformly distributed across the planet. Consider a particular area at Earth’s surface with an imaginary column extending upward to the top of the atmosphere, as shown in the top right of Figure 4-1-1, Greater surface pressures exist at the bases of atmospheric columns that contain a greater number of molecules, and lower surface pressures are found where less air occupies the column. Just how these differences in pressure arise is considered later in this chapter; for the time being, the important point is that surface pressure reflects the mass of atmosphere within the column, as shown in Figure 4-1-1.FIGURE 4-1-1 Gravity, Mass, and Pressure. The downward force of the atmosphere is equal to the mass of the entire atmosphere times the acceleration of gravity. Because the amount of mass and the acceleration of gravity are constant through time, the total force of the entire atmosphere does not change. Pressure is defined as the amount of force exerted per unit of area. Thus, the shaded area in the figure experiences a certain amount of pressure Pressure varies because the mass of overlying air varies from place to place and time to time....If the acceleration of gravity were to double with no change in the atmosphere’s mass, what would happen to air pressure? Get solution
