Newton’s next assertion, based on much experiment and observation, is that, for a given body, the acceleration produced is proportional to the strength of the external force, so doubling the external force will cause the body to pick up speed twice as fast.
The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
Mass and Weight
To return to the concept of mass, it is really just a measure of the amount of stuff. For a uniform material, such as water, or a uniform solid, the mass is the volume multiplied by the density—the density being defined as the mass of a unit of volume, so water, for example, has a density of one gram per cubic centimeter, or sixty-two pounds per cubic foot.
Hence, from Galileo’s discovery of the uniform acceleration of all falling bodies, we conclude that the weight of a body, which is the gravitational attraction it feels towards the earth, is directly proportional to its mass, the amount of stuff it’s made of.
The Unit of Force
All the statements above about force, mass and acceleration are statements about proportionality. We have said that for a body being accelerated by a force acting on it the acceleration is proportional to the (total) external force acting on the body, and, for a given force, inversely proportional to the mass of the body.
If we denote the force, mass and acceleration by F, m and a respectively (bearing in mind that really F and a are vectors pointing in the same direction) we could write this:
F is proportional to m.a
To make any progress in applying Newton’s Laws in a real situation, we need to choose some unit for measuring forces. We have already chosen units for mass (the kilogram) and acceleration (meters per second per second). The most natural way to define our unit of force is:
The unit of force is that force which causes a unit mass (one kilogram) to accelerate with unit acceleration (one meter per second per second).
This unit of force is named, appropriately, the newton.
If we now agree to measure forces in newtons, the statement of proportionality above can be written as a simple equation:
F = ma
which is the usual statement of Newton’s Second Law.
If a mass is now observed to accelerate, it is a trivial matter to find the total force acting on it. The force will be in the direction of the acceleration, and its magnitude will be the product of the mass and acceleration, measured in newtons. For example, a 3 kilogram falling body, accelerating downwards at 10 meters per second per second, is being acted on by a force ma equal to 30 newtons, which is, of course, its weight.
The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
Mass and Weight
To return to the concept of mass, it is really just a measure of the amount of stuff. For a uniform material, such as water, or a uniform solid, the mass is the volume multiplied by the density—the density being defined as the mass of a unit of volume, so water, for example, has a density of one gram per cubic centimeter, or sixty-two pounds per cubic foot.
Hence, from Galileo’s discovery of the uniform acceleration of all falling bodies, we conclude that the weight of a body, which is the gravitational attraction it feels towards the earth, is directly proportional to its mass, the amount of stuff it’s made of.
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The Unit of Force
All the statements above about force, mass and acceleration are statements about proportionality. We have said that for a body being accelerated by a force acting on it the acceleration is proportional to the (total) external force acting on the body, and, for a given force, inversely proportional to the mass of the body.
If we denote the force, mass and acceleration by F, m and a respectively (bearing in mind that really F and a are vectors pointing in the same direction) we could write this:
F is proportional to m.a
To make any progress in applying Newton’s Laws in a real situation, we need to choose some unit for measuring forces. We have already chosen units for mass (the kilogram) and acceleration (meters per second per second). The most natural way to define our unit of force is:
The unit of force is that force which causes a unit mass (one kilogram) to accelerate with unit acceleration (one meter per second per second).
This unit of force is named, appropriately, the newton.
If we now agree to measure forces in newtons, the statement of proportionality above can be written as a simple equation:
F = ma
FORCE = MASS times ACCELERATION
which is the usual statement of Newton’s Second Law.
If a mass is now observed to accelerate, it is a trivial matter to find the total force acting on it. The force will be in the direction of the acceleration, and its magnitude will be the product of the mass and acceleration, measured in newtons. For example, a 3 kilogram falling body, accelerating downwards at 10 meters per second per second, is being acted on by a force ma equal to 30 newtons, which is, of course, its weight.
This is an example of how Newton's Second Law works:
Mike's car, which weighs 1,000 kg, is out of gas. Mike is trying to push the car to a gas station,
and he makes the car go 0.05 m/s/s. Using Newton's Second Law, you can compute how much force
Mike is applying to the car.
Answer = 50 newtons
Answer = 50 newtons
