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NEWTON’S LAWS

OF MOTION

According to Newton’s  first law of motion, if no net force acts on it, a body at rest remains at rest and a body in motion remains in motion at constant velocity (that is, at constant speed in a straight line).

This law provides a definition of force: A force is any influence that can change the velocity of a body.

Two or more forces act on a body without affecting its velocity if the forces cancel one another out.

What is needed for a velocity change is a net force, or unbalanced force. To accelerate something, a net force must be applied to it. Conversely, every acceleration is due to the action of a net force.

Mass

The property a body has of resisting any change in its state of rest or uni-form motion is called inertia. The inertia of a body is related to what we think of as the amount of matter it contains. A quantitative measure of in-ertia is mass: The more mass a body has, the less its acceleration when a given net force acts on it. The SI unit of mass is the kilogram (kg).

Note!

A liter of water, which is 1.057 quarts, has a mass of almost exactly 1 kg.

Second Law of Motion

According to Newton’s  second law of motion, the net force acting on a body equals the product of the mass and the acceleration of the body. The direction of the force is the same as that of the acceleration.

In equation form,

F = ma

Net force is sometimes designated F, where  (Greek capital letter sigma) means "sum of.” The second law of motion is the key to understanding the behavior of moving bodies since it links cause (force) and effect (acceleration) in a definite way.

In the SI system, the unit for force is the newton (N): A newton is that net force which, when applied to a 1-kg mass, gives it an acceleration of 1 m/s².

Solved Problem 3.1 A 10-kg body has an acceleration of 5 m/s². What is the net force acting on it?

Solution.

F = ma = (10 kg)(5 m/s²) = 50 N

Weight

The weight of a body is the gravitational force with which the earth attracts the body. If a person weighs 600 N (135 lb), this means the earth pulls that person down with a force of 600 N. Weight (a vector quantity) is different from mass (a scalar quantity), which is a measure of the response of a body to an applied force. The weight of a body varies with its location near the earth (or other astronomical body), whereas its mass is the same everywhere in the universe.

The weight of a body is the force that causes it to be accelerated downward with the acceleration of gravity g. Hence, from the second law of motion, with F = w and a = g,

w = mg

Weight = (mass)(acceleration of gravity)

Because g is constant near the earth’s surface, the weight of a body there is proportional to its mass—a large mass is heavier than a small one.

British System of Units

In the British  system, the unit of mass is the slug and the unit of force is the pound (lb). A net force  of 1 lb acting on a mass of 1 slug gives it an acceleration of 1 ft/s². Table 3.1  shows how units of mass and force in the SI and British systems are related.