Net Force
Net force is the total force acting on an object, calculated as the vector sum of all individual forces. It is crucial to understand that forces are vector quantities, meaning they have both magnitude and direction. According to Newton's laws of motion, the state of an object—whether at rest or in motion—is influenced by net force. If the net force is zero, an object remains in its current state, while a non-zero net force leads to acceleration in the direction of that force. Various forces, such as gravity, friction, and tension, can act on an object simultaneously, and free-body diagrams are often utilized to visualize these forces and determine the net force. Understanding net force is foundational in physics, enabling predictions about motion in everyday activities like driving a car or throwing a ball. The concept plays a significant role in classical mechanics, influencing everything from simple movements to complex astronomical predictions.
Net Force
FIELDS OF STUDY: Classical Mechanics
ABSTRACT: This article describes net force and how it is used to quantify the total force acting on an object and the motion that results. Individual forces, such as frictional, tension, normal, applied, or gravitational forces, may be used to calculate net force on an object. Newton’s laws of motion are used to explain the relationship between force, mass, and motion—the foundation for the study of classical mechanics.
Principal Terms
- acceleration: the rate of change of an object’s velocity.
- friction: the force created by the resistance to relative motion between solid surfaces.
- gravity: the force that describes the attraction between one body and another.
- normal force: the force exerted on an object perpendicular to the surface of contact.
- right-hand rule: the rule that shows the orientation of vector quantities normal to a surface by using the shape of the right hand.
- tension: the force directed along the length of a wire, string, or cable pulled at opposite ends.
- vector: a quantity that has both magnitude and direction.
- velocity: the rate of change of an object’s displacement.
Newton’s Laws of Motion
Force can be thought of simply as a push or a pull. An object may have several forces acting on it at a given time. In order to quantify the net force, or total force, one must consider the vector sum of all the forces acting on an object. Forces are vector quantities because they possess both magnitude and direction.
Newton’s three laws of motion explain the relationship between force, mass, and motion. The first law states that if the net force on a resting object is zero, that object will remain at rest, and if the net force on a moving object is zero, that object’s velocity will remain constant—that is, it will continue to move with the same speed in the same direction. (A net force of zero means that either there are no forces acting on an object or that the forces acting on the object cancel each other out.) This does not mean that if, for example, a person pushes a box across the floor and then stops, the box will continue to move. Even after the person stops pushing, there will still be a force acting on the box: friction. The box will stop moving because the friction between it and the floor is great enough to halt its movement. Pushing the same box across a frictionless surface would result in the box continuing to move at a constant velocity forever, or until it encountered another force.
Newton’s second law states that the net force is equal to the mass of an object multiplied by its acceleration. Acceleration, like force and velocity, is a vector quantity. Mass is the measure of an object’s quantity of matter. It is a scalar quantity, not a vector, because it has magnitude but no direction. Mass can also be thought of as an object’s resistance to being accelerated. When there is no net force acting on an object, its acceleration is zero. This means that the object’s velocity, whether zero or nonzero, will remain constant, because acceleration is change in velocity. When a net force does act on an object, it will cause the object to accelerate. The direction of the acceleration will be the same as the direction of the net force.
Newton’s third law states that when one object exerts a force on another object, the second object will exert an answering force on the first object that is equal in magnitude but opposite in direction. For example, if a shoe is leaning against a box, the shoe is exerting a horizontal force on the box, while at the same time the box is exerting a horizontal force on the shoe. These two forces are equal in magnitude, but they act in opposite directions.
Identifying Different Forces
In order to quantify the net force, one must consider all of the various forces acting on an object. There are many different types of force. In the International System of Units (SI), these forces are measured in newtons (N). One newton is equal to the mass of the object in kilograms (kg) multiplied by its acceleration due to force in meters per second per second, or meters per second squared (m/s2).
The force of gravity is the pull exerted by one physical body on another physical body. Generally, when one speaks of gravitational force on a body, one is referring to the force that pulls the body toward Earth. If an object is in free fall and the effects of air resistance are neglected, then gravitational force is the only force acting on that object.
Newton’s second law can be expressed in the form
F = ma
where F is force, m is mass, and a is acceleration. This equation can be used to calculate gravitational force by replacing a with acceleration due to gravity (g), which on Earth is approximately 9.81 m/s2. The magnitude of the gravitational force experienced by a body is equal to the mass of the body multiplied by g. This quantity is also what is meant by the term "weight." In physics, weight is defined as the force exerted on a body due to gravity. That body does not have to be in free fall for this relationship to work. An object at rest on a tabletop still experiences the same magnitude of gravitational force.
When an object is placed on a table, its weight is countered by what is called a normal force, which pushes up against the object. This force is always perpendicular to the surface on which the object rests. The greater the weight of the object, the greater the normal force exerted by the table to maintain its shape and resist being compressed. For the object on the table, the magnitude of the normal force is equal to the object’s weight. However, in other situations, the normal force can be greater or less than the object’s weight.
Friction is the resistance to motion that occurs as an object slides over a surface. It is caused by small irregularities that add to the roughness of the surface. Frictional force is parallel to the surface and acts in the opposite direction of the motion. In some situations, a surface will be considered frictionless, so that frictional forces can be neglected in calculations.
Tension is the pulling force exerted by a rope, cable, or similar cord that is pulled taut by an object at each end. To exert a tension force on an object, the rope must be in contact with the object. Tension force is directed away from the object and along the rope.
Free-Body Diagrams and Determining Net Force
To find the net force from two or more forces acting on an object, one needs to add the individual vector forces. Because forces can act on an object in different directions, each of the three physical dimensions—height, width, and depth—must be considered.
Free-body diagrams are sketches that show all of the different forces acting on an object. The object may be drawn as a box or as a point particle. The number of forces drawn will depend on the specific situation. Each force is represented by an arrow pointing in the direction in which the force is acting, with a label indicating its force type. A three-dimensional coordinate system can then be used to resolve each force into components so that Newton’s second law can be applied to each component separately.
The most commonly used system is the Cartesian coordinate system, which uses numbers in the form (x, y, z) to represent width, height, and depth. The right-hand rule is a helpful way to remember how these three dimensions, or axes, are positioned relative to one another. The first or index finger represents the x axis, the second or middle finger represents the y axis, and the thumb represents the z axis. (Alternatively, the thumb can represent the x axis, the index finger can represent the y axis, and the middle finger can represent the z axis.) When these fingers are spread apart, their position resembles the orientation of the three axes. The right-hand rule can be used as a basis for finding vectors.
Consider a box sitting at rest on a table. There are two forces acting on this box: the normal force from the table surface and the gravitational force from Earth. The normal force is perpendicular to the surface of the table and drawn up through the top of the object. The gravitational force is directed toward Earth and is drawn from the object directly down. The normal force is equal to the object’s weight, because the object is at rest and no other forces are acting on it. By Newton’s second law, because the forces are balanced and there is no acceleration, the net force is zero.
Now, consider that same box with a force applied to it from the right. In addition to the normal and gravitational forces, one must take into account the magnitude of the force used to push the box and the frictional force opposing this motion. In the free-body diagram, the force pushing the box is drawn pointing from right to left and is positive, and the frictional force is drawn pointing from left to right and is negative. If the force used to push the box is greater than the frictional force, then there is a net force, and the box experiences an acceleration.
Applications of Net Force
Newton’s laws of motion are an inescapable part of everyday life. Throwing a ball, driving a car, and simply walking are all activities that obey Newton’s laws. Understanding these laws and how net force relates to motion forms the foundation for the study of classical mechanics and dynamics and allows one to quantify and predict outcomes of certain events. For example, English astronomer Edmond Halley (1656–1742) used Newton’s laws to correctly predict the periodicity of a comet, which was later named Halley’s comet in his honor.
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