The student is expected to calculate the effect of forces on objects, including the law of inertia, the relationship between force and acceleration, and the nature of force pairs between objects. The student is also expected to develop and interpret free-body force diagrams.
Newton’s First Law of Motion states that the velocity of a body remains constant unless a net force acts upon it.
Newton’s Second Law of Motion states that acceleration is directly proportional to the net force acting on the object and inversely proportional to its mass. Acceleration is parallel to the direction of the net force.
Newton’s Third Law of Motion states that the mutual forces of action and reaction between two objects are equal, opposite in direction and collinear.
Free body diagrams reduce objects to particles. All forces acting on the object are drawn as labeled arrows acting on the particle. The length of the arrows is proportional to the magnitude of the force. The direction of the arrow indicates the direction of the force.
The net force acting on an object is equal to the vector sum of all the forces. When no net force is acting on an object, the object is in equilibrium.
The dynamics of a system explain why objects move. The law of inertia, or Newton’s First Law of Motion, tells us an object will preserve its velocity as long as the object is acted upon by a constant external force. Inertia is the object’s resistance to changes in its motion. What this means is that the only way to cause a change in an object’s motion is to change something about the forces acting on it. Changing an object’s motion includes speeding it up, slowing it down, or changing its direction. To find out how much force is required to make a change in motion, the two equations below can be combined and used to analyze changes in the motion of an object.
The acceleration of an object is a measure of its change in motion. It is defined as the rate at which the velocity of an object changes. Newton connected the acceleration of an object to the amount of force that had been applied to it with his second law of motion. He said that the acceleration of an object is equal to the force applied per amount of mass. This relationship is shown below.
Newtons Second Law is a bridge that links force and acceleration. To fully understand this, the concept of net force must be introduced. The net force is the sum of all of the forces acting on a single object.
Sometimes the sum of the forces is zero. When this happens, the system is at equilibrium and there will be no changes to the objects motion. Stationary objects and objects traveling in a straight line at a constant speed have a net force of zero and are at equilibrium.
When the sum of forces is not zero, the net force is equal to the mass times acceleration, which is Newton’s Second Law of Motion. Objects that are speeding up, slowing down, or changing directions have a net force acting on them that is not zero.
Newton’s Third Law of Motion describes the relationship between pairs of forces. It says that every action force is met with an equal and opposite reaction force. This relationship is especially useful when a system, or parts of a system are balanced. Consider the diagram below. In this situation, the worker is pushing the crate across the floor in the horizontal direction. Since the box is not moving in the vertical direction, the net force in the vertical direction is zero. This means that the weight force and the normal force have to be equal. Since they are acting in opposite directions, they cancel out and the net force is zero. This is an example of a force pair.
The following is an example of how force pairs can be used in calculating the force on an object:
A worker is moving a 225 kg crate across a warehouse floor. He is pushing it at a speed of 3.0 m/s. If he is pushing with a force of 525 N, what is the coefficient of friction between the wooden crate and the cement floor?
FREE BODY DIAGRAMS
Constructing Free-Body Diagrams
A free-body diagram is a way to illustrate the forces acting on an object and simplify the environment for the proposed problem, leaving related factors only. All the forces acting on the system are considered to be acting at a single point. The free-body diagram below was made to represent the crate in the diagram above. Here are the steps that were followed:
Identify the system, the object on which the forces are acting, which is the crate
Identify all of the acting forces. Forces happen where the system and the environment are in contact with each other. For the crate, this is the interaction between the floor and the crate and the place where the worker is touching the crate. Each of these contact points represent a pair of forces.
Draw a dot to represent the system and an arrow to represent each force. The arrows are vectors. They should extend from the dot in the direction the force is acting and their length should represent the magnitude of the force. Forces that are equal should have arrows of equal length.
Label each arrow with its respective force.
Interpreting Free-Body Diagrams
Free-body diagrams are useful in that they summarize all of the forces acting on an object. With a quick glance, an understanding of the motion of an object can be reached. Consider the first free-body diagram below. From the forces acting on it, it is understood that the object is in free-fall. Since gravity is the only force acting, it must be falling. Consider the second free-body diagram. This object is at rest on a surface. This is obvious from the equal and opposite weight and normal forces. In the third free-body diagram, the object is accelerating to the right along a surface. The applied force arrow is longer than the friction force arrow, so there is a net force to the right, causing the object to accelerate. The weight and normal force arrows are equal and opposite, so there is no change in the motion of the object in the vertical direction.