How do we represent interactions of forces within a system? Dynamics: Interactions of Forces

What is a Force? The word force is used in physics for a physical quantity that characterizes the interaction of two objects. A single object does not have a force by default, as the force is defined through the interaction of two objects. Remember that all physical quantities are measured in units. The unit of force is called the Newton (N), where 1 N = (1 kg)(1 m/s2).

What is a force diagram?diagram Force diagrams are used to represent the forces exerted on an object of interest (system) by other objects. A system is an object or group of objects that we are interested in analyzing. Everything outside the system is called the environment and consists of objects that might interact with and affect the system objects motion. These are external interactions. When we draw force diagrams, we only consider the forces exerted on the system object(s).

In the example below, the first image is a picture of a climber on the side of a cliff. The second image shows just the object of interest (the climber) and has vectors drawn representing the different forces on the climber, which are labeled with everyday language. The third image is a force diagram; the object of interest is simply represented by a dot, and the vectors are labeled by the type of force, the object exerting the force, and the object receiving that force.

Did you know? When the forces exerted on an object of interest are balanced, we say that the object is in EQUILIBRIUM (equilibrium does not necessarily mean rest). For example: Lets take the situation of a puppy curled up in your lap. We can write the total force exerted on the puppy by your legs and Earth as: F legs on dog + F Earth on dog = 0. Does it matter whether you chose up as (+) or down? How does it change your equation above?

How do we ADD vectors?ADD Suppose we want to add the two vectors A and B. To add them graphically, we redraw A and place the tail of B at the head of A. While we can move vectors from one place to another for addition, we cannot change the magnitude or direction of a vector while moving it.

How do we SUBTRACT vectors? You are familiar with subtraction a little bit already – this is what we do when we find the v vector on motion diagrams. Basically, to find the vector which is equal to A-B, you need to find the vector that you need to add to B to get A. Or simply ADD the negative vector (-B), which has the same magnitude opposite sign (direction).

What is an Inertial Reference Frame?Reference Frame Inertial reference frame: Inertia is the phenomenon when an object continues moving at constant velocity if no other objects interact with it or if the sum of all these interactions is zero. Reference frames in which we can observe this phenomenon are called inertial reference frames. If the sum of all forces exerted on the object is zero, then in an inertial reference frame, the objects velocity remains constant.

Lets Look at an Example You are driving in a car and you have a cup of coffee on the dashboard. The car in front of you stops so you slam on the brakes, from your frame of reference, what would happen to the cup of coffee? Now look at from the frame of reference of a pedestrian on the street watching the car and the coffee cup, what would they see? Which person is in the inertial frame of reference?

Newtons 1 st Law Newtons first law of motion: We choose a particular object as the object of interestthe system. Newtons If no other objects interact with the system object or if the sum of all the external forces exerted on the system object is zero (forces in the y direction are balanced and forces in the x direction are balanced), then the system object continues moving at constant velocity (including remaining at rest) as seen by observers in the inertial reference frames.

Newtons 2 nd Law

Mass: Mass (m) characterizes the amount of matter in an object and the ability of the object to change velocity in response to interactions with other objects The unit of mass is called a kilogram (kg). Mass is a scalar quantity, and masses add as scalars. Gravitational force: The magnitude of the gravitational force that Earth exerts on any object near its surface equals the product of the objects mass m and the gravitational constant g: F E on O = m g where g = 9.8 m/s 2 = 9.8 N/kg on or near the earths surface. The force points toward the center of Earth.

Newtons 3 rd Law Newtons Third Law of Motion: When two objects interact, object 1 exerts a force on object 2. Object 2 in turn exerts an equal-magnitude, oppositely directed force on object 1: