Dynamics Part 2
Mass vs Weight: Now can discuss mass vs. weight. We correlate mass with inertia. Think back to the first law. This means that the more mass an object has, the more inertia it has, which implies that a greater force is needed to accelerate a greater mass. We can define weight now. Weight is the force of gravity. Recall that F=ma. Weight is the force that acts on an object with some mass. Newton's equation gives us Weight = mass * gravity.
Normal Force: Let's start talking about the basic types of forces that we find in classical mechanics. The normal force is the result of direct contact between two objects and "normal" means that the force is always perpendicular to the surface of the object that exerts the force. For example, if we leave a book on a table, we know that gravity is pulling it down. The force of gravity on the object is equal to its weight. However, the book isn't accelerating downward even though gravity is pulling it down. This is because the table is exerting an upward force back up on the book. This is the normal force. The normal force will be equal to the weight because the book doesn't accelerate so the forces must be balanced out. In a system like this where we look at only a small part of what's happening, we can assume that the normal force will become large enough to match gravity and make a net force of 0. It may be helpful to note that weighing scales work by displaying your normal force, not your weight. It is the same when you and the scale are not accelerating.
Friction Force: Our talk about normal force will lead us directly into describing friction. Friction is a force that always opposes motion. If our book is sliding to the right on a table, the table will exert a friction force to the left to go against the friction. The third will still apply here and the book exerts the same friction force on the table towards the right. The formula for friction is the normal force times a coefficient of friction. The coefficient of friction describes the roughness between the two objects. There are two types of friction and coefficients of friction. Static friction is when the relative velocity between the two objects is 0. Static friction can range from 0 to its maximum (Normal force * Coefficient of Static Friction) to balance out whatever force is applied against it. Whenever there is relative motion between the two objects, there is kinetic friction which has a constant value of Normal Force * Coefficient of kinetic friction. Coefficients of friction are represented by μ.
Tension: Tension is fairly simple. It's the translation of a force through something like a rope. At a basic level, we can assume the rope is massless, so the force will be constant throughout. If you have a mass hanging from a roof we know the weight of the mass is mg. Because it is hanging, and not accelerating, the tension needs to supply an upward force of mg also to keep the net force at 0. Something that is a little trick with tensions is the following concept. If you have someone pulling on a rope attached to a wall with force F, and 2 people pulling on each side of a rope with force F, the tension in the rope will be the same. This is because even though we don't see it stated explicitly, the wall is also pulling back with force F on the rope to keep the net force at 0.
Spring Force: A spring force is special because it depends on the compression or extension of the spring. A spring has a spring constant "k" which essentially defines its thickness. A spring has a resting length on which there are no forces. When we extend or compress a string a length "x" from the resting length, a force is created. This force is calculated by the formula F = -kx. The reason that there is a negative sign in the formula is because the spring force is a restoring Force. The force always acts in the opposite direction of the change in length. This makes intuitive sense because if we compress a spring, it pushes to decompress and if we stretch a string it pulls to compress.
