2-Dynamics (Forces)

Click here for the Forces Slideshow from class

Text Book: Chapter 2 & 3 in Mastering Physics (get online code for registration on about page of google classroom)

Basic Overview

All changes in motion arise from force interactions; hence the name Dynamics for this unit. An analysis of the net force on any object or system can help predict or explain changes in motion.

Equations

Main Ideas

  • Newton's Laws describe how forces relate to motion
    • 1st law states that there is no net force, there is no change in motion
      • So . . . constant velocity means forces are balanced, there's no net force, acceleration is zero
    • 2nd law states that when there is a net force, an object accelerates in proportion to the net force divided by the mass. (a = Fnet/m)
    • 3rd law states that all forces come in pairs that are equal an opposite. Fa-->b = - Fb-->a
      • Tip: 3rd law pairs are always acting on different objects, so they will not be drawn on the same free body diagram
      • Classic misconception: Huge truck collides with little car, both at same speed and opposite direction. Most people think the little car experiences a bigger force, but we know that they each experience a force of the same magnitude, but opposite direction
  • Net forces (or total forces) are determined by adding vectors
    • If they are on the same axis, you add forces in the same direction and subtract opposing forces
    • If more than one axis is involved, find the components of angled forces and figure the net force on each axis separately before combining to find the total net force.
  • Types of forces: Only 4 main types
    • Gravitational Force: Fg = mg. The only force we are discussing at this point in the year that can act at a distance
    • Strong Nuclear Force: holds the nucleus together (something that wouldn't normally happen to a bunch of + charged protons with no electrons in the immediate vicinity (we won't talk about this force more until next year)
    • Weak Nuclear force: controls the decay of nuclei (we won't talk about this force more until next year)
    • Electromagnetic Force: the force of charged particles and magnetic fields - we talk more about this later & next year, but there are some everyday forces that are really caused by electromagnetic interactions.
      • Contact forces: These are any forces that arise from direct contact with an object. Contact forces may have other ways of being classified as well, such as applied forces, normal forces, etc. The way contact forces work is that the electrons on the outside of the atoms/molecules of one object push against the electrons on the outside of atoms/molecules - which is actually an electromagnetic force.
      • Tension forces: These are forces that arise from a flexible object not breaking apart when pulled at each end. Examples include ropes, leashes, chains, or springs being pulled on in order to pull a third object. A point of misconception is that people may think a rope being pulled by a 50 N force on one side and 50 N on the other might have a tension of 100 N within it, but that is not true. The way tension actually works is that the molecules within the rope (or similar functioning object) are being held in place due to their electrostatic bonds (hydrogen bonding, etc). These forces act as extenders of the force from one end through a series of gazilliions of Newton's 3rd law pairs to the other side of the rope. What this means is that the force exerted at one end is really determined by the resistance force at the other end.
      • Normal forces: Normal forces are the perpendicular components of contact forces between any two surfaces. Many normal forces occur between objects that are blocking each other from passing through each other. We usually use the term when at least one of the objects is passively resisting (for example, when a table blocks a book that is resting on it from falling right through the table we say that the table exerts a normal force upward on the book). As a 3rd law pair, though, each normal force will have an opposite and equal normal force (The book must be exerting a force downward on the table).
        • If the surface of the object is angled, remember to normal force will still be perpendicular, as shown in the diagram below.
      • Fictional forces: Friction is the parallel component of contact forces that resists slipping between the surfaces. In the case of the book on the table, there was no tendency to slip, so there was no friction, but if the table is angled, as shown below, friction will resist the slipping.
        • As long as friction is holding things in place it is called static friction and can be any value between 0 and Ff maxsFN, where µs is the coefficient of static friction.
        • Once the book starts slipping, the friction is called kinetic friction and is always equal to Ff kFN,(independent of the speed of motion) where µk is the coefficient of kinetic friction.
image showing normal force deceasing as an angle of a surface increases. As a result friction changes.
  • Angled forces
    • to be continued
  • Connected objects and systems
    • to be continued

Videos

Angled forces intro:

Angled ramps intro:

Misconceptions

The following are common misconceptions from this unit. It is likely that the AP test will use these as a basis for writing believable distractors in multiple choice questions or look to uncover these in your writing in the free response section. See if you can explain why they are not always true (some are true sometimes, while others are not true at all).

    • Misconception: Forces are required for motion with constant velocity. Physics Principle: Constant velocity can be maintained if there are no forces acting on an object (example: in space) Reasoning: We live in a world with friction and air drag. Under these conditions constant velocity is maintained by maintaining a force to overcome these resistive forces, so our personal experiences all show that we need forward force to keep going. In Physics 1 we often simplify our circumstances to the point where these forces are not present. In that case, an object with no forward force will continue indefinitely.
    • Misconception: Inertia is the force that keeps objects in motion. Physics Principle: Inertial mass is a property of an object that corresponds to its resistance to change in velocity. Forces are interactions between 2 objects. Reasoning: The more inertia an object has, the more tendency to keep moving it has, but that does not require a force. For it to be a force you would have to be able to explain the object causing the force and the object receiving the force. See the reasoning for the misconception above for why people confuse this.
    • Misconception: If two objects are both at rest, they have the same amount of inertia. Physics Principle: the more massive object has more inertia. Reasoning: Consider a little kid on ice skates pushing against a much bigger kid on ice skates. The smaller once speeds up more. This demonstrates the inverse nature of inertial mass and acceleration. (If F1=F2 then m1a1 = m2a2 and in the same amount of time m1∆v1 = m2∆v2
    • Misconception: All objects can be moved with equal ease in the absence of gravity. Physics Principle: Newton's 2nd law states a = Fnet/m
    • Reasoning: Consider the case of a jet pack in space. You would not be able to use a tiny jet pack suitable for maneuvering an astronaut to reposition the entire ship in case of a system failure. The same force applied to the astronaut and the ship would produce a much larger effect on the astronaut than on the spaceship.
    • Misconception: Action-reaction forces act on the same body (and can cancel out on an object). Physics Principle: Newton's third law describes to sides of the same force interaction. FA on B = –FB on A Reasoning: Using our subscript notation, you can see that the first force is acting on object B and the second force is acting on object A. I consider them two different expressions of the same interaction, sort of from the opposite perspective. These forces cannot cancel out on a single object because they are acting on different objects (although they do cancel out if both objects are part of the same system).
    • Misconception: The product of mass and acceleration, ma, is a force.
    • Physics Principle: The product of mass and acceleration is the net force, or the vector sum of all the forces acting on the object.
    • Reasoning: There may not be any object actually pushing or pulling in the direction of the net force, for example, in the case of two angled forces pulling against friction in the top down diagram below. You can see that there is no actual force aligned with the direction of the net force.
diagram showing 3 angled forces where vector sum is in direction different from individual forces
    • Misconception: Friction can't act in the direction of motion.
    • Physics Principle: Friction acts in a direction that opposes sliding motion between 2 surfaces.
    • Reasoning: In the case of a simple object sliding across a surface friction does oppose motion. However, in many cases friction is required to cause motion. This often happens by having tires or shoes or something in contact with the ground where friction prevents sliding at that surface, which then is an unbalanced force forward, causing the bicycle, car, or person to move forward.
    • Another example would be a box in the back of a wagon. In that case, the resistance to slipping causes the box to move along with the wagon. Without friction the box would have slipped and stayed at rest while it slid to the back of the wagon.
    • Misconception: The normal force on an object is equal to the weight of the object by the 3rd law.
    • Physics principle: Newton's third law describes to sides of the same force interaction. Newton's 2nd law is used to determine how forces of different interactions relate to each other. Reasoning: The long form of the superscripts includes both the objects involved as well as the type of interaction. Using this method for a box at rest on a table you would see that the weight interaction would be Fg earth on box = – Fg box on earth and that FN table on box = – FN box on table. Using this method you can see that Newton's 3rd law does not relate the normal force to the gravitational force. As shown in the diagram below of a box at rest, if I push downward on the top of a box, the normal force will need to balance both the weight and the added force. Alternatively, if an object is accelerating, the forces do not balance.
Free body diagram showing normal force to be greater than weight.
    • Misconception: Equilibrium means that all the forces on an object are equal.
    • Physics Principle: Equilibrium is when there is an overall balance of forces.
    • Reasoning: While it can be true that equal forces can balance, it can also be true that they do not. In the instance of a forward force of 10 N and a downward force of 10 N there would be equal forces without equilibrium (there is a net force of √20 N 45º below the horizontal).
    • Forces can be balanced (in equilibrium) without being equal. As shown in the diagram above, none of those forces are equal and yet the net force is 0N.
    • In addition, angled forces have components that may balance each other without having an equality of forces.
    • Misconception: Only animate things (people, animals) exert forces; passive ones (tables, floors) do not exert forces.
    • Physics Principle: Newton's 3rd law (explains force pairs), Objects are composed of particles (atoms or molecules) held in place by electrostatic forces.
    • Reasoning: Due to Newton's 3rd law, we know that when I sit on a table, I exert a force FN me on table and the table must exert a force FN table on me or we have violated that law. The same can be said for any inanimate object. Another way of explaining this is to consider that the particles within the table have an ideal location based on the interactions between the particles around them (hydrogen bonding, etc). Pushing downward on the table moves these particles ever so slightly out of place, which behave kind of like a spring in that each particle is pulled additionally back towards its original position. The sum of those additional forces is equal to the normal force upward on me.
    • Misconception: Newton's 3rd law can be overcome by motion (such as by a jerking motion).
    • Experience: We can observe this is not true when we use sensors or spring scales. In the case of the sensors, the each sensor creates a mirror image of the other one. See the graph below for an example.
image showing identical spikes in force magnitudes, but opposite directions, confirming Newton's 3rd law.
    • Misconception: A force applied by, say a hand, still acts on an object after the object leaves the hand.
    • Physics Principle: Forces are interactions between 2 objects. Reasoning: Since the hand's force on the object is a contact force, as soon as the hand loses contact with the object, the interaction ceases and there no longer is a force acting on the object. The reason this is difficult to grasp is that the result of the interaction (the motion) is continuing and may even be in the same direction as the force used to be. Don't be fooled, though; contact forces end when the contact ends.

Other Learning Resources

  • See Mrs. Twu's page for very extensive resources on Forces: https://sites.google.com/site/twuphysicslessons/home/forces
    • She has 39 short videos that include explanations and example problems. She also has a set of practice problems.
  • Edx.org's Challenging Concepts in AP Physics 1 & 2 course has a unit called Force Diagrams that covers the basics as well as angled forces in detail.