Still talking about things with constant velocities Equilibrium Still talking about things with constant velocities

Remember Newton’s 1st Law (The Law of Inertia): Static Equilibrium Static (not moving/stationary/at rest) Equilibrium (balanced forces = constant velocity = 0) The sum of the forces acting on the object in any direction is zero. The resultant force is zero. 𝐹 𝑥 =0 𝐹 𝑦 =0 Remember Newton’s 1st Law (The Law of Inertia): An object at rest stays at rest unless acted upon by a net external force.

Remember Newton’s 1st Law (The Law of Inertia): Dynamic Equilibrium Dynamic (moving) Equilibrium (balanced forces = constant velocity ≠ 0) The sum of the forces acting on the object in any direction is zero. The resultant force is zero. 𝐹 𝑥 =0 𝐹 𝑦 =0 Remember Newton’s 1st Law (The Law of Inertia): An object in motion stays in motion (in a straight line & at a constant velocity) unless acted upon by a net external force.

Forces A force is a push or pull on an object and is directional, (making it a vector) When forces are balanced (they add to zero) the velocity of the object is constant. Units: Newton = 𝑘𝑔 𝑚 𝑠 −2 Types of Forces: Weight (W) Friction (fs or fk) Tension (T) Drag (D) Normal (N) Upthrust/Lift/Buoyant (U)

Weight (W) ≠ mass The result of the gravitational attraction between the object in question and the Earth. If the object were on another planet, then its weight is defined as the gravitational interaction between its mass and that planet’s mass. On Earth, W = mg; where m is the mass of the object and g is the gravitational field strength of the Earth (a property of the gravitational field of the Earth with units N kg-1).

Tension Tension is created when two forces are applied in opposite directions at the ends of the string. Any arbitrary point on the string is acted upon by 2 forces. A string that is taught is said to be under tension. A spring that is stretched is also said to be under tension. This means that In most cases, the string is idealized by assuming it is massless. (really 𝑚 𝑠𝑡𝑟𝑖𝑛𝑔 << 𝑚 𝑎𝑛𝑦𝑡ℎ𝑖𝑛𝑔 𝑒𝑙𝑠𝑒 )

Normal reaction (contact forces) If a body touches another body, there is a force of reaction or contact force between the two bodies. This force is perpendicular to the body exerting the force.

Frictional Force Acts to oppose the (potential) motion of a body. Kinetic friction arises whenever one body slides (moves) over another (NOT a static force) Static friction arises whenever there is just a tendency for motion, not necessarily motion itself, such as when a block rests on an inclined plane but does not move.

Drag (not a STATIC force) Oppose the motion of a body through a fluid (a gas or liquid). Typical examples: air resistance on a car or plane, or the resistance force experienced by a steel marble dropped into a jar of honey. Directed opposite to the velocity of the body and magnitude generally depends on the speed of the body.

Upthrust Any object placed in a fluid experiences an upward force called upthrust If 𝑢𝑝𝑡ℎ𝑟𝑢𝑠𝑡=𝑤𝑒𝑖𝑔ℎ𝑡 then the body will float on the fluid If 𝑢𝑝𝑡ℎ𝑟𝑢𝑠𝑡<𝑤𝑒𝑖𝑔ℎ𝑡 then the body will sink. Caused by the pressure that the fluid exerts on the body

Force (Symbol) Description Weight (W) The gravitational attraction between the mass in question and the Earth. On Earth, W=mg; where g = 9.8 m/s2. Tension (T) The force that arises in any body when it is stretched is called tension. The direction of the tension force is along the string Normal reaction (contact force) If a body touches another body, there is a force of reaction or contact force between them. This force is perpendicular to the body exerting the force Drag (drag) Forces that oppose the motion of a body through a fluid (a gas or liquid). This includes air resistance on a car or plane & a marble dropped in a jar of honey. Upthrust (upthrust) Any object placed in a fluid experiences an upward force called upthrust. If this force is equal to the weight of the object, then the object floats. This is caused by the pressure exerted on the body by the fluid. Static Friction (fs) Opposes the tendency of objects to move. An example might include a block on an inclined plane. Kinetic friction (fk) Opposes the motion of an object.

Rules for Free-body Diagrams The diagram is for one body only and the force vectors are represented as arrows Only the forces acting on the body are considered The force/vector arrows are drawn to scale originating at a point that represents the center of mass. All forces have a clear label Procedures for drawing & using FBDs Sketch the general situation with all the bodies that interact Select the body of interest and draw it again removed from the situation. Draw, to scale, and label all the force that act on this body Add the force vectors together (by drawing or calculating) to give the net force on the body. (There won’t be one of these yet, so skip this step for now.)

Force Diagrams Account for all forces acting in all directions There’s pretty much always weight in every force diagram… Is it in contact with something? You need a normal force and probably some friction somewhere unless the problem states frictionless. Is something holding it up (like a string/rope or spring)? You need a tension force somewhere. Remember: THE SUM OF THE FORCES IN THE X AND Y DIRECTIONS IS ZERO IN EQUILIBRIUM!

Example 1: A block of mass m rests on a flat table.

Example 2: A block of mass m rests on an inclined plane.

Example 3: A block of mass m is suspended from a surface by a massless cable.

Example 3: A block of mass m is suspended from a surface by two massless cables.

You Try! Draw force diagrams for each of the static equilibrium stations around the room.

Investigating Springs What do you observe? What can we measure? What can we manipulate?

Hooke’s Law If we try to extend a spring, a force pulls the spring back to its original length. If we try to compress a spring, a force pushes the spring back to its original length. The force in the spring, the tension, has a simple relationship to the amount by which the spring is extended or compressed… let’s try to figure that out.

Research Question: What is the relationship between the force applied to a spring and the amount a spring is displaced from its equilibrium? Important things to include: Research Question IV, DV, Control variables Hypothesis Materials list & labelled apparatus diagram