Topics for today: Breaking down vectors, again Equilibrium Free Body Diagrams New forces!

1. Topics for today: • Breaking down vectors, again • Equilibrium • Free Body Diagrams • New forces! • Relationship between position, velocity, and accelleration VECTORS Usually, forces and motion in the x- and y-dimension are independent of eachother. We can break down vectors into components. If there is an object with a force acting on it in one dimension (say gravity pulling down on an object in the y-direciton) this force will not affect motion in the x-direction. Because of this, it is often helpful and necessary to break down forces into easy to you coordinate systems, in this class usually the x-and y-dimensions. Equilibrium If an object is stable, that is, not accelerating, the sum of the forces IN EACH DIRECTION must be zero. Later you will come to know this as newton’s second law. This is a very valuable tool, but you can only use it in one direction at a time. You MUST break forces into components! If there is an object, lets say a TA, sitting on a table, and the TA is not accelerating, then the forces on the TA must add up to equal zero.

2. Free Body Diagrams A skill that you must master in order to do well in this class is drawing free body diagrams. Returning to the TA on the table, lets draw a picture of the TA, all by himself. (Assume a cube TA and a flat table) Drawing the TA without showing other objects allows us to concentrate on the motion of and forces on the TA. After we have all the forces on the TA, we are free from considering other objects (hence the name, or at least that’s how I interpret it). Also, lets draw the forces on the TA Normal force, aka, a contact force. It’s the force of the table pushing back on the TA TA Since we see the TA not accelerating, we know that the forces must sum up to equal zero. We can write this down algebraically as: We can further simplify this as: By breaking things into components, we can find relations between forces in certain directions.

3. Three definitions…. Normal Force – a contact force, such as a table preventing a TA from falling to the ground, or the ground keeping your TA from falling to the center of the earth. If an object is not moving, the normal force is always opposite all the forces pushing in the other direction. Tension – an inward pulling force. As far as this class is concerned, the tension in a string will be constant throughout the string. This force is always inward – thing of your hand holding up a rock on a string. The rock isn’t moving, so its downward gravitational force is being held up by an upward pull from the string. Your hand feels a downward force that is equal to the rock’s weight, so the string is pulling down on your hand. Thus, the tension on the string always pulls inward. Frictional forces – always found by finding the contact force – the normal force – and multiplying by the coefficient of friction. Static - When an object is not moving with respect to what its touch, static friction applies. If the object is under another force, the force of STATIC friction will only OPPOSE that force with a value equaling that force, up until its maximum value. After that, the object is no longer in equilibrium (the sum of the forces is no longer zero), and the object should start moving, and then we move into the realm of kinetic friction. Kinetic – When an object is moving across a surface, kinetic friction applies in the direction opposite motion.

4. Position, Velocity and Acceleration Position, velocity, and acceleration are all intertwined. Position is a measurement of length. Velocity is a length per time. Its fairly obvious that one could say velocity is a position per time, or a rate of change of position. Thus if you have the information on all the positions a thing is at at all times, you can find the velocity by looking at how the position changes. Vice versa, you can look at velocity information and infer how a position changes. The same relationship applies between velocity and acceleration – acceleration is a length per time squared, or a velocity per time – the time rate of change of the velocity. This is most often used in this class and seen in position, velocity, and acceleration vs. time graphs. The slope (rate of change) of a position vs. time graph gives you the velocity vs. time graph, and the slope of that gives you acceleration vs. time! position velocity Acceleration Note how the slope of the position vs. time starts out negative, hits zero, then goes positive, as does the value of the velocity vs. time graph. Same goes for the acceleration: the slope of the velocity graph is constant, as is the value of the acceleration.