Physics Review Chapters 1 – 3 C. Buttery 9/16/16

overview Vectors & Vector Addition Kinematics in 1D Kinematics in 2D Newton’s Laws (if time)

Vectors Vectors can only be added tip to tail The resultant vector is drawn from the tail of the first to the tip of the last Remember trig functions! SOH CAH TOA Also Pythagorean Theorem: 𝑎 2 + 𝑏 2 = 𝑐 2 Vectors can be moved anywhere, typically drawn from the origin and then moved Also remember scalar vs vector: speed, distance are scalars; velocity, displacement, acceleration, vectors

Practice problems

Practice Problems

Kinematics in 1D Five Kinematic Variables: 𝑥 (or 𝑦) displacement 𝑎 acceleration 𝑣 or 𝑣 𝑓 final velocity 𝑣 𝑜 or 𝑣 𝑖 initial velocity 𝑡 elapsed time Velocity, displacement, and acceleration are either positive or negative

Kinematics in 1D Three equations to know how to use: 𝑣= 𝑣 𝑜 +𝑎𝑡 𝑣 2 = 𝑣 𝑜 2 +2𝑎𝑥 𝑥= 𝑣 𝑜 𝑡+ 1 2 𝑎 𝑡 2 Also these are useful as well: 𝑣 𝑎𝑣𝑔 = Δx Δ𝑡 𝑎= Δ𝑣 Δ𝑡

Kinematics in 1D Tips for solving problems: Draw a picture! Decide which direction is positive and which is negative Write down what you have in terms of each variable All you need is 3 of the 5 variable to solve for any 4th There may be multiple ways to get the same answer Remember if a problem is divided into segments, the final velocity for one section could be the initial for another

Practice Problems

Practice Problems

Practice Problems Answer: 𝑥=4.5𝑚

Practice Problems

Practice Problems (this is 1.6 𝑚/ 𝑠 2 )

Kinematics in 2D Works almost the same as kinematics in 1D Same equations Directions are independent of each other Time is usually the same across both x and y directions

Kinematics in 2D Three important things to remember: 𝑎 𝑥 =0 Therefore, 𝑣 𝑜𝑥 = 𝑣 𝑓𝑥 𝑎 𝑦 =10 𝑚/ 𝑠 2 or 9.8 𝑚/ 𝑠 2 Basically, gravity If finding max height, 𝑣 𝑓𝑦 =0

Practice Problems

Practice Problems Answer: 𝐷=3.4 𝑚

Practice Problems

Practice Problems

Practice problems Answer: 𝑣 𝑜 =45.5 𝑚/𝑠 So in other words, not possible.

Forces and Newton’s Laws Newton’s Laws (abridged) 1st: An object continues at a constant velocity or at a state of rest until a force acts on it 2nd: 𝐹=𝑚𝑎 3rd: Equal and opposite reactions

Forces and Newton’s Laws Types of forces: Normal Force – perpendicular to a surface Weight – mass times gravity Tension – along a rope Friction – either static or kinetic, opposes motion 𝐹 𝑓 = 𝜇 𝑓 𝑁 Centripetal (think chapter 5)

Forces and Newton’s Laws Remember that every force can be written as 𝐹=𝑚𝑎 Sum your forces in both 𝑥 and 𝑦 directions separately 0<𝜇<1 Normal force isn’t necessarily equal to weight Draw your free body diagrams! What constitutes equilibrium and what will have a net force

That’s It! Questions, comments, concerns, more problems? Make sure you study and practice over the weekend Good luck!