Transcript Document
Reminders: NO SI THURSDAY!! Exam Overview “Approximately 1/3 of the problems will stress understanding of the physics concepts, whereas the remainder will be numerical problems to test ability to apply these concepts.” -Syllabus 27 Questions Don’t be tricked! Breakdown 16% Mathematical Basics Vectors!!! 27% Position, Velocity, Acceleration (Know how to flow) 13% Circular Motion (𝛼, 𝜔, 𝜃, 𝑇, 𝑓, 𝑎𝑡𝑎𝑛 , 𝑎𝑟𝑎𝑑 , 𝑎𝑡𝑜𝑡 , 𝐹𝑟𝑎𝑑 ) 44% Forces, Work, Newton’s Laws Normal force, friction, springs Breakdown 16% Mathematical Basics Vectors!!! 27% Position, Velocity, Acceleration (Know how to flow) 13% Circular Motion (𝛼, 𝜔, 𝜃, 𝑇, 𝑓, 𝑎𝑡𝑎𝑛 , 𝑎𝑟𝑎𝑑 , 𝑎𝑡𝑜𝑡 , 𝐹𝑟𝑎𝑑 ) 44% Forces, Work, Newton’s Laws Normal force, friction, springs Do you find yourself in any one of these situations? Being chased by angry killer bees and running from them at constant speed Swimming in an ironman triathlon at constant speed Giving someone a piggy back ride at constant speed Lying in bed on a Saturday morning (at constant speed) THEN The sum of the forces on you are ZERO, and your acceleration is ZERO. 2: B 3: C 16. E 17. C Position, Velocity, Acceleration 16% Mathematical Basics Vectors!!! 27% Position, Velocity, Acceleration (Know how to flow) 13% Circular Motion (𝛼, 𝜔, 𝜃, 𝑇, 𝑓, 𝑎𝑡𝑎𝑛 , 𝑎𝑟𝑎𝑑 , 𝑎𝑡𝑜𝑡 , 𝐹𝑟𝑎𝑑 ) 44% Forces, Work, Newton’s Laws Normal force, friction, springs Difference between Average and Instantaneous Ball thrown in the air INSTANTANEOUS AVERAGE INSTANT INTERVAL Here, take this: Position 𝑥 = 3𝑡 3 + 10𝑡 Find velocity at t=3 Find acceleration at t=4. 𝑦 = 𝑡 5 + 2𝑡 3 Look at the graph Velocity at t=2? Here, take this: Velocity From a graph Find the acceleration at t=2 Find the position change between t=1 s and t=5 s. Where is the object moving in the positive direction? 𝑣 = 9𝑡 2 + 10 What is the acceleration at t=4? Here, take this: Acceleration 𝑎 = 3𝑡 + 5 (we’re told the thing is moving at 10 m/s at t=0, assume it starts from the origin) Velocity at t=3? Position at t=2? Throw Ball (or bomb) Straight Up How does the velocity change? How does the acceleration change? Our friend projectile motion Speed at top of trajectory Equal to the horizontal component of velocity Constant acceleration equations REALLY USEFUL, but not used everywhere Relative Motion Position, Velocity, Acceleration 16% Mathematical Basics Vectors!!! 27% Position, Velocity, Acceleration (Know how to flow) 13% Circular Motion (𝛼, 𝜔, 𝜃, 𝑇, 𝑓, 𝑎𝑡𝑎𝑛 , 𝑎𝑟𝑎𝑑 , 𝑎𝑡𝑜𝑡 , 𝐹𝑟𝑎𝑑 ) 44% Forces, Work, Newton’s Laws Normal force, friction, springs 𝛼, 𝜔, 𝜃 http://www.youtube.com/watch?v=WKvh gkg2_dw&feature=related http://www.youtube.com/watch?v=zuVD 1OXquvo&feature=related 𝜃 = 3𝑡 2 + 5𝑡 𝜃 = 8𝑡 (R=30 m) 𝑣 = 𝜔𝑅, 𝑣2 𝑎𝑟𝑎𝑑 = 𝑅 𝑅 2𝜋𝑓 2 = 𝑅𝜔2 = A particle moves with constant angular velocity 3 rad/s in a circle of 5 m. What is the centripetal acceleration, and the velocity? 𝑎𝑡𝑎𝑛 = 𝑅𝛼 𝒂𝐭𝐨𝐭 = 𝐚𝑡𝑎𝑛 + 𝒂𝑟𝑎𝑑 These above are VECTORS!!! Centripetal Force http://www.youtube.com/watch?v=fSfVV z0eIis Position, Velocity, Acceleration 16% Mathematical Basics Vectors!!! 27% Position, Velocity, Acceleration (Know how to flow) 13% Circular Motion (𝛼, 𝜔, 𝜃, 𝑇, 𝑓, 𝑎𝑡𝑎𝑛 , 𝑎𝑟𝑎𝑑 , 𝑎𝑡𝑜𝑡 , 𝐹𝑟𝑎𝑑 ) 44% Forces, Work, Newton’s Laws Normal force, friction, springs F=ma Normal Force Is the normal force always equal to mg? Friction Mass-Mass-Force Problems Newton’s 3rd Law Your turn Inclined Plane Know what’s going on. What if you add friction? Selected Problem: Solve intuitively, or exactly Work Basics When is it positive? When is it negative? Work done by gravity What is the work done by gravity on a 5 kg block starting from rest as it moves downward 10 m? What is its speed at that time? Work Spring Two equations of importance: 𝐹 = −𝑘𝑥 𝐹= 1 − 𝑘𝑥 2 2 Work-Energy Theorem Power What is the power as an object moves 10 m under a force of 30 N from rest? The object has a mass of 2 kg. Tougher… What is your SI Leader’s name? Jacob 2. Jacub 3. Jakob 4. Jackob 5. Jackub 6. Jakub 7. Xenlor 1.