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Welcome back to Physics 211

Welcome back to Physics 211. Today’s agenda: Kinetic energy, gravitational and elastic potential energy Collisions Please read Ch. 11. Work, Energy. Newton’s Laws are vecto r equations

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Welcome back to Physics 211

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  1. Welcome back to Physics 211 Today’s agenda: Kinetic energy, gravitational and elastic potential energy Collisions Please read Ch. 11 PHY211 Fall 2011 Lecture 11-1

  2. Work, Energy • Newton’s Laws are vector equations • Sometimes easier to relate speed of a particle to how far it moves under a force – a single equation can be used – need to introduce concept of work • Leads to concept of energy PHY211 Fall 2011 Lecture 11-1

  3. What is work? • Assume constant force in 1D • Consider: vf2 = vi2 + 2ay • Multiply by m/2  (1/2)mvf2 - (1/2)mvi2 = may • But: F = ma  (1/2)mvf2 - (1/2)mvi2 = Fy PHY211 Fall 2011 Lecture 11-1

  4. Work-Kinetic Energy theorem (1) (1/2)mvf2 - (1/2)mvi2 = Fy Points: • W = Fy defineswork done on particle = force times displacement • K = (1/2)mv2 defineskinetic energy = 1/2 mass times square of v PHY211 Fall 2011 Lecture 11-1

  5. Work-Kinetic Energy demo • Cart, force probe, and motion detector • Plot v2vs. x – gradient 2F/m • constant F (measure) -- pulling with string • Weigh cart and masses in advance PHY211 Fall 2011 Lecture 11-1

  6. Two carts accelerated by constant force through same distance PHY211 Fall 2011 Lecture 11-1

  7. Conclusions from experiment • Although the motion of the two carts looks very different (i.e., different amounts of time, accelerations, and final speeds), there is a quantity that is the same for both at the end of the motion. It is (1/2) mv2 and is called the (final) kinetic energy of the carts. • Moreover, this quantity happens to have the same value as Fy, which is given the name work. • Remember, F is really Fnet and IS a vector! PHY211 Fall 2011 Lecture 11-1

  8. KE and PE (for object in freefall) PHY211 Fall 2011 Lecture 11-1

  9. KE and PE (general case) (1) Recall Chain Rule y = u10 where u = 2x3 – 5x2 + 4 What is dy/dx? PHY211 Fall 2011 Lecture 11-1

  10. Choosing the correct ‘zero’ for Ug • Result of integral of –mgdy  -mg(yf-yi) • Means U = -mg(yf-yi) • Propose Ug = mgy or Ug = mgy + C • If position changes, U has same value! PHY211 Fall 2011 Lecture 11-1

  11. Path dependence PHY211 Fall 2011 Lecture 11-1

  12. Conservation of Energy • Kf + Ugf = Ki + Ugi • True for any particle moving along any frictionless surface! • Mechanical energy Emech = K + U • Emech = K + U = 0 PHY211 Fall 2011 Lecture 11-1

  13. Two identical blocks slide down two frictionless ramps. Both blocks start from the same height, but block A is on a steeper incline than block B. The speed of block A at the bottom of its ramp is less than the speed of block B. equal to the speed of block B. greater than the speed of block B. “Can’t tell.” PHY211 Fall 2011 Lecture 11-1

  14. Conservation of Energy in Mechanical Systems • Double ramp • Large pendulum • 4 steel balls + ramps PHY211 Fall 2011 Lecture 11-1

  15. When released from the top of the longer ramp, the ball will • Not reach the end of the short ramp. • Roll off the top of the short ramp. • Just reach the top of the short ramp. • Not enough info to determine this. PHY211 Fall 2011 Lecture 11-1

  16. When released from rest next to the student’s nose, the ball will • Not come close to the student’s nose • Just barely reach the student’s nose • Likely to break the student’s nose • Not enough information to determine PHY211 Fall 2011 Lecture 11-1

  17. Demo: stretch a spring m L L-L0 0 1 2 3 4 5 Restoring forces and stretched springs PHY211 Fall 2011 Lecture 11-1

  18. Hooke’s Law • Plot F vs. s  straight line • Implies F = k s where k is spring constant (units of k?) • (Fsp)s opposite to s • (Fsp)s = -ks; exerts a variable force PHY211 Fall 2011 Lecture 11-1

  19. Elastic Potential Energy PHY211 Fall 2011 Lecture 11-1

  20. Conservation of Energy (again) • Kf + Usf = Ki + Usi (energy conserved) • True for any particle moving without friction on ideal spring • Mechanical energy Emech = K + U • Emech = K + Ug + Us PHY211 Fall 2011 Lecture 11-1

  21. Perfectly Elastic Collisions • Sometimes Kf < Ki (non-bouncy ball) • If Kf = Ki, then perfectly elastic collision (bouncy ball) • Objects do NOT stick! • Momentum conservation not sufficient PHY211 Fall 2011 Lecture 11-1

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