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PHYS 1443 – Section 501 Lecture #5

PHYS 1443 – Section 501 Lecture #5. Wednesday, February 4, 2004 Dr. Andrew Brandt. Motion in Two Dimensions Vector Components 2D Motion under constant acceleration Projectile Motion. Announcements.

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PHYS 1443 – Section 501 Lecture #5

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  1. PHYS 1443 – Section 501Lecture #5 Wednesday, February 4, 2004 Dr. Andrew Brandt Motion in Two Dimensions Vector Components 2D Motion under constant acceleration Projectile Motion PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

  2. Announcements • Your lab-sessions began Monday, Feb. 2. Be sure to attend the lab classes (20% of your grade) • Homework: 21/40 (out of 44) have submitted some answers • HW1 due midnight tonight • HW2 (Ch 3) due 2/11 • Read the text book! PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

  3. Vector Addition Find the resultant vector which is the sum of A=(2.0i+2.0j) and B =(2.0i-4.0j) OR Magnitude Direction Find the resultant displacement of three consecutive displacements: d1=(15i+30j +12k)cm, d2=(23i+14j -5.0k)cm, and d1=(-13i+15j)cm Magnitude PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

  4. Kinetic Quantities in 1d and 2d PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

  5. 2-dim Motion Under Constant Acceleration • Position vectors in x-y plane: • Velocity vectors in x-y plane: Velocity vectors in terms of acceleration vector Velocity vector components Putting them together in a vector form PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

  6. 2-dim Motion Under Constant Acceleration • How are the position vectors written in terms of velocity and acceleration vectors? Position vector components Putting them together in vector form Regrouping above results PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

  7. Example: 2-D Kinetic Eq.of Motion A particle starts at origin when t=0 with an initial velocity v=(20i-15j)m/s. The particle moves in the xy plane with ax=4.0m/s2. Determine the components of velocity vector at any time, t. Compute the velocity and speed of the particle at t=5.0 s. Magnitude PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

  8. Example in 2-D Kinetic EoM cont’d Direction Determine the x and y components of the particle at t=5.0 s. Can you write down the position vector at t=5.0s? PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

  9. Projectile Motion • 2-dim motion of an object under gravitational acceleration with the assumptions • Free fall acceleration, -g, is constant over the range of the motion • Air resistance and other effects are negligible • Superposition of two motions • Horizontal motion with constant velocity ( no acceleration ) • Vertical motion under constant acceleration ( g ) monkey in tree PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

  10. The only acceleration in this motion. It is a constant!! Projectile Motion PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

  11. Show that projectile motion is a parabola x-component y-component In projectile motion, the only acceleration is a gravitational one whose direction is always toward the center of the earth (downward). ax=0 Plug t into the above PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

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