PHYS 1443 Section 501 Lecture 5 Wednesday February

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

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 • HW 1 due midnight tonight • HW 2 (Ch 3) due 2/11 • Read the text book! Wednesday, Feb. 4, 2004 PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 2

Vector Addition Find the resultant vector which is the sum of A=(2. 0 i+2. 0 j) and B =(2. 0 i-4. 0 j) OR Magnitu de Directio n Find the resultant displacement of three consecutive displacements: d 1=(15 i+30 j +12 k)cm, d 2=(23 i+14 j -5. 0 k)cm, and d 1=(-13 i+15 j)cm Magnitu de Wednesday, Feb. 4, 2004 PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 3

Kinetic Quantities in 1 d and 2 d Quantities 1 Dimension 2 Dimension Displacement Average Velocity Inst. Velocity Average Acc. Inst. Acc. Wednesday, Feb. 4, 2004 PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 4

• 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 Wednesday, Feb. 4, 2004 a vector PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 5

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 Wednesday, Feb. 4, 2004 PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 6

Example: 2 -D Kinetic Eq. of Motion A particle starts at origin when t=0 with an initial velocity v=(20 i-15 j)m/s. The particle moves in the xy plane with ax=4. 0 m/s 2. Determine the components of velocity vector at any time, t. Compute the velocity and speed of the particle at t=5. 0 s. Magnitu de Wednesday, Feb. 4, 2004 PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 7

Example in 2 -D Kinetic Eo. M cont’d Directio n Determine the x and y components of the particle at t=5. 0 s. Can you write down the position vector at t=5. 0 s? Wednesday, Feb. 4, 2004 PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 8

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 ) 4, 2004 under PHYS 1443 -501, Spring 2004 –Wednesday, Vertical. Feb. motion Dr. Andrew Brandt constant acceleration ( g ) monkey in tree 9

Projectile Motion Wednesday, Feb. 4, 2004 The only acceleration in this motion. It is a PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 10

xcomponent Show that projectile motion is a parabola ycomponent 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 Wednesday, Feb. 4, 2004 PHYS 1443 -501, Spring 2004 Dr. Andrew Brandt 11