1. Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 5,6

2. If a=a c =Const:

3. A “police car” problem x=0 x1x1 x2x2 V 3 =20m/s a=0 a p =kt x 2 – x 1 = 3.5 km V 1 =30m/sV 2 =40m/s You start moving from rest with constant acceleration. There is a police car hiding behind the tree. The policeman has a metric radar. He measures your velocity to be 30 m/s. While the policeman is converting m/s to mph, you continue accelerating. You meet another police car. This policeman measures your velocity to be 40 m/s. You also notice the police, drop your velocity to 20 m/s and start moving with a constant velocity. However, it is too late. This police car starts chasing you with acceleration kt (k is a constant). After some distance he catches you. a=const V(t=0)=0

4. A “police car” problem x=0 x1x1 x2x2 V 3 =20m/s a=0 a p =kt x 2 – x 1 = 3.5 km V 1 =30m/sV 2 =40m/s 1. What was your acceleration before you meet the second police car? 2. How long did you travel from x 1 to x 2 ? 3. Find x 1 4. At which distance does the police car catch you? 5.Convert the velocity from m/s to mph a=const V(t=0)=0

5. An object’s velocity is measured to be, where  =4.00 m/s and  =2.00 m/s 3. At t=0 the object is at x=0. Calculate the object’s position and acceleration as functions of time.

6. Free fall g-positive! On planet Earth, if you neglect air resistance, any body which is dropped will experience a constant acceleration, called g, independent of its size or weight. g=9.8 m/s 2 =32 ft/s 2

7. a v a = g = const for all bodies independently on their masses Galileo Galilei (1564-1624), the basic law of motion

8. Galileo's “Law of Falling Bodies” distance (S) is proportional to time (T) squared

9. Galileo’s notes

10. Free fall

13. A person throws a ball upward into the air with an initial velocity of 15 m/s. Calculate a)How much time does it take for the ball to reach the maximum height? b)How high does it go? c)How long is the ball in the air before it comes back to the thrower’s hands d)The velocity of the ball when it returns to the thrower’s hand e)At what time t the ball passes a point 8.00 m above the person’s hand

14. A ball is thrown vertically upward with a velocity of magnitude v 1 from a window at height H. What is the ball’s position and velocity at any time moment? How long does it take to reach the highest point? How long does it take to reach the ground? What is the velocity of the ball when it hits the ground?

15. A ball is thrown vertically upward with a velocity of magnitude v 1 from a window at height H. In addition to gravity acting on the ball there is another force so that the acceleration in the up direction is –g+  t where  is a constant and t is the time. What is the ball’s position when the acceleration is zero?

16. A rat is running with known constant velocity v 1 when she passes you at t=0. You start from rest with acceleration c 1 where c 1 is an unknown constant. What does c 1 have to be in order to catch the rat after she has gone a distance D?

17. Falling with air resistance

19. Terminal Velocity with Coffee Filters where is the resistance force. 1.A penny and a quarter dropped from a ladder land at the same time (air resistance is negligible). 2.A coin dropped in a coffee filter from a ladder lands later than a coin without coffee filter (the terminal velocity is smaller for larger cross-section area). 3.A quarter dropped in a coffee filter will land faster than a penny in a coffee filter (the terminal velocity is larger for larger mass) 4.Two identical coins dropped in coffee filters of different diameters land at different times (the terminal velocity is smaller for larger cross-section area).

20. Resistance force: A – area of the projectile For a spherical projectile in air at STP: Terminal velocity: A 70-kg man with a parachute: v T ~ 5 m/s A 70-kg man without a parachute: v T ~ 70 m/s

21. Have a great day! Reading: Chapters 3,4