How many significant figures are there in 0.0143 10 -4 cm ?

1. How many significant figures are there in 0.0143 10-4 cm ? • 9 • 5 • 4 • 3

2. What does the prefix “M” in front of a unit mean? • Multiply by 10-6 • Multiply by 10-3 • Multiply by 103 • Multiply by 106

3. How many professors are there at Otterbein? • 10 • 100 • 1000 • 10000

4. Somebody claims the correct equation to calculate the position of an object from its (constant) velocity v and the elapsed time t is x(t) = x(t=0) + v t2. Can this be correct? • No • Yes • Not enough information

5. A red and an orange car make a race. When do they have the same velocity? x t A B At point A Between point A and B At point B Never

6. A red and an orange car make a race. Who wins? x t Red car Yellow car Insufficient information

7. Motion at constant acceleration • If (and only if) acceleration is constant, we can calculate x,v,a in any instant by using a(t) = a(t=0) v(t) = v(t=0) + a(t=0)t x(t) = x(t=0) + v(t=0)t + ½ a(t=0)t2 Green represent independent variable, darker hues initial values. Additionally, we may use v2(t) = v2(t=0) + 2 a(t=0) [x(t)-x(t=0)]

8. In the equation below, the following is NOT true… v2(t) = v2(t=0) + 2 a(t=0) [x(t)-x(t=0)] • We need to know the position of the object in the moment at which we want to calculate its velocity • We need to know the initial velocity of the object to calculate its velocity at time t • This equation is only true if the acceleration of the object is constant. • The equation is only true for positive velocities, since we have to take the square root eventually.

9. v(t) v(t2) v(t1) Example for derivation ∆v ∆t • Constant acceleration means linear rising (or falling) velocity  velocity at later time is velocity at earlier time plus slope times time elapsed. • Slope of velocity curve is acceleration v(t2) = v(t1) + a(t2-t1) t1 t2 t

10. A car accelerates at constant (non-zero) rate. Which of the following motion diagrams is NOT correct? v a t t v x t t

11. An dropped object accelerates downward at 9.8 m/s2. If instead you throw it downward, its downward acceleration after release is … • less than 9.8 m/s2 • exactly 9.8 m/s2 • more than 9.8 m/s2 • Insufficient information

12. Solving Kinematic Problems • Read problem carefully • Draw diagram • List knowns and unknowns • What physics principles do apply? • Find equations that do apply • Solve algebraically (with variables, not values!) • Calculate numerically • Check results: Numbers reasonable? Units correct?

13. Vectors • “Directions with magnitudes” that can be shifted around

14. Addition: Tail-to-Tip or Parallelogram

15. Subtraction by adding negative vector a-b = a + (-b)

16. 3D Vectors • 3D vector as a sum of multiples of the three unit vectors i,j,k • Example: a=1.5 i + 2.5j +3 k

17. To which quadrant does the following vector belong? A = - 4 i + 6.5 j • 1st Quadrant • 2nd Quadrant • 3rd Quadrant • 4th Quadrant

18. To which quadrant does the following vector belong? |B| = 4.5, φB = -45º • 1st Quadrant • 2nd Quadrant • 3rd Quadrant • 4th Quadrant

19. To which quadrant does the following vector belong? |c| = 4.5m/s, φc = 3.10 • 1st Quadrant • 2nd Quadrant • 3rd Quadrant • None of the above

20. To which quadrant does the following vector belong? • 1st Quadrant • 2nd Quadrant • 3rd Quadrant • None of the above

21. To which quadrant does the following vector belong? • 1st Quadrant • 2nd Quadrant • 3rd Quadrant • Not enough information

22. What is the length of the following vector? • -1 m/s • 1 m/s • 5 m/s • 25 m2/s2

23. What is the length of this vector? • Upper formula • Middle formula • Bottom formula • None of the above

24. Which is a correct statement concerning this vector? |B| = 4.5, φB = -45º • Its magnitude is negative • Its x component is negative • Its y component is positive • Its x and y component have the same absolute value

25. Projectile Motion

26. By aiming a gun higher (increasing the angle of the barrel w.r.t. the x-axis), I achieve the following: • Higher initial position • Larger initial y-component of velocity • Higher initial velocity • None of the above

27. gutter A gun is accurately aimed at a dangerous terrorist hanging from the gutter of a building. The target is well within the gun’s range, but the instant the gun is fired and the bullet moves with a speed v0, the terrorist lets go and drops to the ground. What happens? v0 • The bullet hits the terrorist regardless of the value of v0 • The bullet hits the terrorist only if v0 is large enough • The bullet misses the terrorist • Not enough information gun

28. A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic paths shown, which ship gets hit first? • A • B • Both at the same time • Need more information A B

29. Circular Motion

30. An object at the end of an r=1m string in circular motion completes 10 revolutions in one second. How long does each revolution take? • (2 π r)(1s) • 1s/(2π r) • 0.1 s • Need more information

31. An object at the end of an r=1m string in circular motion completes 10 revolutions in one second. What is its speed? • 6.3 m/s • 3.1 m/s • 63 m/s • 0.31 m/s

32. An object at the end of an r=1m string in circular motion completes 10 revolutions in one second. What is its frequency? • 10 Hz • 1 Hz • 1/10 Hz • 3.14 Hz

33. Newton’s first Law • In the absence of a net external force, a body either is at rest or moves with constant velocity. • Motion at constant velocity (may be zero) is thus the natural state of objects, not being at rest. Change of velocity needs to be explained; why a body is moving steadily does not.

34. Mass & Weight • Mass is the property of an object • Weight is a force, e.g. the force an object of certain mass may exert on a scale

35. Mass: On the surface of the Moon a standard block of lead … • … has a different mass • … has a different weight • Its weight is unchanged, but g has a different value • Need more information

36. Newton’s first law states that objects remain at rest only when they no net force acts on them. A book on a table is subject to the force of gravity pulling it down. Why doesn’t it move? • Newton’s first law does not apply (obstacle!) • There must be another force opposing gravity • Table shelters book from force of gravity • Not enough information

37. Newton’s second Law • The net external force on a body is equal to the mass of that body times its acceleration F = ma. • Or: the mass of that body times its acceleration is equal to the net force exerted on it ma = F • Or: a=F/m • Or: m=F/a

38. Newton II: calculate Force from motion • The typical situation is the one where a pattern of Nature, say the motion of a projectile or a planet is observed: • x(t), or v(t), or a(t) of object are known, likely only x(t) • From this we deduce the force that has to act on the object to reproduce the motion observed

39. Calculate Force from motion: example • We observe a ball of mass m=1/4kg falls to the ground, and the position changes proportional to time squared. • Careful measurement yields: xball(t)=[4.9m/s2] t2 • We conclude v=dx/dt=2[4.9m/s2]t a=dv/dt=2[4.9m/s2]=9.8m/s2 • Hence the force exerted on the ball must be • F = 9.8/4 kg m/s2 = 2.45 N • Note that the force does not change, since the acceleration does not change: a constant force acts on the ball and accelerates it steadily.

40. Newton II: calculate motion from force • If we know which force is acting on an object of known mass we can calculate (predict) its motion • Qualitatively: • objects subject to a constant force will speed up (slow down) in that direction • Objects subject to a force perpendicular to their motion (velocity!) will not speed up, but change the direction of their motion [circular motion] • Quantitatively: do the (vector) algebra!

41. Newton II: calculate motion from force • Say a downward force of 4.9N acts on a block of 1 kg (we call the coordinate y and start at y=0) • We conclude that the block will be accelerated: ay = F/m= -4.9N / 1kg = -4.9 m/s2 • We use this constant acceleration to calculate y = -1.225m/s2 t2 + b t + c , where b &c are constants, c=0 Q: What physical situation is this?

42. Newton II: calculate mass from force and acceleration • Pretty simple, if you know force and acceleration we have m=F/a