1. Chapter 2
Motion
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2. What is Motion?

3. Describing Motion Three basic concepts Applications
Position
Speed and velocity
Acceleration
Applications
Horizontal motion (along a line)
Vertical motion (falling objects)
Compound motion (2-D)

4. Explaining Motion Basic ideas Applications Forces Momentum and impulse
Inertia and mass
Newton’s laws
Applications
Momentum and impulse
Circular motion
Newton’s law of gravitation
Earth satellites

5. Measuring Motion Two fundamental components: Change in position
Change in time
Three important combinations of length and time:
Speed
Velocity
Acceleration

6. Speed Change in position with respect to time
Average speed - most common measurement
Instantaneous speed - time interval approaches zero

7. Example: Average Speed
Calculate average speed between trip times of 1 h and 3 h

8. Velocity
Describes speed (How fast is it going?) and direction (Where is it going?)
Graphical representation using vectors:
length = magnitude; arrowheads = direction

9. Acceleration Rate at which motion changes over time Speed can change
Direction can change
Both speed and direction can change

10. Movement relative to some reference, usually a stationary object.
Problem (A) 11
How long will be required for a car to go from a speed of 20.0 m/s to a speed of 25.0 m/s if the acceleration is 3.0 m/s2?
What is Motion?
Movement relative to some reference, usually a stationary object.

11. Uniform Acceleration Constant, straight line acceleration
Average velocity simply related to initial and final velocities in this case

12. Movement relative to some reference, usually a stationary object.
Example Problem 2.6
Find acceleration (deceleration) of the automobile in Example 2.5 (car moving at 25.0 m/s and stops in 10.0 seconds).
What is Motion?
Movement relative to some reference, usually a stationary object.

13. Forces - Historical Background
Aristotle
Heavier objects fall faster
Objects moving horizontally require continuously applied force
Relied on thinking alone
Galileo and Newton
All objects fall at the same rate
No force required for uniform horizontal motion
Reasoning based upon measurements

14. Force A push or pull capable of changing an object’s state of motion
Overall effect determined by the (vector) sum of all forces - the “net force” on the object

15. Fundamental Forces Most basic of all interactions Gravitational
Mass interactions
Motions of planets, stars, galaxies…
Electromagnetic
Charge interactions
Electricity and magnetism
Atoms and molecules, chemistry
3. Weak force
Involved in certain nuclear reactions
4. Strong force
Holds nuclei together

16. Horizontal Motion on Land
“Natural motion” question: Is a continuous force needed to keep an object moving?
No, if there are no unbalanced retarding forces
Inertia - measure of an object’s tendency to resist changes in its motion (including rest)

17. Balanced and Unbalanced Forces
Motion continues unchanged w/o unbalanced forces
Retarding force decreases speed
Boost increases speed
Sideways force changes direction

18. Falling Objects
Free fall - falling under influence of gravity w/o air resistance
Distance proportional to time squared
Speed increases linearly with time
Trajectories exhibit up/down symmetries
Acceleration same for all objects

19. Movement relative to some reference, usually a stationary object.
Problem (A) 16
A ball thrown straight up climbs for 3.0 s before falling. Neglecting air resistance, with what velocity was the ball thrown?
What is Motion?
Movement relative to some reference, usually a stationary object.

20. Movement relative to some reference, usually a stationary object.
Free Fall
Acceleration due to gravity (free fall neglecting air resistance)
g = 9.8 m/s2 (downward)
= 32 ft/s (downward)
What is Motion?
Movement relative to some reference, usually a stationary object.

21. Summary of Motion Equations (see page 55)
Average velocity
vavg = d / t vavg = (vf + vi) / 2
Acceleration
a = (vf - vi) / t vf = vi + at t = (vf - vi) / a
Free fall distance from rest
d = ½at where, a = g = 9.8 m/s2
What is Motion?
Movement relative to some reference, usually a stationary object.

22. Compound Motion Three types of motion: Vertical motion
Horizontal motion
Combination of 1. and 2.
Projectile motion
An object thrown into the air
Basic observations:
Gravity acts at all times
Acceleration (g) is independent of the object’s motion

23. Projectile Motion Vertical projectile Slows going up Stops at top
Accelerates downward
Force of gravity acts downward throughout
Horizontal projectiles
Horizontal velocity remains the same (neglecting air resistance)
Taken with vertical motion = curved path

24. Fired Horizontally Versus Dropped
Vertical motions occur in parallel
Arrow has an additional horizontal motion component
They strike the ground at the same time!

25. Example: Passing a Football
Assume only force = gravity (down)
Vertical velocity decreases, stops and then increases
Horizontal motion is uniform
Combination of two motions = parabola

26. Three Laws of Motion First detailed by Newton (1564-1642 AD)
Concurrently developed calculus and a law of gravitation
Essential idea – forces

27. Newton’s 1st Law of Motion
“Law of inertia”
Every object retains its state of rest or its state of uniform straight-line motion unless acted upon by an unbalanced force
Inertia resists any changes in motion

28. Newton’s 2nd Law of Motion
“F = ma”
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to the mass of the object.
Depends both on the net force applied and the mass of the object.

29. Newton’s 2nd Law of Motion
Forces cause accelerations
Units = Newtons (N), kg-m/s2
Proportionality constant = mass
More force, more acceleration
More mass, less acceleration

30. Examples - Newton’s 2nd More mass, less acceleration
She’s not pedaling
where, m = mb + mg

31. Examples - Newton’s 2nd Focus on net force Net force zero here
Air resistance + tire friction match applied force
Result: no acceleration; constant velocity

32. Movement relative to some reference, usually a stationary object.
Problem (A) 19
What is the resulting acceleration when an unbalanced force of 100 N is applied to a 5 kg object?
What is Motion?
Movement relative to some reference, usually a stationary object.

33. Weight and Mass
Mass = quantitative measure of inertia; the amount of matter
Weight = force of gravity acting on the mass
Pounds and newtons measure of force
Kilogram = measure of mass

35. Newton’s 3rd Law of Motion
Source of force - other objects
3rd law - relates forces between objects
“Whenever two objects interact, the force exerted on one object is equal in size and opposite in direction to the force exerted on the other object.”

36. Momentum Important property closely related to Newton’s 2nd law
Includes effects of both velocity (motion) and mass (inertia)

37. Conservation of momentum
The total momentum of a group of interacting objects remains the same in the absence of external forces
Applications: analyzing action/reaction interactions, collisions

38. Movement relative to some reference, usually a stationary object.
Problem (A) 22
A 15 g bullet is fired with a velocity of 200 m/s from a 6 kg rifle. What is the recoil velocity of the rifle?
What is Motion?
Movement relative to some reference, usually a stationary object.

39. Impulse A force acting on an object for some time t
An impulse produces a change in momentum
Applications: padding for elbows and knees, airbags, protective plastic barrels on highways

40. Forces and Circular Motion
Circular motion = accelerated motion (direction changing)
Centripetal acceleration present
Centripetal force must be acting
Centrifugal force - apparent outward tug as direction changes
If centripetal force ends:
motion = straight line

41. Movement relative to some reference, usually a stationary object.
Problem (A) 30
How much centripetal force is needed to keep a 0.20 kg ball on a 1.50 m string moving in a circular path with a speed of 3.0 m/s?
What is Motion?
Movement relative to some reference, usually a stationary object.

42. Newton’s Law of Gravitation
“Universal Law of Gravitation”
Every object in the universe is attracted to every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distances between them.
F = G m1m2 / d (Eq. 2.12)

43. Newton’s Law of Gravitation
Attractive force between all masses
Directly proportional to product of the masses
Inversely proportional to separation distance squared
Explains why g=9.8m/s2
Provides centripetal force for orbital motion

44. Application of Forces Fdrag = f(area,v,ρatm) Fmass = mg
Fnet = ΣFi = manet
-Fthrust = Fupward =
Mass decreases with time
Fthrust

45. Application of Forces At liftoff: gross mass = 2.04 x 106 kg
total thrust = MN
assume drag = 0 N
Fmass = - mg = -(2.04x106)(9.81)
Fupward = -Fthrust = MN
Fnet = ΣFi = manet = MN
anet = 5.0 m/s2
d(1s) = ½ at2 = 2.5 m (~8.2 ft)
Mass change = 10,400 kg/s