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Force and Motion. PHYS 1090 Unit 2. Force and Motion. Fundamentals: position , mass and time Velocity = rate of change of position. Motion Graphs (one dimension). D r. D r. position. D t. D t. Velocity = . = slope!. time. Steeper slope. D r. position. D t. time.

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force and motion

Force and Motion

PHYS 1090 Unit 2

force and motion1
Force and Motion
  • Fundamentals: position, mass and time
  • Velocity = rate of change of position
motion graphs one dimension
Motion Graphs (one dimension)

Dr

Dr

position

Dt

Dt

Velocity =

= slope!

time

steeper slope
Steeper slope

Dr

position

Dt

time

  • Greater Dr in same Dt
  • Faster
  • Higher velocity
horizontal p t plot
Horizontal p-T plot

position

time

  • Dr = 0
  • Slope = 0
  • Velocity = 0
downward slope
Downward slope

position

Dr

Dt

time

  • rdecreases as t increases
  • Backward motion
  • Negative velocity
curved p t plot
Curved p-T plot

position

time

  • Slope is not constant
  • Velocity changes

What motion would have a p-T plot like this?

acceleration
Acceleration
  • Rate of change of velocity

a =

Dv

  • A change in velocity with time
  • Rate of change of a rate of change
  • Another level of abstraction

Dt

newton s first law
Newton’s First Law
  • Exemplified by ball-on-tray activity
newton s first law1
Newton’s First Law

“An object at rest will remain at rest, and an object in motion will continue in motion in a straight line and at a constant speed unless acted on by an outside force.”

  • Specifies not only speed, but also direction of motion
  • Force changes an object’s motion
force
Force
  • Any influence changing an object’s velocity (speed or direction)
  • Examples:
    • Gravity
    • Friction
    • Contact support
    • Any push or pull
newton s second law
Newton’s Second Law

“The acceleration of an object is directly proportional to the net force applied to it, and inversely proportional to the object’s mass.”

F

a=

m

  • F = net force = sum of all external forces on the object
rail carts
Rail Carts
  • For the same mass, a greater force gives a greater acceleration
  • The greater the cart’s mass, the slower the acceleration from the same force
  • The greater the cart’s mass, the greater the force needed to achieve the same acceleration
drag races plot
Drag Races Plot

F2

F2

m2

F1

F2

m2

  • F2, m2 adjusted so a2 = a1
  • a1 = F1/m1; a2 = F2/m2

F1

m1

m1

m2

m1

F1

=

=

  • Plot should be a straight line through (0,0) with slope = 1
drag races plot1
Drag Races Plot

F2

m2

F1

m1

Sources of Error:

  • Friction
  • Mis-matched masses
  • Sloping tracks
force of gravity
Force of Gravity
  • Newton’s second law: the more massive something is, the more force is needed to accelerate it

F = ma

  • Gravity: the more massive something is, the harder gravity pulls on it

F = mg

acceleration by gravity
Acceleration by Gravity
  • Newton’s second law: a = F/m
  • Gravity: F = mg

So,

= g

mg

F

a =

=

  • All objects fall at the same rate (if gravity is the only force acting)!
  • Acceleration depends on g, not m

m

m

vectors
Vectors
  • Position, velocity, acceleration, force all have direction
  • Newton’s second law: a = F/m
  • a and F have direction; m does not
  • a and F are always in the same direction
stick ball
Stick Ball
  • Push in direction ofv: speeds up
  • Push in direction oppositev: slows down, stops, or reverses
  • Push at an angle tov: a and v in different directions

final v

a

v

vectors and scalars
Vectors and Scalars
  • Vector: quantity needing a direction to fully specify (direction + magnitude)
  • Scalar: directionless quantity
represent as arrows

these are identical

Represent as Arrows

direction: obvious

magnitude: length

location is irrelevant

add vectors

A

A

C

B

B

A +B=C

Add Vectors

Head-to-tail (not in your book)

how to add vectors
How to Add Vectors
  • Place following vector’s tail at preceding vector’s head
  • Resultant starts where the first vector starts and ends where the last vector ends
oblique force
Oblique Force
  • Push at an angle tov: a and v in different directions
  • Add Dv = aDt to initialv to find final v

final v

a

Dv = aDt

v

Initial v

uniform circular motion
Uniform Circular Motion
  • Speed is constant, direction changes
  • This still means velocity changes with time
  • The object accelerates
  • Acceleration requires a nonzero net force
  • Acceleration and force are toward the center of the circular path