Force and Motion

1. Force and Motion PHYS 1090 Unit 2

2. Force and Motion • Fundamentals: position, mass and time • Velocity = rate of change of position

3. Motion Graphs (one dimension) Dr Dr position Dt Dt Velocity = = slope! time

4. Steeper slope Dr position Dt time • Greater Dr in same Dt • Faster • Higher velocity

5. Horizontal p-T plot position time • Dr = 0 • Slope = 0 • Velocity = 0

6. Downward slope position Dr Dt time • rdecreases as t increases • Backward motion • Negative velocity

7. Curved p-T plot position time • Slope is not constant • Velocity changes What motion would have a p-T plot like this?

8. 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

9. Cart Coasting on a Ramp r v a t

10. Newton’s First Law • Exemplified by ball-on-tray activity

11. 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

12. Force • Any influence changing an object’s velocity (speed or direction) • Examples: • Gravity • Friction • Contact support • Any push or pull

13. 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

14. 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

15. 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

16. Drag Races Plot F2 m2 F1 m1 Sources of Error: • Friction • Mis-matched masses • Sloping tracks

17. 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

18. 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

19. 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

20. 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

21. Vectors and Scalars • Vector: quantity needing a direction to fully specify (direction + magnitude) • Scalar: directionless quantity

22. these are identical Represent as Arrows direction: obvious magnitude: length location is irrelevant

23. A A C B B A +B=C Add Vectors Head-to-tail (not in your book)

24. 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

25. 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

26. 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