1. Physics 2.2

2. Speed and Velocity, Distance and Displacement:
Speed is a scalar quantity.
Velocity is a vector quantity.
Distance is a scalar.
Displacement is a vector.

3. Solve:
A car begins to ride at 20 m/s north and finishes at 30 m/s north. What is the average velocity?
Average velocity= initial + final velocity 2

4. Graphs you should know:
Distance vs Time
Slope = ?
Velocity vs Time
Area = ?

5. Distance vs Time

6. Velocity vs Time

7. Velocity vs Time
We can deduct interesting information from a velocity-time graph: The slope of the line is the acceleration, but the area under the line is the displacement!
Let's see how to determine the displacement an object undergoes during a given time:

8. Free Fall: Use the Kinematic equations for constant acceleration.
Use 0 m/s for initial and starting velocities, and g for acceleration (-9.81 m/s).
After 1 second of free fall, what is the velocity of an object in free fall? 2 seconds?

9. Time, Distance, and Velocity of an Object in Free Fall:
Top of Cliff
4.9 m
19.6 m
44.1 m
78.5 m
Velocity
v = 0 m/s
v = 9.81 m/s
v = 19.6 m/s
v = 29.4 m/s
v = 39.2 m/s

10. Statics: Forces which act on objects
Combined concurrent forces are called the resultant force

11. Question?
Two concurrent forces on and object have a maximum resultant of 45 newtons and a minimum resultant of 5 newtons. What is the magnitude of each of these forces?
Solution: find the resultants in the same and opposite directions.
(20 N and 25 N).

12. Finding the Resultant Graphically:
Parallelogram method:
Draw a mirror image of the two force vectors opposite them.
Measure the resultant.
Triangle method:
Draw the second force vector from the head of the first.

13. Parellelogram

14. Triangle-method

15. Equilibrium Static equilibrium: Dynamic equilibrium:
An object at rest.
Dynamic equilibrium:
An object with the net forces acting on it are equal to zero. Ex/ an object in free fall that has reached terminal velocity.

16. Free body diagram

17. Sir Isaac Newton’s Three Laws:
An object in motion tends to stay in motion, unless acted upon by a force.
When a force acts on an object, it will accelerate in the direction of that force
When a force acts upon and object, that object will act with and equal and opposite force.

18. More…
Law of Inertia.
F = ma
F12 = F21

19. ??? Which object has the most inertia?
A 0.1 kg baseball travelling 20 meters/second.
A 10 kg sled at rest.
A 5 kg bowling ball traveling 3 meters/ second.

20. ???
An 8 N force is applied to a 4 kg block on a frictionless table. What is the magnitude of the block’s acceleration?
F = ma
2 m/s²

21. ???
Which unit is equivalent to a newton per kg?
m/s²
W/m
j·s
kg·m/s

22. Projectile moving Horizontally:
When an object is thrown from a height, there is both a horizontal and vertical component.
Find time in the air with:
dy = vit + ½at²

23. ???
A baseball is thrown horizontally at 25 m/s from a cliff 45 meters above the level ground. How far from the base of the cliff does the ball hit the ground?
dx = vxt
dy = vit + ½at²

24. A Projectile fired at an Angle:
Set up two sets of data:
Horizontal component x;
Vertical component y;
Use the kinematic equations to solve for both the horizontal and vertical components.

25. ???
A ball is thrown in the air at a 30˚ angle from the horizontal at a speed of 100 m/s. Find:
Time in the air
Max height
range

26. Circular Motion Centripetal acceleration Centripetal force a = v²/r
F = mv²/r

27. ???
A 2.0 E3 kg car travels at a constant speed of 12 m/s around a circular curve of radius 30. meters.
What is the magnitude of the centripetal acceleration of the car as it goes around the curve?
What direction is the centripetal force directed?

28. Newton’s Universal Law of Gravity
F = Gm1m2/r²
Weight = mg

29. Friction Static friction: object is not moving
Fs = Us x Fn
Kinetic friction: object is moving
Fk = Uk x Fn

30. Impulse and momentum Impulse is the change in momentum.
J = Ft = ∆p
Momentum is mass x velocity.
p = mv

31. A Simple pendulum:
Does mass effect the period?

32. More pendulum stuff: