1. Physics Subject Area Test
MECHANICS:
DYNAMICS

2. Dynamics: Newton’s Laws of Motion
Newton’s First Law

3. Force Dynamics – connection between force and motion
Force – any kind of push or pull
required to cause a change in motion (acceleration)
measured in Newtons (N)

4. Dynamics: Newton’s Laws of Motion
Newton’s First Law of Motion

5. Newton’s First Law of Motion
First Law – Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.
First Law – (Common) An object at rest remains at rest, and a object in motion, remains in motion unless acted upon by an outside force.

6. Newton’s First Law of Motion
Newton’s Laws are only valid in an Inertial Frame of Reference
For example, if your frame of reference is an accelerating car – a cup in that car will slide with no apparent force being applied

7. Newton’s First Law of Motion
An inertial frame of reference is one where if the first law is valid
Inertia – resistance to change in motion

8. Dynamics: Newton’s Laws of Motion
Mass

9. Mass Mass – a measurement of inertia
A larger mass requires more force to accelerate it
Weight – is a force, the force of gravity on a specific mass

10. Dynamics: Newton’s Laws of Motion
Newton’s Second Law

11. Newton’s Second Law
Second Law – acceleration is directly proportional to the net force acting on it, and inversely proportional to its mass.
-the direction is in the direction of the net force
Easier to see as an equation
more commonly written

12. SF – the vector sum of the forces
Newton’s Second Law
SF – the vector sum of the forces
In one dimension this is simply adding or subtracting forces.

13. Free Body Diagram
The most important step in solving problems involving Newton’s Laws is to draw the free body diagram
Be sure to include only the forces acting on the object of interest
Include any field forces acting on the object
Do not assume the normal force equals the weight
F table on book
F Earth on book

14. Free Body Diagram

15. Objects in Equilibrium
Objects that are either at rest or moving with constant velocity are said to be in equilibrium
Acceleration of an object can be modeled as zero:
Mathematically, the net force acting on the object is zero
Equivalent to the set of component equations given by

16. Equilibrium, Example 1
A lamp is suspended from a chain of negligible mass
The forces acting on the lamp are
the downward force of gravity
the upward tension in the chain
Applying equilibrium gives

17. Equilibrium, Example 2
A traffic light weighing 100 N hangs from a vertical cable tied to two other cables that are fastened to a support. The upper cables make angles of 37 ° and 53° with the horizontal. Find the tension in each of the three cables.
Conceptualize the traffic light
Assume cables don’t break
Nothing is moving
Categorize as an equilibrium problem
No movement, so acceleration is zero
Model as an object in equilibrium

18. Equilibrium, Example 2 Need 2 free-body diagrams
Apply equilibrium equation to light
Apply equilibrium equations to knot

19. Inclined Plane
Suppose a block with a mass of 2.50 kg is resting on a ramp. If the coefficient of static friction between the block and ramp is 0.350, what maximum angle can the ramp make with the horizontal before the block starts to slip down?

20. Inclined Plane
Newton 2nd law:
Then So

21. Multiple Objects
A block of mass m1 on a rough, horizontal surface is connected to a ball of mass m2 by a lightweight cord over a lightweight, frictionless pulley as shown in figure. A force of magnitude F at an angle θ with the horizontal is applied to the block as shown and the block slides to the right. The coefficient of kinetic friction between the block and surface is μk. Find the magnitude of acceleration of the two objects.

22. We all remember the fun see-saw of our youth.
Center of mass
We all remember the fun see-saw of our youth.
But what happens if . . .

23. Balancing Unequal Masses
Moral
Both the masses and their positions affect whether or not the “see saw” balances.

24. Balancing Unequal Massesd1 d2
Need:
M1 d1 = M2 d2

25. Changing our Point of View
The great Greek mathematician Archimedes said, “give me a place to stand and I will move the Earth,” meaning that if he had a lever long enough he could lift the Earth by his own effort.

26. We can think of leaving the masses in place and moving the fulcrum.
In other words. . .
We can think of leaving the masses in place and moving the fulcrum.
It would have to be a pretty long see-saw in order to balance the school bus and the race car, though!

27. In other words. . . M1 M2 d1 d2
(We still) need:
M1 d1 = M2 d2