From Rileys Dynamics Chapter 16 Kinetics of Rigid Bodies: Newtons Laws.
Physics Subject Area Test MECHANICS: DYNAMICS. Newtons First Law.
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Transcript of Physics Subject Area Test MECHANICS: DYNAMICS. Newtons First Law.
Physics Subject Area Test
MECHANICS:DYNAMICS
Newton’s First Law
Dynamics: Newton’s Laws of Motion
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)
Force
Newton’s First Law of Motion
Dynamics: Newton’s Laws 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.
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
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
Newton’s First Law of Motion
Mass
* Dynamics: Newton’s Laws of Motion
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
* Mass
Newton’s Second Law
* Dynamics: Newton’s Laws of Motion
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
Newton’s Second Law
Fa
m
F ma
SF – the vector sum of the forces
In one dimension this is simply adding or subtracting forces.
* Newton’s Second Law
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
Free Body Diagram
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
F 0
0a
Fx 0
Fy 0
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
gives0 0 y g gF T F T F
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
Fx 0
Fy 0
Equilibrium, Example 2
NFT
FTF
g
gy
100
00
3
3
Need 2 free-body diagrams Apply equilibrium equation to
light
Apply equilibrium equations to knot
Fx T1x T2x T1 cos37 T2 cos53 0
Fy T1y T2y T3y
T1 sin37 T2 sin53 100N 0
T2 T1
cos37
cos53
1.33T1
T1 60N T2 1.33T1 80N
Fy 0 T3 Fg 0
T3 Fg 100N
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?
Newton 2nd law:
Then
So
Inclined Plane
0cos
0sin
mgNF
NmgF
y
sx
cosmgN
0cossin mgmgF sy
350.0tan s3.19)350.0(tan 1
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.
Center of mass
We all remember the fun see-saw of our youth.
But what happens if . . .
Balancing Unequal Masses
MoralBoth the masses and their positions affect
whether or not the “see saw” balances.
*Balancing Unequal Masses
Need:M1 d1 = M2 d2
M1
M2
d1 d2
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.
*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!
In other words. . .
(We still) need:M1 d1 = M2 d2
M2
d1 d2
M1