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