force n motion

7/27/2019 Force n Motion

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Chapter 5. Force and Motion I

5.1. What is Physics?

5.2. Newtonian Mechanics

5.3. Newton's First Law5.4. Force

5.5. Mass

5.6. Newton's Second Law

5.7. Some Particular Forces5.8. Newton's Third Law

5.9. Applying Newton's Laws


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What Causes Acceleration?

Dynamicsthe study of causes of

motion. The central question in dynamics

is: What causes a body to change its

velocity or accelerate as it moves?


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Newtonian Mechanics

1.When the speed of objects approaches (1%

or more) the speed of light in vacuum (c= 8108

m/s). In this case we must use Einsteinsspecial theory of relativity (1905) .

2. When the objects under study become verysmall (e.g., electrons, atoms, etc.). In this casewe must use quantum mechanics (1926).

Newtons laws fail in the following two circumstances:


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Force

A forceis a push or a pull. Force is a vector. All forces result from interaction.

Contact forces: forces that arise from the physical contact between two

objects.

Noncon tact forces: forces the two objects exert on one another even

though they are not touching.


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External fo rces include only the forces

that the environment exerts on the object

of interest.

In ternal fo rcesare forces that one part of

an object exerts on another part of the

object.


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Combining Forces


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Principle of superposition for forces

When two or more forces act on a body, we

can find their net force or resultant force byadding the individual forces as vectors takingdirection into account.

Note: The net force involves thesum of external forces only

(internal forces cancel each other).


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Exercise 1The figures that follow show overhead views of

four situations in which two forces acting on thesame cart along a frictionless track. Rank thesituations according to the magnitudes of the netforce on the cart, greatest first.


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Newtons FIRST LAW


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Newton's First law:Consider a body on which no

net force acts. If the body is at rest, it will remain at

rest. If the body is moving, it will continue to

moving with a constant velocity.

Net force is crucial. Often, several forcesact simultaneously on a body, and the net

force is the vector sum of all of them

An inertial reference frameis the one has

zero acceleration. All newtons laws are valid only in the inertia

reference frames.


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Mass

The larger the mass,

the harder is to

cause its motion

Mass and weight

are different

concepts


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DEFINITION OF INERTIA AND MASS

1. Inertiais the natural tendency of an

object to remain at rest or in motion at a

constant speed along a straight line.

2. The massof an object is a quantitative

measure of inertia.

SI Unit o f Inert ia and Mass :kilogram (kg)


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NEWTONS SECOND LAW OF MOTION

When a net external force acts on an objectof mass m, the acceleration athat results isdirectly proportional to the net force and has amagnitude that is inversely proportional to the

mass. The direction of the acceleration is thesame as the direction of the net force.

F

Fa

m

SI Unit of Force:kgm/s2 =newton (N)

=

Only External forc es are considered in the Newtons second law.


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Example 1 Pushing a Stalled Car

Two people are pushing a stalled car, as Figure 4.5a

indicates. The mass of the car is 1850 kg. One personapplies a force of 275 N to the car, while the other applies aforce of 395 N. Both forces act in the same direction. A thirdforce of 560 N also acts on the car, but in a directionopposite to that in which the people are pushing. This force

arises because of friction and the extent to which thepavement opposes the motion of the tires. Find theacceleration of the car.


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Examp le 2 Hauling a Trailer

A truck is hauling a trailer along a level road, as Figure4.32aillustrates. The mass of the truck is m1=8500 kgand that of the trailer is m2=27 000 kg. The two movealong thexaxis with an acceleration of ax=0.78 m/s

2.Ignoring the retarding forces of friction and air resistance,determine (a) the tension Tin the horizontal drawbar

between the trailer and the truck and (b) the force Dthatpropels the truck forward.


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Questions

The net external force acting on an object is zero. Is itpossible for the object to be traveling with a velocity thatis not zero? If your answer is yes, state whether anyconditions must be placed on the magnitude anddirection of the velocity. If your answer is no, provide areason for your answer.

Is a net force being applied to an object when the objectis moving downward (a) with a constant acceleration of9.80 m/s2and (b) with a constant velocity of 9.80 m/s?Explain.

Newtons second law indicates that when a net forceacts on an object, it must accelerate. Does this mean thatwhen two or more forces are applied to an object

simultaneously, it must accelerate? Explain.


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Newton's Third Law


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Newton's Third Law

If one object is exerting a force on a second object,

then the second object is also exerting a force backon the first object. The two forces have exactly the

same magnitude but act in opposite directions.

B A A BF F Forces always exist in

pairs.

It is very important that

we realize we are talking

about two differentforcesacting on two

different objects.


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Question

A father and his seven-year-old daughterare facing each other on ice skates. Withtheir hands, they push off against one

another.(a) Compare the magnitudes of the pushing

forces that they experience.

(b) Which one, if either, experiences thelarger acceleration? Account for youranswers.


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EXAMPLE 3: Pushing Two Blocks

In Fig. 3-29a, a constant horizontal force of

magnitude 20 N is applied to blockAof mass 4.0kg, which pushes against block Bof mass 6.0 kg.The blocks slide over a frictionless surface, alonganxaxis.

a) What is the acceleration of the blocks?b) What is the force acting on block Bfrom blockA


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Example 4 The Accelerations Produced by Action and Reaction Forces

Suppose that the mass of the spacecraft inFigure 4.7 is m

S=11 000 kg and that the mass

of the astronaut is mA=92 kg. In addition,assume that the astronaut exerts a force ofP=+36 N on the spacecraft. Find theaccelerations of the spacecraft and the

astronaut.


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NEWTONS LAW OF UNIVERSAL GRAVITATION


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NEWTONS LAW OF UNIVERSAL GRAVITATION

Every particle in the universe exerts an attractiveforce on every other particle. For two particles that

have masses m1 and m2 and are separated by a

distance r, the force that each exerts on the other is

directed along the line joining the particles and has a

magnitude given by:

The symbol Gdenotes the universal gravitationalconstant, whose

value is found experimentally to be


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DEFINITION OF WEIGHT

Theweightof an object on or above the earth is thegravitational force that the earth exerts on the object. The

weight always acts downward, toward the center of theearth. On or above another astronomical body, the weight isthe gravitational force exerted on the object by that body.

SI Unit o f Weight:newton (N)


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When the height of object H above the Earth is small

2 2 2

2

2

2

( )

( )

9.8 m/s

E E E

E E

E

E

E

E

M m M m M mW G G G

r R H R

MW G m mg

R

Mg GR


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The Gravitational Acceleration Constant

When air resistance can be ignored andE

H R

any object under only gravitational force will

free fall with a constant acceleration:

2

9.8 m/sg


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RELATION BETWEEN MASS AND WEIGHT

Mass is an intrinsic property of matter and does not

change as an object is moved from one location toanother.

Weight, in contrast, is the gravitational force acting on the

object and can vary, depending on how far the object isabove the earths surface or whether it is located nearanother body such as the moon.


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Questions

When a body is moved from sea level to

the top of a mountain, what changesthe

bodys mass, its weight, or both? Explain.


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Questions

The force of air resistance acts to oppose the

motion of an object moving through the air. A

ball is thrown upward and eventually returns to

the ground. (a) As the ball moves upward, is the net force

that acts on the ball greater than, less than, or

equal to its weight? Justify your answer.

(b) Repeat part (a) for the downward motion of

the ball.


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The Normal Force

The normal force FNis one component of the

force that a surface exerts on an object withwhich it is in contactnamely, thecomponent that is perpendicular to thesurface.


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APPARENT WEIGHT


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The Friction Force

When the object moves or attempts to move along a

surface, there is a component of the force that is parallel

to the surface. This parallel force component is called thef r ic t ional force, or simply f r ic t ion. It is always against the

relative motion or the attempts of the motion between

object and surface.


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Tension

1. Tension in a Nonaccelerating rope: the magnitude of

tention is the same everywhere in the rope.

2. An Accelerating rope: the magnitude of tension is not

the same everywhere in the rope that has a mass;

however, the magnitude of tension is the same

everywhere in the rope that is massless.

Tension is the force exerted by a rope or a cable attached toan object


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For a massless string

1. It is always directedalong the rope.

2. It is always pulling

the object.

3. It has the samevalue along the

rope


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Applying Newton's Laws

Newton's Second Law:

It can be written as two (or three) component equations:


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Equilibrium Applications of Newton's Laws of Motion

DEFINITION OF EQUILIBRIUM:An object is in

equilibrium when it has zero acceleration.

0netF

0 and 0 and 0x y z

F F F

EXAMPLE 5 Th C d


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EXAMPLE 5: Three Cords

In Fig. 6-25a, a block Bof

mass M= 15 kg hangs by acord from a knot Kof massmK, which hangs from aceiling by means of two other

cords. The cords havenegligible mass, and themagnitude of thegravitational force on theknot is negligible comparedto the gravitational force onthe block. What are thetensions in the three cords?

F B d Di


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Free-Body Diagrams

(1) Identify the object for which the motion is to be

analyzed and represent it as a point.

(2) Identify all the forces acting on the object andrepresent each force vector with an arrow. The

tail of each force vector should be on the point.Draw the arrow in the direction of the force.Represent the relative magnitudes of the forcesthrough the relative lengths of the arrows.

(3) Label each force vector so that it is clear whichforce it represents.


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Example 6 Replacing an Engine

An automobile enginehas a weight W, whosemagnitude is W=3150 N.This engine is beingpositioned above an

engine compartment, asFigure 4.29aillustrates.To position the engine, aworker is using a rope.Find the tension T1in the

supporting cable and thetension T2in thepositioning rope.


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Example 7 Equilibrium at Constant Velocity

A jet plane is flying with a constant speed along a straight line,

at an angle of 30.0

above the horizontal, as Figureindicates. The plane has a weight Wwhose magnitude isW=86 500 N, and its engines provide a forward thrust Tofmagnitude T=103 000 N. In addition, the lift force L(directedperpendicular to the wings) and the force Rof air resistance

(directed opposite to the motion) act on the plane. Find LandR.


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Non-quilibrium Applications of Newton's Laws of Motion

DEFINITION OF NONEQUILIBRIUM:

An object is in nonequilibrium when it has non-zero

acceleration.

netF ma

and andx x y y z z

F ma F ma F ma

Example 8 Applying Newtons Second Law Using Components


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Example 8 Applying Newton s Second Law Using Components

A man is stranded on a raft(mass of man and

raft=1300 kg), as shown inFigure a. By paddling, hecauses an average force Pof 17 N to be applied to theraft in a direction due east

(the +xdirection). The windalso exerts a force Aon theraft. This force has amagnitude of 15 N andpoints 67 north of east.

Ignoring any resistancefrom the water, find thexand ycomponents of therafts acceleration.

Example 9 Towing a Supertanker


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Example 9Towing a Supertanker

A supertanker of mass m=1.50108 kg is being towed bytwo tugboats, as in Figure. The tensions in the towingcables apply the forces T1and T2at equal angles of 30.0

with respect to the tankers axis. In addition, the tankersengines produce a forward drive force D, whosemagnitude is D=75.0103N. Moreover, the water appliesan opposing force R, whose magnitude is R=40.0103N.The tanker moves forward with an acceleration that points

along the tankers axis and has a magnitude of 2.00103

m/s2. Find the magnitudes of the tensions T1and T2.


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Conceptual Questions

According to Newtons third law, when you push on an object, the

object pushes back on you with an oppositely directed force of equalmagnitude. If the object is a massive crate resting on the floor, it willprobably not move. Some people think that the reason the cratedoes not move is that the two oppositely directed pushing forcescancel. Explain why this logic is faulty and why the crate does notmove.

A stone is thrown from the top of a cliff. As the stone falls, is it inequilibrium? Explain, ignoring air resistance.

Can an object ever be in equilibrium if the object is acted on by only(a) a single nonzero force, (b) two forces that point in mutually

perpendicular directions, and (c) two forces that point in directionsthat are not perpendicular? Account for your answers.


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A circus performer hangs stationary from a rope. She thenbegins to climb upward by pulling herself up, hand overhand. When she starts climbing, is the tension in the rope

less than, equal to, or greater than it is when she hangsstationary? Explain.

A weight hangs from a ring at the middle of a rope, as thedrawing illustrates. Can the person who is pulling on the

right end of the rope ever make the rope perfectlyhorizontal? Explain your answer in terms of the forces thatact on the ring.

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