AP Physics Motion & Force Dynamics

8/9/2019 AP Physics Motion & Force Dynamics

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MOTION AND FORCE:

DYNAMICS

Weve been dealing with the fact that objects move. Velocity, acceleration, projectile motion, etc.

WHY do they move? Forces act upon them, thats why! The connection between Force and motion is

DYNAMICS.

FORCE

A push or pull on an object. An object falls due to the force of gravity. Forces do not always

give rise to motion.

! Spring Scale--a device used to measure force

! Weight--a measure of the FORCE on an object, carries a unit of Newtons (N).

! Forces--are vectors that carry a magnitude and direction.

NEWTONS FIRST LAW OF MOTION [Law of Inertia]

An object in motion remains in motion along a straight line path untila force acts upon that object. An

object at rest remains at rest untila force acts upon that object.

! Inertia--tendency of a body to maintain its state of rest or uniform motion.

! Friction--a force that acts against motion

! Inertial Reference Frame--Newtons first law holds true. Rest a cup on a

dashboard in your car before leaving your garage--back out of the garage--

splash! That is NOT an inertial frame of reference!

! Mass--a property; measure of the inertia of a body (kg)

! Weight--a force; Fg= mg measured in Newtons. A word that has a casual

meaning on Earth since g is relatively constant @ 9.8 m/s2. Mass and weight

have often been used interchangeably during your short lifetime!

NEWTONS SECOND LAW OF MOTION [F = ma]

The acceleration of an object is directly proportional to the net force acting on it and is inversely

proportional to its mass. The direction of the acceleration is in the direction of the net force acting on

the object.

a = E F

m

In English:

When a net force acts upon an object, its rest or uniform motion is changed. That means it experiences

an acceleration, technically defined as a change in velocity.!!!! E F = ma

! E F = net force

! Force--an action capable of accelerating an object; measured in Newtons

! 1 N = kg Cm/s2

! ONE Dimensional L F = ma

! TWO Dimensional L Fx = max& Fy= may & Fz = maz


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Rene McCormick, AP Strategies, Inc.

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Example 4.1

Estimate the net force needed to accelerate a 1000-kg car at 1/2 g.

Example 4.2

What net force is required to bring a 1500-kg car to rest from a speed of 100 km/h within a distance of

55 m?

NEWTONS THIRD LAW [action-reaction]

Whenever on object exerts a force on a second object, the second object exerts an equal and opposite

force on the first object. Often stated, To every action there is an equal and opposite reaction.

The second law quantifies how forces affect motion. But, where do forces come from? A force is

exerted ON an object and BY another object. Hit a nail with a hammer--the force is applied ON the nail

BY the hammer BUT, the nail exerts a force back on the hammer. How do we know? 1) the speed of

the hammer is rapidly reduced to zero! 2) this force must be strong to so rapidly reduce the speed of the

hammer 3) the nail rarely sinks all the way into the wood on the first try!

Example 4.3What makes a car go forward?


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Forces 3

Example 4.4

Michelangelos assistant has been assigned the task of moving a block of marble using a sled. He says

to his boss, When I exert a forward force on the sled, the sled exerts an equal and opposite force

backward, so how can I ever start it moving? No matter how hard I pull, the backward reaction force

always equals my forward force, so the net force must be zero. Ill never be able to move this load. Is

this a case of a little knowledge being dangerous? Explain.

WEIGHT--THE FORCE OF GRAVITY; AND THE NORMAL FORCE

! Weight--The force of gravity originates at the center of the Earth.

Fg= Fw= mg always directed downward, toward the center

of the Earth.

! g--9.8 m/s2

The moons gravity is 1/6 that of the Earth since the moons mass is 1/6 that of theEarths. Your weight on the moon is 1/6 that of your weight here on Earth--I find

this a pleasant thought!

So why dont we go crashing through the floor on to the poor souls below? The

force of the floor exerts force right back at ya due to its elasticity. This force is

the normal force and is NOT a case of action-reaction!

! Normal force-- normal means z (usually thought of as z to the motion!). FN! Since E F = 0 for an object at rest and g is acting downward this force often balances the force

of weight for a stationary object.


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Example 4.5

A friend has given you a special gift, a box of mass 10.0 kg with a mystery surprise inside.

Its a reward for your fine showing on the physics final. The box is resting on a smooth

(frictionless) horizontal surface of a table.

a) Determine the weight of the box and the normal force acting on it.

b) Now your friend pushes down on the box with a force of 40.0 N. Again determine

the normal force acting on the box.

c) If your friend pulls upward on the box with a force of 40.0 N, what now is thenormal force on the box?

Notice that the normal force is elastic in origin! THATS WHY IS NOT AN ACTION-REACTION

PAIR WITH THE WEIGHT!

Example 4.6

What happens when a person pulls upward on the box in Example 4.5 c) with a

force equal to, or greater than, the boxs weight, say Fp= 100.0 N rather than the

40.0 N shown in figure 4-16 c)?


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SOLVING PROBLEMS WITH NEWTONS LAWS:

VECTOR FORCES AND FREE-BODY DIAGRAMS

Net force = vector sum = E F and is % to acceleration of

an object

Example 4.7

Calculate the sum of the two forces acting on the boat shown in Fig. 4-19a.

Free-Body diagram:

! Show all forces acting on EACH object involved

! Point masses for now..... until we start rotating stuff!

Example 4.8

A hockey puck is sliding at constant velocity across a flat

horizontal ice surface that is assumed to be frictionless.

Which of the sketches is the correct free-body diagram for

this puck? What would your answer be if the puck was

slowed down?


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Forces 6

Example 4.9

Suppose a friend asks to examine the 10.0 kg box you were given earlier, hoping to guess whats inside.

You respond, Sure, pull the box over to you. She then pulls the box over by an attached

ribbon/string/cord/rope along the smooth surface of the table. The magnitude of the force exerted by theperson is 40.0 N and is exerted at a 30.0 angle with the table top. Calculate

a) the acceleration of the box.

b) the magnitude of the upward force, FNexerted by the table on the box. Assume that friction can be

neglected.

! Tension--FT--when a flexible cord/rope/etc. pulls on an object it is said to be under tension.

These can only pull, NOT push since they are flexible pieces of matter!

Example 4.10

Two boxes are connected by a lightweight cord and are resting on a table. The boxes have masses of

12.0 kg and 10.0 kg. A horizontal force Fpof 40.0 N is applied by a person to the 10.0 kg box. Finda) the acceleration of each box


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b) the tension in the cord.

Example 4.11

Two masses suspended over a pulley by a cable is sometimes referred to as an

Atwoods machine. Consider the real-life application of an elevator (m1) and

its counterweight (m2). To minimize the work done by the motor to raise and

lower the elevator safely, m1and m2are similar in mass. We leave the motor

out of the system for this calculation, and assume the cables mass is negligible

and the pulley is frictionless and massless, which assures that the tension, FT, inthe cord has the same magnitude on both sides of the pulley. Let the mass of

the counterweight be m2= 1,000 kg. Assume the mass of the empty elevator is

850 kg, and its mass when carrying 4 passengers is m1= 1150 kg. For the latter

case (m1= 1150 kg), calculate

a) the acceleration of the elevator and

b) the tension in the cable.


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Example 4.12

Muscleman is trying to lift a piano (slowly) up to a second-story apartment. He is using a rope looped

over two pulleys as shown. How much of the pianos 2000 N weight does he have to pull on the rope?

Example 4.13Finding her car stuck in the mud, a bright graduate student of a good physics course ties a strong rope to

the back bumper of the car, and the other end to a tree. She pushes at the midpoint of the rope with her

maximum effort, which she estimates to be a force Fp. 300 N. The car just begins to budge with the

rope at an angle 2 which she estimates to be 5. With what force is the rope pulling on the car? Neglect

the mass of the rope.


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APPLICATIONS INVOLVING FRICTION; INCLINES

Friction--exists between 2 solid surfaces because even the smoothest looking

surface is quite rough on a microscopic scale. When we try to slide an object

across another surface, these microscopic bumps impede motion. Additionally,

the atoms snuggle up next to one another and have interactions of an attractive

nature and can further impede motion.

kinetic friction--sliding friction; the friction that persists

even once the object is in motion. This force acts

opposite to the bodys velocity and is determined by the

nature of the two surfaces. The force of kinetic friction is

approximately proportional to the normal force. [the normal force is the force

that either object exerts on the other perpendicular to their common surface of

contact]

Ff% FN insert a proportionality constant and presto, an equals sign appears along with a constant!

Ff= :KFN

:K--the coefficient of kinetic friction; its value depends on the nature of the 2 surfaces; its an

approximation since polishing/ sanding, etc. alters the surfaces.

This is not a vector equation since the two vectors act z to one another. It is also an experimental

relationship NOT a fundamental law. The force of friction depends very little on surface area. It

doesnt matter whether you slide your book flat along the table or on its spine along the table--its

frictional force is essentially unaffected.


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Static friction--force applied to get an object moving; it is always present between 2

stationary objects and increases when the force applied increases untilthe force

applied overpowers the static frictional force and the kinetic frictional force takes

over. At the point it begins to move you have applied the maximum force of static

friction

FMAX# : SFN youve probably noticed its easier to keep an object movingthan get it to move!

Example 4.14

Our 10.0 kg mystery box rests on a horizontal floor. The coefficient of static friction is : s= 0.40 and the

coefficient of kinetic friction is:

K= 0.30. Determine the force of friction, Ff, acting on the box if ahorizontal external applied force FAis exerted on it of magnitue [answer in 2 sig. figs for each part!]

a) 0 N

b) 10 N

c) 20 N

d) 38 N

e) 40 N


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Forces 11

Notice that BOTH the normal force and the

frictional forces are exerted by one surface ON

another.

FNis perpendicular to the contact surface

Ffis parallel to the contact surface and in theopposite direction of the x velocity.

Example 4.15

Your little sister wants a ride on her sled. If you are on flat ground, will ou exert less force if you push

her or pull her? Assume the same angle 2 in each case.

Example 4.16

Two boxes are connected by a cord running over a pulley. The coefficient of kinetic friction between

box I and the table is 0.20. We ignore the mass of the cord and pulley and any fricion in the pulley,

which means we can assume that a force applied to one end of the cord will have the same magnitude at

the other end. We wish to find the acceleration, a, of the system, which will have the same magnitude

for both boxes assuming the cord doesnt stretch. As box II moves down, box I moves to the right.


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OBJECTS MOVING ON AN INCLINE

Easier to choose the xy coordinate system so that the x-axis is parallel to the

incline surface and the y-axis is therefore, perpendicular to the incline. This

helps because then ahas only one component and if friction is present, two of the

forces will have only one component:Ffalong the plane, opposite ot the objects

velocity, and FNwhich is NOT vertical but is perpendicular to the plane. Apicture will help!

F F

F F mg

N W

applied W

=

= =

cos

sin sin

Example 4.17

A skier has just begun descending a 30.0 slope. Assuming the coefficient of kinetic friction is 1.10,

a) draw the free body diagram

b) calculate her acceleration

c) calculate the speed she will reach after 4.0 seconds.

Example 4.18

Suppose the snow is slushy and the skier moves down the 30.0 slope at constant speed. Determine thecoefficient of friction, :K?

AP Physics Motion & Force Dynamics

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