AP* PHYSICS B MOTION AND FORCE: DYNAMICS

AP* PHYSICS B

MOTION AND FORCE:

DYNAMICS

We’ve been dealing with the fact that objects move. Velocity, acceleration, projectile motion, etc. WHY dothey move? Forces act upon them, that’s why! The connection between Force and motion is DYNAMICS.

FORCEA push or pull on an object. An object falls due to the force of gravity. Forces do notalways 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.

NEWTON’S FIRST LAW OF MOTION [Law of Inertia]

An object in motion remains in motion along a straight line path until a force acts upon that object. An objectat rest remains at rest until a 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--Newton’s 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)

g! Weight--a force; F = mg measured in newtons. A word that has a casual meaningon Earth since g is relatively constant @ 9.8 m/s . Mass and weight have often been used2

interchangeably during your short lifetime!

NEWTON’S SECOND LAW OF MOTION [F = ma]

The acceleration of an object is directly proportional to the net force acting on it and is inversely proportionalto its mass. The direction of the acceleration is in the direction of the net force acting on the object.

a = Ó F m

In English:When a net force acts upon an object, it’s rest or uniform motion is changed. That means it experiences anacceleration, technically defined as a change in velocity. ! Ó F = ma! Ó F = net force! Force--an action capable of accelerating an object; measured in Newtons! 1 N = kg Cm/s2

! ONE Dimensional L F = ma

x x y y z z! TWO or THREE Dimensional L F = ma & F = ma & F = ma

AP is a registered trademark of the College Board. The College Board was not involved in the production of and does not endorse this product. ®

© 2009 by René McCormick. All rights reserved

Example 1

Estimate the net force needed to accelerate a 1000-kg car at ½ g.

Example 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?

NEWTON’S THIRD LAW [action-reaction]

Whenever on object exerts a force on a second object, the second object exerts an equal and opposite force onthe 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 ONan object and BY another object. Hit a nail with a hammer--the force is applied ON the nail BY the hammerBUT, the nail exerts a force back on the hammer. How do we know? 1) the speed of the hammer is rapidlyreduced to zero! 2) this force must be strong to so rapidly reduce the speed of the hammer 3) the nail rarelysinks all the way into the wood on the first try!

Example 3

What makes a car go forward?

Motion and Force Dynamics 2

planman

Sticky Note

Example 4

Michelangelo’s assistant has been assigned the task ofmoving a block of marble using a sled. He says to his boss,“When I exert a forward force on the sled, the sled exerts anequal and opposite force backward, so how can I ever start itmoving? No matter how hard I pull, the backward reactionforce always equals my forward force, so the net force mustbe zero. I’ll never be able to move this load.” Is this a caseof 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.

g wF = F = mg always directed downward, toward the center of the Earth.

! g = 9.8 m/s2

The moon’s gravity is 1/6 that of the Earth since the moon’s mass is 1/6 that of theEarth’s. Your weight on the moon is 1/6 that of your weight here on Earth--I find this apleasant thought!

So why don’t we go crashing through the floor on to the poor souls below? The force ofthe floor exerts force “right back at ‘ya” due to it’s elasticity. This force is the normalforce and is NOT a case of action-reaction!

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

weight for a stationary object.


Example 5

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

It’s 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 the

normal force on the box?

Notice that the normal force is elastic in origin! THAT’S WHY IT IS NOT AN ACTION-REACTION PAIRWITH THE WEIGHT!

Example 6

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

pequal to, or greater than, the box’s weight, say F = 100.0 N rather than the 40.0 Nshown in figure 4-16 c)?


SOLVING PROBLEMS WITH NEWTON’S LAWS:VECTOR FORCES AND FREE-BODY DIAGRAMS

Net force = vector sum = Ó F and is % to acceleration of an object

Example 7

Calculate the sum of the two forces acting on the boat shown in the figure.

Free-Body diagram:! Show all forces acting on EACH object involved! Point masses for now..... until we start rotating stuff!

Example 8

A hockey puck is sliding at constant velocity across a flat horizontal ice surface that is assumed to befrictionless. Which of the sketches is the correct free-body diagram for this puck? What would your answerbe if the puck was slowed down?


Example 9

Suppose a friend asks to examine the 10.0 kg box you were given earlier, hoping to guess what’s inside. Yourespond, “Sure, pull the box over to you.” She then pulls the box over by an attached ribbon/string/cord/ropealong the smooth surface of the table. The magnitude of the force exerted by the person is 40.0 N and isexerted at a 30.0E angle with the table top. Calculate

a) the acceleration of the box.

Nb) the magnitude of the upward force, F exerted by the table on the box. Assume that friction can beneglected.


T! Tension--F --when a flexible cord/rope/etc. pulls on an object it is said to be under “tension”. Thesecan only pull, NOT push since they are flexible pieces of matter!

Example 10

Two boxes are connected by a lightweight cord and are resting on a table. The boxes have masses of 12.0 kg

pand 10.0 kg. A horizontal force F of 40.0 N is applied by a person to the 10.0 kg box. Find

a) the acceleration of each box

b) the tension in the cord.

Example 11

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

1 2machine. Consider the real-life application of an elevator (m ) and its counterweight (m ).

1 2To minimize the work done by the motor to raise and lower the elevator safely, m and mare similar in mass. We leave the motor out of the system for this calculation, and assumethe cable’s mass is negligible and the pulley is frictionless and massless, which assures that

Tthe tension, F , in the cord has the same magnitude on both sides of the pulley. Let the

2mass of the counterweight be m = 1,000 kg. Assume the mass of the empty elevator is

1 1850 kg, and its mass when carrying 4 passengers is m = 1150 kg. For the latter case (m =1150 kg), calculate

a) the acceleration of the elevator and

b) the tension in the cable.


Example 12

Muscleman is trying to lift a piano (slowly) up to a second-story apartment. He is usinga rope looped over two pulleys as shown. How much of the piano’s 2000 N weight doeshe have to pull on the rope?

Example 13

Finding her car stuck in the mud, a bright graduate student of a good physicscourse ties a strong rope to the back bumper of the car, and the other end toa tree. She pushes at the midpoint of the rope with her maximum effort,

pwhich she estimates to be a force F = 300 N. The car just begins to budgewith the rope at an angle è which she estimates to be 5E. With what force isthe rope pulling on the car? Neglect the mass of the rope.


APPLICATIONS INVOLVING FRICTION; INCLINES

Friction--exists between 2 solid surfaces because even the smoothest looking surface isquite rough on a microscopic scale. When we try to slide an object across anothersurface, these microscopic bumps impede motion. Additionally, the atoms snuggle upnext to one another and have interactions of an attractive nature and can further impedemotion.

kinetic friction--sliding friction; the friction that persists evenonce the object is in motion. This force acts opposite to thebody’s velocity and is determined by the nature of the twosurfaces. The force of kinetic friction is approximatelyproportional to the normal force. [the normal force is the forcethat either object exerts on the other perpendicular to theircommon surface of contact]

f NF % F insert a proportionality constant and presto, an equals sign appears along with a constant!

f K NF = ì F

Kì --the coefficient of kinetic friction; its value depends on the nature of the 2 surfaces; it’s an approximationsince 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 surfacearea. It doesn’t matter whether you slide your book flat along the table or on itsspine along the table--it’s frictional force is essentially unaffected.

Static friction--force applied to get an object moving; it is always present between 2 stationary objects andincreases when the force applied increases until the force applied overpowers the static frictional force and thekinetic frictional force takes over. At the point it begins to move you have applied the maximum force ofstatic friction

MAX S NF # ì F you’ve probably noticed it’s easier to keep an object moving than get it to move!


Example 14

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

K fcoefficient of kinetic friction is ì = 0.30. Determine the force of friction, F , acting on the box if a horizontal

Aexternal applied force F is 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

Notice that BOTH the normal force and the frictionalforces are exerted by one surface ON another.

NF is perpendicular to the contact surface

fF is parallel to the contact surface and in the oppositedirection of the x velocity.


Example 15

Your little sister wants a ride on her sled. If you are on flat ground, will you exert less force if you push heror pull her? Assume the same angle è in each case.

Example 16

Two boxes are connected by a cord running over a pulley. The coefficient of kineticfriction between box I and the table is 0.20. We ignore the mass of the cord andpulley and any friction in the pulley, which means we can assume that a force appliedto one end of the cord will have the same magnitude at the other end. We wish to findthe acceleration, a, of the system, which will have the same magnitude for both boxesassuming the cord doesn’t stretch. As box II moves down, box I moves to the right.

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 a has only one component and if

ffriction is present, two of the forces will have only one component: F along the

Nplane, opposite ot the object’s velocity, and F which is NOT vertical but isperpendicular to the plane. A picture will help!


Example 17

A skier has just begun descending a 30.0E 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 18

Suppose the snow is slushy and the skier moves down the 30.0E slope at constant speed. Determine the

Kcoefficient of friction, ì ?


AP* PHYSICS B MOTION AND FORCE: DYNAMICS

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