The first exam will be on Tuesday, September 25, room 109 in Heldenfels building.

Section 807 and half of the Section 808 (students with last name starting with A to H) will have exam from 7 to 8 pm.

Students from Section 808 with last name starting with J to Z, and all students from Section 809, will have exam from 8:15 pm to 9:15 pm.

Students that have the exam from 7 to 8 pm will not be allowed to leave earlier than 8 pm.

No calculators and cell phones in the room during the test.

Don’t use your own scratch paper; there will be plenty of it in the room.

Please DO NOT FORGET TO BRING YOUR STUDENT ID!

Ch. 6 Quiz

A block of mass M is pushed against a vertical surface. The coefficient of friction between the surface and the block is equal to . If angle is known, what is the minimum magnitude of P to hold the block still?

P

What is included?

Chapters 1-6

Kinematics, 2D motion, vectors, Newton’s Laws

Kinematics

dt

Vda

dt

rdV

In components:

dt

dVa

dt

dVa y

yx

x ;

dt

dyV

dt

dxV yx ;

If is given, you can find anda

V

r

dtaVdtaV yyxx ;

dtVydtVx yx ;

Vectors

jAiAA yx

jBiBB yx

? BAC

jCiCC yx

xxx BAC yyy BAC

Newton’s 2nd Law

amF

xx maF yy maF

DO NOT use Const acceleration case formulas when acceleration is a function of time. You have to integrate or differentiate! What are the Const acceleration case formulas?

)0()0(2

1)( 2 xtvtatx c

)0()( vtatv c

))()((2)()( 1212

22 txtxatvtv c

DO NOT write the vector sign over a projection!

!,

,FF

scalarsareFF

jFiIf

yx

yx

DO NOT forget that Fp has two components: Fpcos θ and Fpsin θ

DO NOT forget that Vi has two components: Vicos θ and Vi sin θ

x

y

iV

Do Not Forget to

•Write down what is given and express the answer in terms of what is given

•Box the answer

Double play problem

A Recipe for Solving Second Law Problems1. Sketch Isolate the body (only external forces but not forces

that one part of the object exert on another part)

2. Write down 2nd Newton’s law

amF

Choose a coordinate system Write 2nd Newton’s law in component form:

yyxx

yxyx

maFmaF

jmaimajFiFF

,

3. Solve for acceleration

Pulling Against FrictionA sled of mass m is on a surface with coefficients of kinetic

friction and static friction s. You pull with a constant force F at an angle The sled does not leave the surface and moves to the right.

1. What is a minimum force needed to bring the sled in motion?2. What is the magnitude of the acceleration? 3. What angle maximizes the acceleration?

Friction

Two types of friction:1. Kinetic: The friction force

that slows things down2. Static: The force that

makes it hard to even get things moving

Kinetic Friction

• For kinetic friction, it turns out that the larger the Normal Force the larger the friction. We can write

FFriction = KineticFNormal

Here is a constant• Warning:

– THIS IS NOT A VECTOR EQUATION!

Static Friction• This is more complicated• For static friction, the friction force can vary

FFriction StaticFNormal

Example of the sled: – If I don’t push, what is the static friction

force?– What if I push a little?

Box on an inclined planeA box with mass m is placed on a frictionless incline

with angle and is allowed to slide down.

a) What is the normal force?

b) What is the acceleration of the box?

No friction

Massless, unstretchable string; frictionless pulley

The advantage of a pulley

What minimum force F is needed to lift the piano of mass M?