Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova

Sections 818, 819, 820, 821

Lecture 11

Quiz (folders)

A rocket is fired from a tower of height H, at t=0, with an initial velocity of magnitude W at an angle Θ above horizontal. The rocket’s engine supplies an acceleration that increases with time according to a(t)=αt2. The acceleration is always directed at an angle β with the horizontal. The rocket’s fuel runs out after 2 sec. What will its velocity and position be when the fuel runs out? Consider α, β, Θ, H, and W as known constants and neglect gravity.

amF

Newton’s second law

The vector acceleration of an object is in the same direction as the vector force applied to the object and the magnitudes are related by a constant called the mass of the object.

Kinetic Friction

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

FFriction = KineticN

Here is a constant• Warning:

– THIS IS NOT A VECTOR EQUATION!

A Recipe for Solving 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 box of mass m is on a surface with coefficient

of kinetic friction . You pull with constant force FP at angle The box does not leave the surface and moves to the right.

1. What is the magnitude of the acceleration?

2. What angle maximizes the acceleration?

H

Coefficient of friction:

What is the normal force?

What is the velocity of the block when it reaches the bottom?

First exam Tuesday, September 22

102 CHEN

Sections 818 and 819 start at 7 pm

Sections 820 and 821 start at 8:05 pm

All liquids, gels and aerosols must be in three-ounce or smaller containers.

No calculators and cell phones

BRING YOUR STUDENT ID!

What is included?

Chapters 1-6

Kinematics, vectors, Newton’s 2nd Law

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

daVdtaV yyxx ;

dtVydtVx yx ;

ty

Vectors

jAiAA yx

jBiBB yx

? BAC

jCiCC yx

xxx BAC yyy BAC

Newton’s 2nd Law

amF

xx maF yy maF

Friendly advice

DO NOT…

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 to

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

•Box the answer

•Indicate the origin and positive x and y

Have a great day!

Reading: Chapter 5,6Hw: Chapter 6 problems and exercises