Two iceboats (one of mass m,

one of mass 2m) hold a race on a

frictionless, horizontal, frozen

lake. Both iceboats start at rest,

and the wind exerts the same

constant force on both iceboats.

A. The iceboat of mass m: it has twice as much KE as the other.

B. The iceboat of mass m: it has 4 times as much KE as the other.

C. The iceboat of mass 2m: it has twice as much KE as the other.

D. The iceboat of mass 2m: it has 4 times as much KE as the other.

E. They both cross the finish line with the same kinetic energy.

Which iceboat crosses the finish line with more kinetic

energy (KE)?

Review: Newton’s Laws

Newton’s First Law

The velocity of an object does not change

unless a force acts on the object

Newton’s Second Law: Fnet= m a

The acceleration of an object is

proportional to the net force on the object

Newton’s Third Law

For every force an object exerts on a

second object, there is an equal and

opposite force exerted on the first object

1F

2F 3F

4F

More force was

needed to stop the rock

These are equal and

opposite forces even if

you break the wall or

your fist keeps going!

ALWAYS!

A

B

C

D

E

A

B

C

D

E

Free-Body Diagrams (FBDs)

• A FBD labels all of the

forces acting on (not

by) an object.

• Only forces acting on

an object will affect its

motion (acceleration).

weightFG

If it doesn’t have units of

Newtons (kg m/s2), then it

doesn’t belong on a FBD!

(No velocity or acceleration)Fpull

n

fk

mg

Friction• Static Friction: Force that keeps object from

sliding against a surface when it is at rest

fstat msn

• Kinetic Friction: Force that slows you down

when moving

fk = mkn

Ffr=µsn

Once it starts moving,

kinetic friction takes

over.

Why it is easier to

move something after

it gets started moving.

Ffr=µsnFfr=µkn

Work Done by a Constant (or

Average) Force

• Force F acting on an object causes the

object to move a distance Δx does work W

xFW ||

x magnitude of displacement of object

F|| component of force parallel to displacement of object

Units: N m = Joule (J)

Or equivalently:

Only concerned with

movement in the

direction of the force

The Work-Energy Principle

2

212

21

onet mvmvW

The work done on an object by a net force is

Translational kinetic energy (energy of motion) of an object:

2

21 mvKE

The net work done on an object is equal to

the change in its kinetic energy

ofnet KEKEKEW

KE increases KE decreases

Gravitational Potential Energy

)( oG yymgymgW

ymgmgymgy o if PEPEPE

PEGW

Work done by gravity in going

between two points is equal to the

negative of the change in PE

Note:

1. Origin to measure y is arbitrary, thus so is PE (PE is not)

2. Gravity does work only in the vertical direction, so work done by

gravity in going from point 1 to point 2 only depends on y,

independently of path taken

oy

fy

Δy

mgygravPE

Mechanical Energy

Last Time: Work-energy principle KEWnet Separate net work done into work done by conservative and

nonconservative forces:

KE CNCnet WWW

But WC = -PE

KEPE NCW

If WNC = 0, 0)KEKE()PEPE(KEPE0 fif i

PEi + KEi = PEf + KEf

Mechanical energy (PE + KE) of an object remains the same (is

conserved) if only conservative forces act on the object

KEPE)( NCW

Last Time: Linear Momentum & Impulse

vmp

• Linear momentum of an object is mass times velocity

• Linear momentum is a vector. Direction of linear

momentum is the same as the velocity of the object

Units: kg m/s

tFpI

1. A force must act on an object for impulse to occur

2. In a collision, an impulse occurs in the direction of

the force acting on the object

t

pFnet

Conservation of Linear Momentum

in Isolated Systems.

systemisystemf pp ,,

ffii vmvmvmvm 22112211

A system is a set of objects interacting with each other

An isolated system has no unbalanced external forces, meaning no unbalanced forces outside the system (e.g., normal/gravity)

Elastic and Inelastic Collisions

• Inelastic collisions: mechanical energy (KE+PE)

is not conserved

• Special case: Perfectly inelastic, objects stick

• Elastic collisions: mechanical energy is conserved

For both elastic and inelastic collisions

linear momentum is conserved

Clicker answers

• E, A, A