The first exam will be held on Tuesday, September 23, in room 109 Heldenfels from 7 to 9:30 p.m.

Section 807 and half of section 808 (students with last names beginning from letters A through K) should come at 6:55 p.m. for an exam that starts at 7:00 and ends at 8:00 p.m. The rest of section 808 and section 809 should come at 8:10 for an exam that starts at 8:15 and ends at 9:15 p.m. Those who take the first exam cannot leave before 8 p.m.

No textbook, calculators, or notes are permitted on the exam.

The exam will include Chapters I through VI.

A Recipe for Solving Problems1. Sketch Identify all forces acting on each body, or “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 convenient coordinate system Write 2nd Newton’s law in component form:

yyxx

yxyx

maFmaF

jmaimajFiFF

,

4. Solve for acceleration or whatever is asked

3. Apply 3rd Law

Units of Force

2/111 smkgNNewton

British system:

kgslug 59.141 units of mass:

units of force: Nsftsluglbpound 448.4/111 2

One pound is 0.4536 kg

One pound is the weight of 0.4536 kg on the Earth

Weight, the force of gravity, and the normal force

Pm1

m2

No friction

m1

Free body diagram

m1

m1g

P

N1

F21

m2g

F12

N2

m2

F12=F21

P

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

Refrigerator

• If you push a refrigerator when there is no friction what happens?

• In the real world what happens? Especially when it’s fully loaded and on a sticky kitchen floor?–When does static friction kick in?

–When does kinetic friction kick in?

Friction

There is some maximum value the friction force can achieve, and once we apply a force greater than this maximum there is a net force on the object, so it accelerates.

The maximum of the force of friction varied linearly with the amount that the block pushes on the table.

NFfriction

< 1- coefficient of friction, is the normal forceN

The friction force only exists when there is another force trying to move an object

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 refrigerator: – If I don’t push, what is the static friction

force?– What if I push a little?

Is it better to push or pull a sled?

You can pull or push a sled with the same force magnitude, FP, and angle , as shown in the figures.Assuming the sled doesn’t leave the ground and has a constant coefficient of friction, , which is better?

FP

FP

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?

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?

c) What is the box velocity at the bottom of the plane?

H

A small block, mass 2kg, rests on top of a larger block, mass 20 kg. The coefficient of friction between the blocks is 0.25. If the larger block is on a frictionless table, what is the largest horizontal force that can be applied to it without the small block slipping?

F

gm1

1N

1NF

1N

gm2

2N

1N

A block of mass 20 kg is pushed against a vertical surface as shown. The coefficient of friction between the surface and the block is 0.2. If θ=300, what is the minimum magnitude of P to hold the block still?

θ

P