Forces of Friction

Contact between bodies with a relative velocity produces friction

• Friction is proportional to the normal force• The force of static friction is generally greater

than the force of kinetic friction• The coefficient of friction (µ “mu”) depends on • The coefficient of friction (µ “mu”) depends on

the surfaces in contact• The direction of the frictional force is opposite

the direction of motion• The coefficients of friction are nearly

independent of the area of contact

Fig. 4-19, p.101

• Static friction acts to keep the object from moving

• If F increases, so does ƒs

• If F decreases, so does ƒs

• ƒs ≤ µ n where n = normal force vector

Static Friction ƒs

• ƒs ≤ µ n where n = normal force vector

-Fsf =uur uur

Kinetic Friction , ƒk

• The force of kinetic friction acts when the object is in motion

• ƒk = µk n– Direction of ƒk opposite to – Direction of ƒk opposite to

motion: opposes motion– Variations of coefficient

of friction with speed will be ignored

HITT RF Remote Login Procedure:(If you have a really old IR remote you do not need to login.)

1. PRESS AND HOLD THE DOWN ARROW KEY until the GREEN light on the remote turns RED.

The radio channel number for this room is “07” (zero, seven).

It is STRONGLY recommended to login your remote for every class justto be sure it is on the correct radio channel and working before class.

GREEN light on the remote turns RED.

2. PRESS THE “0” KEY and you will see the RED light flash GREEN.

3. PRESS THE “7” KEY and you will see the RED light flash GREEN.

4. PRESS AND RELEASE THE DOWN ARROW KEY again and you will see the red light search for the receiver, if it BLINKS GREEN MULTIPLE TIMES you are logged in.

In-class Quiz 2/3If you press a book flat against a vertical wall with your hand, in what direction is the friction force

exerted by the wall on the book?

1. downward2. upward2. upward3. out of the wall4. into the wall5. Can not be

determined

In-class Quiz 2/23A crate is sitting on the center of a flatbed truck.

As the truck accelerates to the east, the crate moves with it, not sliding on the bed of the truck. In what direction is the friction force exerted by the bed of

the truck on the crate?1. To the west1. To the west2. Upward3. To the east4. Downward5. Can not be

determined

In-class Quiz 2/23There are six books in a stack, each with a weight of 5.0 N. The coefficient of friction between all the books is 0.20 as is the coefficient between the table and the bottom book. What horizontal push must I just exceed on the next to bottom book to start sliding the top five books off the bottom one?books off the bottom one?

1. 1.0 N

2. 5.0 N

3. 3.0 N

4. 7.0 N

Ex. Suppose a block with a mass of 2.50 kg is resting on a ramp. If the coefficient of static friction between the block and ramp is 0.35, what maximum angle can the ramp make with the horizontal before the block starts to slip down?

In-class Quiz 2/3For the block on the ramp

the frictional force is pointed--

1. Normal to the ramp2. Down the down3. Up the ramp3. Up the ramp4. Out of the page5. Can not be

determined

Block on a Ramp

• Axes are rotated as usual on an incline

• The direction of impending motion would be down the planeplane

• Friction acts up the plane– Opposes the motion

• Draw Free Body Diagram yada yada yada

Ex 4.13

m1=4kg

m2=7kg

µµk =0.3

Find acc. and tension.

Chapter 5.1-5.2Energy and Work

•Mechanical Energy

•Kinetic (associated with motion)

•Potential (associated with position)

•Chemical Energy

•Electromagnetic Energy

•Nuclear Energy

Energy can be transformed from one form to anotherBut not destroyed--Conserved

Work/Energy can be used in place of Newton’s laws to solve certain problems more simply

Work

F is the magnitude of the net force

∆ x is the magnitude of the object’s displacement

θ is the angle between

x)cosF(W ∆θ≡

and ∆F xr r

• This gives no information about

– the time it took for the displacement to occur

– the velocity or acceleration of the object

• Work is a scalar quantity

Lecture Quiz 2/3What are the units of Energy & Work?

A. Newton • meter

B. kg • m2 / s2

C. foot • pound

D. Joule

E. All of the above

Units of Work

• SI

– Newton • meter = Joule

• N • m = J

• J = kg • m2 / s2

• US Customary

– foot • pound

• ft • lb

–no special name

Energy: ability to do work

Work is Zero when force and displacement are perpendicular

• Displacement is horizontal

• Force is vertical

• cos 90° = 0

Carrying a bucket of water

• cos 90° = 0

So no work done!

Work Can Be Positive or Negative• Work done on box is

positive when lifting the box

• Work is negative if lowering the box

– The force would still be upward, but the displacement would be downward

OR

Box does positive work on student when lowered

Kinetic Energy

• Energy associated with the motion of an object

• 2mv1

KE =•

• Scalar quantity with the same units as work

• Work is related to kinetic energy

mv2

KE =

Work-Kinetic Energy Theorem

• When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energyenergy

•– Speed will increase if work is positive

– Speed will decrease if work is negative

net f iW KE KE KE= − = ∆

Work and Kinetic Energy

• An object’s kinetic energy can also be thought of as the amount of work the moving object could do in moving object could do in coming to rest– The moving hammer has

kinetic energy and can do work on the nail