Clicker Question Room Frequency BAA mass m is sliding on a frictionless plane tilted at an angle q as shown. The mass is moving up the plane because it was pushed up the plane by a spring a short time before (note that the spring is no longer in contact).

Which of the following free-body diagrams most accurately represents the forces on the mass m at the moment shown in the diagram (after it was given an uphill push)?

59% 32% 1% 8%

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Average = 67.4 out of 100Stan. Dev. = 17.6A range (85-100) B range (70-85)C range (55-70) D range (40-55)F range (0-40)

Clicker Question Room Frequency BA

A mass m is pulled to the right along a frictionless surface by a force of magnitude F at an angle q, as shown.

What is the magnitude of the normal force N exerted on the mass by the table? 31%

3%15%3%48%

mg

N

Fcosq

Fsinq

Fnet,y=N+Fsinq-mg=0N=mg-Fsinq

“Do not try to bend the spoon — that's impossible. Instead, only try to realize the truth: there is no spoon.”

This physics material is hard.It is particularly difficult to overcome preconceived

notions that are backed up by years of observations.

No force is required in the direction of the velocity.

Keep working on these concepts and we are here to help.

Assume an isolated system (no external work).Assume no dissipation from friction (i.e. thermal energy generation)

Roller Coaster ProblemClicker Question Room Frequency BA

Which of the following is true:A) Speed at position A = Speed at position BB) Speed at position A > Speed at position BC) Speed at position A < Speed at position B

A B

Roller Coaster ProblemClicker Question Room Frequency BA

If the car is just sitting at the top of this hill:A) The net force on the car is upward.

B) The net force on the car is downwardC) The net force on the car is zero

mg

NFnet,y = N-mg = may = 0

Roller Coaster ProblemClicker Question Room Frequency BA

If the car moving rightward at the top of this hill:A) The net force on the car is upward.

B) The net force on the car is downwardC) The net force on the car is zero

mg

N Fnet,y = N-mg = may = mv2/r

v

Approximately circular arc

ΔEmechanical + ΔEthermal = Wexternal

Emechanical = KE + PE

ΔEthermal = thermal energy generated = -Wfriction

Wfrict = -Ffriction Δx = -μk N Δx

Wexternal = external work done on the system

General Statement of Conservation of Energy

SystemEnergy can move from

KE to PE to Ethermal

Wexternal

Can change energy of the system

KEi + PEi + Wfrict + Wexternal = KEf + PEf

Wexternal > 0 if external work is done on the system

Wexternal < 0 if external work is done by the system

Wexternal = 0 if no external work is done on or by the system

Wfrict < 0 if there is friction

Wfrict = 0 if there is no friction

or

General Statement of Conservation of Energy

ΔEmechanical + ΔEthermal = Wexternal

Under what condition will the final mechanical energy be greater than the initial mechanical energy?

A) Wexternal > |Wfriction| B) Wexternal < |Wfriction| C) Wexternal = |Wfriction| D) It will never be greater than the initial mechanical energyE) It will always be greater than the initial mechanical energy

Clicker Question Room Frequency BA

KEi + PEi + Wfrict + Wexternal = KEf + PEf

Under what condition will Wexternal be negative?

A) If the external work is done on the system.B) If the external work is done by the system.C) It will never be negative.D) It will always be negative.

Clicker Question Room Frequency BA

KEi + PEi + Wfrict + Wexternal = KEf + PEf

If there is work done by the system, the system loses energy to the

surroundings that it does work on.

System = everything in the boxOne has to be careful about the definition of the “system”

Friction between hippo and rug converts

mechanical energy to thermal energy.

However, no external work. All energy

remains within the system (isolated).

System = everything in the box Friction between hippo and rug converts

mechanical energy to thermal energy.

Friction force of rug on the hippo is now an external

force. Thus energy leaves the system.

A mass m slides down a rough ramp of height h. Its initial speed is zero. Its final speed at the bottom of the ramp is v.

h

m

Which of the following expressions gives the speed squared (v2) of the block when it reaches the bottom of the ramp?

A) 2gh B) 2gh

C) 2gh W frict D) 2gh 2W frict

m

E) 2gh 2W frict

m

Clicker Question Room Frequency BA

KEi + PEi + Wfrict + Wexternal = KEf + PEf

0 + mgh + Wfrict + 0 = ½ mv2 + 0

mW

ghv fric222

Find the work done by friction…

Another Look

h

A mass m slides down a rough ramp of height h. Its initial speed

is zero. Its final speed at the bottom of the ramp is v.

KEi + PEi + Wfrict + Wexternal = KEf + PEf

0 + mgh + Wfrict + 0 = ½ mv2 + 0

Wfrict = ½ mv2 - mgh <0

D(Mechanical Energy) = -Wfric = mgh- ½mv2

Another LookA mass m slides down a rough

ramp of height h. Its initial speed is zero. Its final speed at the

bottom of the ramp is v. h

Find the work done by friction using another method…

Wfric = Forcefric x displacement

Wfric = mk N x displacement

Wfric = mk (mgcosq) x (h/sinq)

q

Wfric = mk mgh cot(q) =DME = ½ mv2 - mgh

)cot(1(2 qmkghv

The effect of some forces is expressed as a Potential Energy:e.g., gravity, elastic forces produced by springs (later)

These forces are said to be Conservative.

They have the property that the work done depends only on the starting and ending points, not the path taken while the force is being applied.

The work done by some other forces depends on the path taken: e.g., friction. Under the action of these forces, mechanical energy is lost.

The friction force is Non-Conservative. Its effect cannot be expressed as a Potential Energy.

Clicker Question Room Frequency BA

A blue car coasts in neutral (no stepping on the gas or brakes) down the blue path.

A red car coasts in neutral (no stepping on the gas or brakes) down the red path.If only gravity is acting, then

A) The red car ends up with a larger velocityB) The blue car ends up with a larger velocity

C) The two velocities are equal at the end

Force = -kxHooke’s “Law”

k = “spring constant” units = N/mx = displacement of spring

SpringsSpring in “relaxed” position

exerts no force

Compressed spring pushes back

Force

Stretched spring pulls back

Force