Recitation QuestionsWednesday, 20 March

1. The work-energy theorem, �KE = ~F ·�~s, is closely related to the “third kinematicsrelation”, v2f � v2i = 2a�x. How are they related? How is the work-energy theoremmore general and more powerful? Discuss this with your group, and call your TA orcoach over when you have an answer and discuss it with them.

2. Think of a situation in which:

(a) Kinetic friction does positive work

(b) Static friction does positive work

(c) Air resistance does positive work

(d) A normal force does negative work

(e) A normal force does positive work

(f) Tension does positive work

(g) Tension does negative work

(h) Tension does zero work

(i) Traction does zero work

1

of you take o : - eh? - 2am '' (F) -

TEIFI, cos @

Thus,the third kinematic relation is a special ease of the work energy theorem in

which the force is in the same direction as the displacement .

2 things with friction between them with one moving faster then the

other

Traction

sailing boat

Punch Stuff

Elevator floor on the person inside of it .

elevator going up

elevator going down

something hanging moving sideways

ear moving on a curve

To solve all parts of the following two problems, take the following steps:

(a) Draw clear cartoons of your “before” and “after” situations. (One of the biggestsources of mistakes is not being explicit about the two pictures that you areconsidering with the work-energy theorem.)

(b) Think carefully about all forces that do work on the object in question betweenthe “before” and “after” states.

(c) Write down the work-energy theorem:

1

2mv20 + work done by force 1 + work done by force 2 + ... =

1

2mv2f

(d) Determine the work done by each force, as either:

• Work equals the component of the force parallel to the motion, multiplied bythe distance moved: W = Fkd

• Work equals the size of the force, multiplied by the component of the distancemoved parallel to the force: W = Fdk

• Work equals the size of the force, multipled by the distance moved, multipliedby the cosine of the angle between them: W = Fd cos ✓

(e) Put these expressions for work into the work-energy theorem, and solve for what-ever you need to solve for.

2

3. Someone drops a penny of mass 2.5g o↵ of the Empire State Building (height 380m). It strikes the ground traveling at 50 m/s, having been slowed somewhat by airresistance.

(a) With what velocity would it have struck the ground if there were no air resistance?

(b) What was the work done by the drag force?

(c) This penny strikes the sidewalk and penetrates the surface, digging a hole 2 cmdeep. What was the upward force exerted on the penny by the pavement?

3

JB2.5×10 -3kg.

Of - ? Before After Forces doing work : . gravity00=0 MI S2

-

•Lesson

µ.

→-

l l 7 1

If there was no air resistance, no energy would be dissipated ,

thus . . .

Mozi - mxzI ⇐ Eg .d- = mg . h cost = mxgh → of =fegh+# = (2×380×10) 't e 87 M/s

Before After Forces doing work : . gravity-

.. air drag

t.

--

l l 7 1

57no

Lz MOH - Azm = Wg + Wdi -

mgh

Wa = Iz MUI - Mgh = 2.5×10-3 { Iz . 502 - no . 380 } = - 6.4 My

Before AfterForces doing work i o gravity

• floor resistance

- -

" I 1111 4/1 , ;11/1050

mefzI.mu/iz2=wg+Ws.mgh

ME - YI - ghee Wf

Wf =- 2.5×10-3

. { 50-22 + 10x2xl0-2tX= - 3.1 if small

Remembering that Wf - Est tout cos 186 → left =- YI = 3%2=155 N

4. A police o�cer sets up a speed trap to catch cars driving over the speed limit comingaround a curve. A car comes around the curve and sees the o�cer, and the driverimmediately slams on her brakes to slow down before the o�cer can take a speedreading. By the time the o�cer measures the car’s speed, the car is traveling 25 m/s,in an area where the speed limit is 30 m/s. However, the o�cer pulls over the driveranyway, saying “I saw you slam on your brakes. You must have been speeding!”

The car’s driver protests the ticket in court. She says to the magistrate, “Your Honor,I can prove that I never exceeded the speed limit. It’s true that I slammed on mybrakes out of reflex as soon as I saw the o�cer. But I went back and measured themarks my tires left on the ground. Those marks are only 10.6 meters long, and bybraking for that distance there’s no way I could have decelerated from over the speedlimit down to the 25 m/s that your o�cer measured.”

Should the magistrate believe the driver? Could the car have been speeding whenshe first applied her brakes? Note that you will need to figure out the frictional forceapplied by the car’s brakes, and to do that you will need to estimate the coe�cient offriction between the tires and the pavement. Hint: do you need to know the mass ofthe car?

4

O 0

Before After-

AI = 10.6 M

{ of = 25M Is ¥E¥ To. ¥E¥ Itf-n

= N . µ n- mg . Mr

1-Mr = 0 . 3

10 .G M

Oi = ?

Wf = Iz MOI - Iz m of = In . AI = my fun . Ax .

,costs752 - n

- 2. Hyun . ax = Xm # - Ui )

- of = - 2µm ax g - offNo = J2µkAXgtOf# =

1210.15×10.6×10+252=-1625+1062= IF = 27.03

Ms

↳She wasn't Speeding