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Physics 101 Tuesday10/4/11 Class 12"

Chapter 8.3 – 8.5"Conservation of mechanical energy"Work by non-conservative forces"Potential energy curves and equipotentials"

A mass attached to a

vertical spring causes

the spring to stretch

and the mass to move

downwards. What can

you say about the

spring’s potential

energy (PEs) and the

gravitational potential

energy (PEg) of the

mass?

a) both PEs and PEg decrease

b) PEs increases and PEg decreases

c) both PEs and PEg increase

d) PEs decreases and PEg increases

e) PEs increases and PEg is constant

Springs  and  Gravity  

Down  the  Hill  

 Three  balls  of  equal  mass  start  from  rest  and  roll  down  different  ramps.    All  ramps  have  the  same  height.    Which  ball  has  the  greater  speed  at  the  bo<om  of  its  ramp?  

a

d) same speed for all balls b c

Conservation of mechanical work!

A marble rolls down a frictionless track, and reaches speed v at the bottom. If you want it to reach a speed of 4 v at the bottom, you need the start of the new track to be A: twice as high B: 4 times as high C: half as high D: 16 times as high E: (need more information) as the original track height.

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Water  Slide  I  

a) Paul

b) Kathleen

c) both the

same

 Paul  and  Kathleen  start  

from  rest  at  the  same  

@me  on  fric@onless  water  

slides  with  different  

shapes,  but  the  same  

height.    At  the  bo<om,  

whose  velocity  is  greater?  

Water  Slide  II  

 Paul  and  Kathleen  start  

from  rest  at  the  same  

@me  on  fric@onless  

water  slides  with  

different  shapes.    Who  

makes  it  to  the  bo<om  

first?  

a) Paul

b) Kathleen

c) both the same

Cart  on  a  Hill  

 A  cart  star@ng  from  rest  rolls  down  a  hill  and  at  the  bo<om  has  a  speed  of  4  m/s.    If  the  cart  were  given  an  ini@al  push,  so  its  ini@al  speed  at  the  top  of  the  hill  was  3  m/s,  what  would  be  its  speed  at  the  bo<om?  

a) 4 m/s

b) 5 m/s

c) 6 m/s

d) 7 m/s

e) 25 m/s

Conservation of mechanical work!

A 10-kg weight is suspended from the ceiling by a spring. The weight-spring system is at equilibrium with the bottom of the weight about 1 m above the floor. The spring is then stretched until the weight is just above the eggs. When the spring is released, the weight is pulled up by the contracting spring and then falls back down under the influence of gravity. On the way down, it A: reverses its direction of travel well above the eggs. B: reverses its direction of travel precisely as it reaches the eggs. C: makes a mess as it crashes into the eggs. © Eric Mazur, "Peer Instruction" 1997

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questions! Worked Example!

(8-31, sort of) A 0.5 kg rock is thrown at an angle of 30 degrees from the top of a cliff that is 20 m high. When it hits the ground at the base of the cliff, the rock has a speed of 30 m/s. Assuming that the air resistance can be ignored find (a) the initial speed of the rock, (b) the greatest height of the rock as measured from the base of the cliff.

Conservation of mechanical energy!

A spring-loaded dart gun shoots straight up, and the dart reaches a maximum height of 24 m. The same dart is shot straight up again, but this time the spring is compressed only half as far before firing. How far up does the dart go this time, neglecting friction and assuming an ideal spring? A: 48 m B: 24 m C: 12 m D: 6 m E: 3 m © From E. Mazur, "Peer Instruction”

Projectiles and conservation of energy!

The same gun is reloaded with the spring compressed like the first time, but now the gun is aimed at an angle of 45o to the horizontal. Will the dart reach the same maximum height of 24 m? A: Yes, the dart will reach the same height B: No, the dart will not reach the same height.

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Conservation of mechanical energy! Conservation of mechanical energy!

Conservation of mechanical energy! Conservation of mechanical energy!

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You see a leaf falling to the

ground with constant

speed. When you first

notice it, the leaf has initial

total energy PEi + KEi. You

watch the leaf until just

before it hits the ground, at

which point it has final total

energy PEf + KEf. How do

these total energies

compare?

a) PEi + KEi > PEf + KEf

b) PEi + KEi = PEf + KEf

c) PEi + KEi < PEf + KEf

d) impossible to tell from the information

provided

Falling  Leaves   Falling  Balls  

a) smaller

b) the same

c) greater

 You  throw  a  ball  straight  up  

into  the  air.      In  addi@on  to  

gravity,  the  ball  feels  a  force  

due  to  air  resistance.      

Compared  to  the  @me  it  

takes  the  ball  to  go  up,  the  

@me  it  takes  to  come  back  

down  is:  

Non-conservative Forces!

A mass slides down a ramp (height h, length L) Its initial speed is v. There is friction along the ramp ( µK) When it reaches the bottom, what is the final kinetic energy of the object?

h L

v

! A: 1/2 mv^2 B: 1/2 mv^2 + mgh C: 1/2 mv^2 + mgh - µK mgL D: 1/2 mv^2 + mgh - µK mg L cos! E: Not enough information to decide.

Non-conservative forces!

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Non-conservative forces!

A 100 kg in-line skater does 3000 J of non-conservative work by pushing against the ground with his skates. In addition friction does -750 J of non-conservative work on the skater. If the initial and final speeds of the skater were 2.0 m/s and 1 m/s, has the skater gone uphill or downhill? The height of the hill is: A) 2 m B) 5 m C) 3 m

height (m)

x (m)

0 20 40 60 80

20

40

80

100

A roller coaster rolls without friction along a track shown below. It’s initial speed at the beginning of the track (which is somewhere off to the left, not shown) is great enough to allow it to coast along the whole track. Neglect friction

At what position, x, is the kinetic energy a maximum, and at what position, x, is the potential energy a minimum? A: KE Max at 100; PE min at 100 B: KE Max at 60; PE Min at 60 C: KE Max at 100; PE Min at 60 D: KE Max at 60; PE Min at 100

Potential energy curves!

A cart rolls without friction along a track. The graph of PE vs. position is shown. The total mechanical energy (KE + PE) is 45 kJ.

0 20 40 60 80 100 120 140 160x(m)

50

40

30

20

10

0

E_tot

PE(kJ)

To within 5 kJ, what is the maximum KE over the stretch of track shown? A: 25 kJ B: 7 kJ C: 45 kJ D: None of these.

Potential energy curves!

A cart rolls without friction along a track. The graph of PE vs. position is shown. The total mechanical energy (KE + PE) is 0 kJ. What is the maximum KE of the cart during its journey (to within 5 kJ)?

0 20 40 60 80 100 120 140 160x(m)

0

-10 kJ

PE(kJ) -20 kJ

-30 kJ

-40 kJ

-50 kJ

A: 12 kJ B: -12 kJ C: 30 kJ D: 40 kJ E: None of these

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Potential energy Turning points!

A 2 kg object moves along the x-axis, subject to the potential energy shown in the figure below. If the objects speed at point C is 2.0 m/s, what are the approximate turning points?

A) A B) A and E C) B D) D E) C

Work energy theorem!

Students are discussing how an object can change its kinetic energy i.e., have a ΔKE. They express the opinions stated below. With which student do you agree? (A): “The Work-Energy Theorem says that the net work done by all the forces on an object gives the change in KE. I think the only way to change the kinetic energy of an object is if there is net work done by the forces on it.” (B): “But, Conservation of Energy says that you can change the KE if the potential energy changes by the opposite amount, so that’s a different way to change KE.” (C): “I think that you could have net work by all the forces AND a change in potential energy that just cancel out, say where the net work by a hand on a book exactly cancels the change in gravitational potential energy, so you can have net work by all the forces and no change in KE.”

Reading Assignment!

Thursday 10/6 9.1-9.4 Tuesday 10/11 9.5 – 9.7