PHYS16 – Lecture 18
Energy Conservation: Sleds and Rollercoasters October 20, 2010
Administration
• TA Help Sessions – Su 8-9 pm, W 8-9 pm, Sa 3-5pm– Merrill 116 (around the corner from my office)
• Course Website– Lectures posted– Assignments + Solutions posted– Announcements posted (in class, by email, on
website)
This Week
• Spring Force and Energy• Conservative vs. Nonconservative Forces• Conservation of Energy– Sleds and Rollercoasters– Springs– Pendulums
Questions from Last time
When is work negative?
• Work is (+) when done on system, (-) when done by system
• Work is (+) when force and displacement in the same direction, (-) when in opposite directions
• Examples of some problems with Work…
P16 is Bulking up…
• Becca decides to move couches and applies 200 N of force and moves a couch 5 m. – What is the work done by Becca to the couch? 1000 J– What is the work done by gravity to the couch? 0 J– What is the work done by the normal force to couch? 0 J– What is the work done by friction to couch if couch moves at
constant speed? -1000 J
P16 is Bulking up…
• Peter builds a weight system where he has to move a weight attached to a spring 5 m. He applies 5 N of force. – What is the work done by Peter to the weight? 25 J– Let’s say that the spring constant is variable so that Peter ends
up moving the weight at a constant speed, then what is the work done by the spring? -25 J
In this instance the spring force would be constant so W=-Fspringxwhere the magnitude of Fspring equals 5 N
P16 is Bulking up…
• Tim uses Peter’s weight system except he applies 10 N of force to move the weight 5 m. – What is the work done by Tim to the weight? 50 J– The weight system hasn’t changed so what is the work done
by the spring? -25 J, the weight is accelerating, so the rest of Tim’s work goes to increasing kinetic energy of weight!
P16 is Bulking up…
• Jorge decides to slow down large moving crates. He pushes a crate with 500 N of force for 100 m, slowing the crate down. – What is the work done by Jorge to the crate? -50,000 J
P16 is Bulking up…
• Who did the most work?– Becca = 1000 J– Peter = 25 J– Tim = 50 J– Jorge = -50,000 J
– Jorge used the most calories, so if you asked which person did the most biological work within their body, it would be Jorge…
– However, if you asked who did the most mechanical work to their particular system, it would be Becca
Zero point of Gravitational Potential
• For gravitational potential energy where you set the zero point is arbitrary. However, once choice is made you have to stick with it.
• Examples for Gravitational Potential
Sledding…
5 m
10 m
20 m
What is the change in energy for the sledder from the top to current position?
Energy Conservation
Conservative vs. Nonconservative Forces
• Conservative Forces– force where work done over ANY closed path is zero
WAtoB = -WBtoA
WAtoB, path 1 = WAtoB, path 2
• Nonconservative force – not conservative
• Conservative– Spring Force– Gravity– Buoyant Force
• Nonconservative– Friction– Air resistance/Drag– Fluid resistance– Applied Forces
Conservative vs. Nonconservative Forces
Situation DependentTensionNormal Force
When is normal force conservative?
FN
FG
)cos(GN FF
Situation #1Block slides down frictionless inclined plane at constant velocity.
Conservative system – Normal force isConservative, but not doing work anyway…
Situation #2Block on table. Table is lifted by person atconstant acceleration.
FN
FG
Fapplied
appliedN FF
Nonconservative system – Normal force isnot conservative, normal force is doing work
When is tension conservative?
GFT
Situation #1Block being lifted by weight atconstant velocity.
Conservative system – Tension isconservative
Situation #2Block being lifted by person.
T
FG
Fapplied
appliedFT
Nonconservative system – Tension isnot conservative
T
FG
Energy Conservation
• For Conservative Forces and an Isolated System:
• For Nonconservative Forces:
0E
0externalor ativenonconserv WE
Sledding
• Ignore friction. What is the velocity of our sledder at the current position if they started from top?
5 m
10 m
20 m
Ground
m/s 10)5)(10(2
)(2
0)(21)(
00
0
20
20
v
yygv
vvmyymg
KUE
Clyde on the Rollercoaster
• Our favorite green dinosaur, Clyde, wants to take a ride on the rollercoaster. What is his speed at the end, if he starts at 62 cm and ends at 18 cm?
• Does it matter that he went over a loop? No
m/s 8.8)62.18)(.10(2
)(2 0
v
yygv
Discussion Question 1
• Why is the second hill in a roller coaster ride always shorter than the first? (Hint: there are two answers.)
Discussion Question 2
• A 0.5 kg ball is on a 0.5 m platform. There is a straight ramp down to the bottom or a ramp that looks more like a slide. Ignore friction.– What is the velocity of the ball at the end of each
ramp?– Which ramp will be the quickest way down?
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