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)(2

1)(

0

0

0

20

20

v

yygv

vvmyymg

KU

E

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?