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Unformatted text preview: his roller
coaster car rolls without friction.
(a) What minimum kinetic energy
does the car need in order to make
it over the hill?
(1/A) mgh
(2/B) mgH
(3/C) mg (H  h)
(4/D) mg (H + h)
(b) How much kinetic energy will
the car then have when it reaches
the bottom of the hill?
(1/A) mgh
(2/B) mgH
(3/C) mg (H  h)
(4/D) mg (H + h) m
H ?!? h Ex. Assume that this roller
coaster car rolls without friction.
(a) What minimum kinetic energy
does the car need in order to make
it over the hill?
(1/A) mgh
(2/B) mgH
(3/C) mg (H  h)
(4/D) mg (H + h)
(b) How much kinetic energy will
the car then have when it reaches
the bottom of the hill?
(1/A) mgh
(2/B) mgH
(3/C) mg (H  h)
(4/D) mg (H + h) m
H ?!? h Ex. The potential energy U(r) for the
interaction between a proton and
nucleus is graphed as a function of their
centertocenter separation r.
(a) Which position r is a point of
unstable equilibrium?
(1/A) 1 fm (2/B) 3 fm (3/C) 4 fm (4/D) 7 fm (5/E) None of these fm (b) Which position r is a point of
stable equilibrium?
(1/A) 1 fm (2/B) 3 fm (3/C) 4 fm (4/D) 7 fm (5/E) None of these
(c) At which position r is the force on
the proton attractive?
(1/A) 1 fm (2/B) 3 fm (3/C) 4 fm (4/D) 7 fm (5/E) None of these r
Nucleus Proton Ex. The potential energy U(r) for the
interaction between a proton and
nucleus is graphed as a function of their
centertocenter separation r.
(a) Which position r is a point of
unstable equilibrium?
(1/A) 1 fm (2/B) 3 fm (3/C) 4 fm (4/D) 7 fm (5/E) None of these fm (b) Which position r is a point of
stable equilibrium?
(1/A) 1 fm (2/B) 3 fm (3/C) 4 fm (4/D) 7 fm (5/E) None of these
(c) At which position r is the force on
the proton attractive?
(1/A) 1 fm (2/B) 3 fm (3/C) 4 fm (4/D) 7 fm (5/E) None of these r
Nucleus Proton Ex. with Univ. Grav: Escape velocity
It’s possible to escape the Earth......otherwise no NASA.
Only because the force of gravity decreases with distance from
the Earth.
A nice illustration of energy ideas:
What is the minimum speed necessary to get infinitely far away
from the Earth?
Result (transparency): vescape = √(2GM/R)
Independent of the mass of the falling object. Meteor Reentry from Space: same as escape velocity Space Shuttle 1.2 km Meteor ~ 50 m dia. ~ 3 x 108 kg @ 13 km/s → 2.5 x 1016 J
Barringer Meteor Crater (Arizona) Engraving of the 1833 Leonid Meteor Storm Power
Power is the rate of doing work or transferring energy.
Units: 1 Watt = Joule/sec Q: How much power does it take to hold a barbell over your head?
A: None
Q: How much power does it take to lift a barbell?
A: It depends how fast you do it. : f f f dU...
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This note was uploaded on 09/29/2012 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell University (Engineering School).
 Spring '06
 PANTANO
 Multivariable Calculus

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