Transcript P221_2008_week6

Chapter 7 problems
• What is the property that a force must possess if
it is possible to define a potential energy
associated with that force? (About 14 said
“conservative, but only a few people explained
what that means; 19 were off the mark)
• there must be a restoring force, a force that pulls an object toward
some original position when the object is displaced.
• In order for a force to define a potential energy, it must act between
a particle-like object in the system and the rest of the system.
• conservative force; When the force does work on an object, the
change (delta U) in the potential energy associated with the system
is negative of the work done. -change in potential energy is caused
by a change in configuration.
• It must be a conservative force. I.e W1=-W2. The transfer of energy
has to be able to be reversed.
• If it has a potential energy then it is conservative, so it would have to
have the conservative force property of irrelevance of path. (This is
the key!)
Chapter 8: Potential Energy
•A conservative force is one for which the work done around ANY closed circuit
is ZERO
•A VERY important consequence of this is that:
•The work done by a conservative force in going from a to b depends ONLY
on the two points a and b, NOT on the path taken between them!!!
•Note: this allows us to define a CHANGE IN ENERGY associated with the
CHANGE IN POSITION (from a to b).
Chapter 8: Potential Energy
Check point 1 is the force acting here conservative?
Chapter 8: Potential Energy
Check point 1 is the force acting here conservative?
NO!!!
Chapter 8: Potential Energy
Check point 1 is the force acting here conservative?
NO!!!
But it could be conservative if the bottom path was -60 J rather than + 60J.
-
Chapter 8 Examples
g. How fast would the car be moving at point C?
Potential Energy Curves and
Conservative Forces
F(x) = - dU/dx
Chapter 8 Examples
g). What is the minimum height, h, needed to make sure that the block maintains
contact with the track as it travels around the loop (assuming it is released only)?
• In class, I will use the expression U = 1/2k (x-x_o)^2 for
the potential energy of a spring. Comment briefly on the
difference between this and U = 1/2kx^2, which is the
form given in most texts. What is the significance of the
term xo? Which form would you find more useful? (20
“initial position” 4 “equilibrium position” 5 Other 16 no
reply)
• The difference is that the second equation assumes that
the starting point is always 0.
• In the latter equation, x(0) is the initial position when it is
assumed to be 0. The first form that includes x(0) is
more useful, definitely
• The expression used in class is more general
than the one used in the book. The text equation
refers to the specific case in which the
equilibrium point of the spring is the origin of the
coordinate system.
•
A parachutist is drifting downward at a constant speed of
roughly 1m/s after his chute has opened. If the combined
mass of the parachutist and his equipment is 85.0 kg, at
what rate is he losing gravitational potential energy?
Where is this lost potential energy going?
1. He is losing gravitational potential at the same rate he is
gaining kinetic energy; so
k=1/2mv^2=1/2(85kg)(1m/s)^2=42.5J (6 answered with
this number, only one with the right unit (W, J/s, or Nm/s)
2. 85 J. The potential energy is going into the kinetic energy
of the parachutist. (4 came up with this, 2 with right units)
3. The parachutist is losing potential energy by 833 Nm per
second. This lost potential energy is converted into
kinetic energy. (9 got the number correct, all but one had
the units right, some had the sign wrong [but the Q is
ambiguous on this so that’s ok])
• Where does the energy go? (15 said “to kinetic”, 5 said
to the “drag force”, and only three said to thermal
energy).
Chapter 8 Problems (cont.)
d. What is the force of friction on the block after it comes to rest?
Chapter 7 problems
Chapter 7 problems
Chapter 8 Problems (cont.)