Learning Goal: To be able to interpret potential energy diagrams and predict the corresponding motion of…
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Question “Learning Goal: To be able to interpret potential energy diagrams and predict the corresponding motion of…”
Learning Goal: To be able to interpret potential energy diagrams
and predict the corresponding motion of a particle. Potential
energy diagrams for a particle are useful in predicting the motion
of that particle. These diagrams allow one to determine the
direction of the force acting on the particle at any point, the
points of stable and unstable equilibrium, the particle’s kinetic
energy, etc. Consider the potential energy diagram shown. (Figure
1) The curve represents the value of potential energy U as a
function of the particle’s coordinate x. The horizontal line above
the curve represents the constant value of the total energy of the
particle E. The total energy E is the sum of kinetic (K) and
potential (U) energies of the particle. The key idea in
interpreting the graph can be expressed in the equation
Fx(x)=−dU(x)dx, where Fx(x) is the x component of the net force as
function of the particle’s coordinate x. Note the negative sign: It
means that the x component of the net force is negative when the
derivative is positive and vice versa. For instance, if the
particle is moving to the right, and its potential energy is
increasing, the net force would be pulling the particle to the
left. If you are still having trouble visualizing this, consider
the following: If a massive particle is increasing its
gravitational potential energy (that is, moving upward), the force
of gravity is pulling in the opposite direction (that is,
downward). If the x component of the net force is zero, the
particle is said to be in equilibrium. There are two kinds of
equilibrium: Stable equilibrium means that small deviations from
the equilibrium point create a net force that accelerates the
particle back toward the equilibrium point (think of a ball rolling
between two hills). Unstable equilibrium means that small
deviations from the equilibrium point create a net force that
accelerates the particle further away from the equilibrium point
(think of a ball on top of a hill). In answering the following
questions, we will assume that there is a single varying force F
acting on the particle along the x axis. Therefore, we will use the
term force instead of the cumbersome x component of the net
force.
Please answer all parts
available.
Answer
A) Directed at the left
B) Directed at the right
C) Equal to zero
D) Equal to zero
E) Directed at left
F) Directed at right
G) BF
H) DH
I) BDFH
J) AE
K) A
L) D
M) B
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