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Home/ Questions/Learning Goal: To be able to interpret potential energy diagrams and predict the corresponding motion of...
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Asked: April 13, 20222022-04-13T09:30:49+00:00 2022-04-13T09:30:49+00:00In: Physics

Learning Goal: To be able to interpret potential energy diagrams and predict the corresponding motion of…

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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:

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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.

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Part A

The force acting on the particle at point A is

A. directed to the right

B. directed to the left

C. equal to zero

Part B

The force acting on the particle at point B is 

A. directed to the right

B. directed to the left

C. equal to zero Submit

Part C

The force acting on the particle at point C is

A. directed to the right

B. directed to the left

C. equal to zero Submit

Part D Complete previous part(s)

Part E If the particle is located slightly to the left of point its acceleration is

A. directed to the right
B. directed to the left
C.equal to zero
Part F
Complete previous part(s)
Part G
Name all labeled points on the graph corresponding to unstable equilibrium.
List your choices alphabetically, with no commas or spaces; for instance, if you choose points α μ and μtype your answer as BDE.
Part H
Complete previous part(s)
Part I
Complete previous part(s)
Part J
Name all labeled points such that when a particle is released from rest there, it would accelerate to the left. List your choices alphabetically, with no commas or spaces; for instance, if you choose points quand , type your answer as BDE. 
Part K
Consider points A,E and G Of these three points, which one corresponds to the greatest magnitude of acceleration of the particle?
1, A
2, E
3, G
Kinetic energy
If the total energy E of the particle is known, one can also use the graph of U (draw conclusions about the kinetic energy of the particle since 
                                                                  K = E- U
As a reminder, on this graph, the total energy E is shown by the horizontal line.
Part L
What point on the graph corresponds to the maximum kinetic energy of the moving particle? 
Part M
At what point on the graph does the particle have the lowest speed? 
♦ Relevant knowledge

Kinetic energy refers to the energy associated with the movement of an object. It is the opposite of the effort needed to bring a moving object to a stop and is based on only two variables that is the weight of the object as well as its speed.

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    Damian Roy
    2022-04-13T09:30:52+00:00Added an answer on April 13, 2022 at 9:30 am

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