Textbook Question
A system consists of interacting objects A and B, each exerting a constant 3.0 N pull on the other. What is (delta)U for the system if A moves 1.0 m toward B while B moves 2.0 m toward A?
489
views
Ch 10: Interactions and Potential Energy
Chapter 10, Problem 10
FIGURE EX10.28 shows the potential-energy diagram for a 500 g particle as it moves along the x-axis. Suppose the particle's mechanical energy is 12 J. (a) Where are the particle's turning points? 
Verified step by step guidance1
Identify the mechanical energy of the particle, which is given as 12 J.
Locate the points on the potential-energy diagram where the potential energy U(x) equals the mechanical energy (12 J). These points are the turning points.
From the graph, observe the x-axis values where the potential energy curve intersects the horizontal line at U = 12 J.
Note the x-coordinates of these intersection points. These coordinates represent the turning points of the particle.
Summarize the turning points by listing the x-coordinates where the potential energy equals the mechanical energy.
Verified Solution
Video duration:
2m
This video solution was recommended by our tutors as helpful for the problem above.Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Potential Energy
Potential energy (U) is the energy stored in an object due to its position in a force field, such as gravitational or elastic fields. In the context of the diagram, it represents the energy of the particle at various positions along the x-axis. The shape of the potential energy curve indicates how the energy changes with position, which is crucial for determining the particle's motion.
Recommended video:
Guided course
07:24
Potential Energy Graphs
Mechanical Energy
Mechanical energy is the sum of kinetic energy (KE) and potential energy (PE) in a system. For the particle in the question, the total mechanical energy is given as 12 J. This total energy remains constant if only conservative forces are acting, allowing us to find the turning points where the particle's kinetic energy is zero, and all mechanical energy is converted to potential energy.
Recommended video:
Guided course
06:24Conservation Of Mechanical Energy
Turning Points
Turning points occur where the particle changes direction, which happens when its kinetic energy is zero. At these points, the total mechanical energy equals the potential energy. By analyzing the potential energy diagram, we can identify the positions along the x-axis where the potential energy equals the mechanical energy of 12 J, indicating the locations of the turning points.
Recommended video:
Guided course
08:35Angular Momentum of a Point Mass
Related Practice
Textbook Question
A system has potential energy U(x)=(10 J)[1−sin((3.14 rad/m) x)] as a particle moves over the range 0 m≤x≤3 m
b. For each, is it a point of stable or unstable equilibrium?
814
views
Textbook Question
CALC A particle that can move along the x -axis is part of a system with potential energy
U(x)= A/x2 − B/x where A and B are positive constants.
a. Where are the particle's equilibrium positions?
491
views