Ch 10: Interactions and Potential Energy

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 10: Interactions and Potential Energy

Problem 28a

Chapter 10, Problem 28a

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. Where are the particle's turning points?

Verified step by step guidance

Step 1: Understand the concept of turning points. Turning points occur where the particle's mechanical energy equals its potential energy, as the kinetic energy becomes zero at these points.

Step 2: Identify the mechanical energy of the particle, which is given as 12 J. This is the total energy of the system, and the particle cannot access regions where the potential energy exceeds this value.

Step 3: Analyze the potential-energy diagram provided. Locate the points along the x-axis where the potential energy curve intersects the value of 12 J. These intersections represent the turning points.

Step 4: From the graph, observe that the potential energy curve intersects the 12 J line at two specific x-values. Carefully read these x-values from the graph.

Step 5: Conclude that the turning points are at the x-values where the potential energy equals 12 J. These points define the limits of the particle's motion along the x-axis.

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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.

Mechanical Energy

Mechanical energy is the sum of kinetic energy (KE) and potential energy (PE) in a system. In this case, the total mechanical energy of the particle is given as 12 J. The turning points of the particle occur where its mechanical energy equals the potential energy, indicating the maximum and minimum positions the particle can reach without additional energy input.

Turning Points

Turning points are positions where the particle changes direction, occurring when its kinetic energy is zero. These points can be found by identifying where the potential energy equals the total mechanical energy. In the provided diagram, the turning points correspond to the x-values where the potential energy curve intersects the horizontal line representing the mechanical energy of 12 J.

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In FIGURE EX10.27, what is the maximum speed of a 2.0 g particle that oscillates between x = 2.0 mm and x = 8.0 mm

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A system in which only one particle moves has the potential energy shown in FIGURE EX10.31. What is the x-component of the force on the particle at x = 5, 15, and 25 cm?

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A particle moving along the y-axis is in a system with potential energy U = 4y³ J, where y is in m. What is the y-component of the force on the particle at y = 0 m, 1 m, and 2 m?

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In FIGURE EX10.26, What minimum speed does a 100 g particle need at point B to reach point A?

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Textbook Question

In FIGURE EX10.28, what is the maximum speed a 200 g particle could have at x = 2.0 m and never reach x = 6.0 m?

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Textbook Question

FIGURE EX10.25 is the potential-energy diagram for a 20 g particle that is released from rest at x = 1.0 m. What is the particle's maximum speed? At what position does it have this speed?

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