Explanation Given data: Refer to the FIGURE P10.52 in the textbook for the energy diagram. Mass of the particle ( m ) is 2.0 g, which is written as 0.002 kg. The particle oscillates between x = 2.0 mm , and x = 8.0 mm . Formula used: Write the expression for kinetic energy of the particle. K = 1 2 m v 2 (1) Here, m is the mass of the particle, and v is the velocity (speed) of the particle. Explanation: From the given figure, the horizontal axis represents the position of the particle and the vertical axis represents the energy in terms of joules. The blue line represents the potential energyof the particle with respect to the various positions. From the given figure, the potential energy decreases from the point x = 2.0 mm to the point x = 4.0 mm , and then it increases. As the potential energy is minimum at x = 4.0 mm , the kinetic energy of the particle must be maximum in order to maintain the constant total energy at all the positions of the particle. As the kinetic energy of the particle is maximum at position x = 4.0 mm , the speed of the particle must be a maximum value at x = 4.0 mm . Therefore, the particle attains its maximum speed at x = 4.0 mm . From the concept of energy diagrams, the maximum kinetic energy of the particle is equal to the maximum potential energy of the particle. Therefore, write the expression as follows. K max = U max (2) Here, K max is the maximum kinetic energy of the particle, and U max is the maximum potential energy of the particle. From the given diagram, calculate the maximum potential energy of the particle as follows. U max = 5.0 J − 1.0 J = 4.0 J Substitute 4.0 J for U max in equation (2), K max = 4

College Physics: A Strategic Approach (4th Edition)

4th Edition

ISBN: 9780134704180

Author: Knight

Publisher: PEARSON

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Chapter 10, Problem 52P

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To find: The maximum speed of a particle that oscillates between x=2.0 mm, and x=8.0 mm.

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Chapter 10, Problem 51P

Chapter 10, Problem 53P

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Car P moves to the west with constant speed v0 along a straight road. Car Q starts from rest at instant 1, and moves to the west with increasing speed. At instant 5, car Q has speed w0 relative to the road (w0 < v0). Instants 1-5 are separated by equal time intervals. At instant 3, cars P and Q are adjacent to one another (i.e., they have the same position). In the reference frame o f the road, at instant 3 i s the speed o f car Q greater than, less than, or equal to the speed of car P? Explain.

Chapter 10 Solutions

College Physics: A Strategic Approach (4th Edition)

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The maximum speed of a particle that oscillates between x = 2.0 mm , and x = 8.0 mm .

To find: The maximum speed of a particle that oscillates between x=2.0 mm, and x=8.0 mm.

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Chapter 10 Solutions