Chapter 3: Problem 14

Describe the motion of an object that possesses kinetic energy yet undergoes no net displacement.

Short Answer

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Question: Describe the motion of an object that has kinetic energy but undergoes no net displacement. Answer: An object undergoing oscillatory motion, such as a pendulum, can possess kinetic energy while experiencing no net displacement. The object gains kinetic energy when it moves, but its initial and final positions are the same, resulting in no net displacement. Overall, the total mechanical energy remains constant throughout the oscillatory motion.

Step by step solution

Understanding the concept of kinetic energy

Kinetic energy is the energy possessed by an object due to its motion. The formula for kinetic energy (KE) is given by: KE = 0.5 * m * v^2, where m is the mass of the object and v is its velocity. For an object to have kinetic energy, it must be moving - that is, it must have a non-zero velocity.

Understanding the concept of no net displacement

Displacement is a vector quantity that represents the change in position of an object. No net displacement means that the initial position and the final position of the object are the same. In other words, the object returns to its starting point.

Identifying the type of motion with kinetic energy and no net displacement

The type of motion that satisfies these conditions is oscillatory motion, such as the motion of a pendulum or a spring-mass system. These objects move back and forth in a periodic manner. At certain points in their motion, they have kinetic energy (when moving) but also undergo no net displacement (when they return to their initial point).

Describing the motion of an oscillating object

Let's consider the motion of a pendulum as an example. When the pendulum is released from its highest point, it swings down, gaining kinetic energy as its potential energy gets converted into kinetic energy. At the lowest point, its velocity is at its maximum and therefore, it possesses the maximum kinetic energy. As the pendulum continues its motion, it swings back up toward its initial position, converting its kinetic energy back into potential energy. Finally, the pendulum returns to its starting point, completing one cycle of motion and undergoing no net displacement. Throughout its motion, the pendulum's total mechanical energy (potential energy + kinetic energy) remains constant.

Conclusion

An object undergoing oscillatory motion, such as a pendulum, can possess kinetic energy while experiencing no net displacement. The object gains kinetic energy when it moves, but its initial and final positions are the same, resulting in no net displacement. Overall, the total mechanical energy remains constant throughout the oscillatory motion.

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Describe the motion of an object that possesses kinetic energy yet undergoes no net displacement.

Short Answer

Step by step solution

Understanding the concept of kinetic energy

Understanding the concept of no net displacement

Identifying the type of motion with kinetic energy and no net displacement

Describing the motion of an oscillating object

Conclusion

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