Simple Harmonic Motion and Elasticity

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Presentation transcript:

Simple Harmonic Motion and Elasticity Chapter 10 Simple Harmonic Motion and Elasticity

10.1 The Ideal Spring and Simple Harmonic Motion spring constant Units: N/m

10.1 The Ideal Spring and Simple Harmonic Motion Example 1 A Tire Pressure Gauge The spring constant of the spring is 320 N/m and the bar indicator extends 2.0 cm. What force does the air in the tire apply to the spring?

10.1 The Ideal Spring and Simple Harmonic Motion

10.1 The Ideal Spring and Simple Harmonic Motion Conceptual Example 2 Are Shorter Springs Stiffer? A 10-coil spring has a spring constant k. If the spring is cut in half, so there are two 5-coil springs, what is the spring constant of each of the smaller springs? ½ k or 2k? All things being equal, shorter springs are stiffer springs

10.1 The Ideal Spring and Simple Harmonic Motion HOOKE’S LAW: RESTORING FORCE OF AN IDEAL SPRING The restoring force on an ideal spring is

10.3 Energy and Simple Harmonic Motion A compressed spring can do work.

10.3 Energy and Simple Harmonic Motion DEFINITION OF ELASTIC POTENTIAL ENERGY The elastic potential energy is the energy that a spring has by virtue of being stretched or compressed. For an ideal spring, the elastic potential energy is SI Unit of Elastic Potential Energy: joule (J)

10.3 Energy and Simple Harmonic Motion Example 8 Changing the Mass of a Simple Harmonic Oscilator A 0.20-kg ball is attached to a vertical spring. The spring constant is 28 N/m. When released from rest, how far does the ball fall before being brought to a momentary stop by the spring?

10.3 Energy and Simple Harmonic Motion

10.2 Simple Harmonic Motion and the Reference Circle amplitude A: the maximum displacement period T: the time required to complete one cycle frequency f: the number of cycles per second (measured in Hz)

10.4 The Period of a Spring and Pendulum A simple pendulum consists of a particle attached to a frictionless pivot by a cable of negligible mass.

Determine the length of a simple pendulum that will 10.4 The Pendulum Example 10 Keeping Time Determine the length of a simple pendulum that will swing back and forth in simple harmonic motion with a period of 1.00 s.