Physics 151 Week 12 Day Topics: Hooke’s Law and Oscillations (Chs. 8 & 14)  Springs  Hooke’s Law  Applications  Oscillations  Period & Frequency

The Spring Force The magnitude of the spring force is proportional to the displacement of its end: F sp = k ∆l Slide 8-21  l (m)

Beyond the Elastic Limit Slide 8-31

Hooke’s Law If you stretch a rubber band, a force appears that tries to pull the rubber band back to its equilibrium, or unstretched, length. A force that restores a system to an equilibrium position is called a restoring force. If s is the position of the end of a spring, and s e is the equilibrium position, we define Δs = s – s e. If (F sp ) s is the s-component of the restoring force, and k is the spring constant of the spring, then Hooke’s Law states that The minus sign is the mathematical indication of a restoring force.

Hooke’s Law

Checking Understanding Which spring has the largest spring constant? Slide 8-23

Which spring has the largest spring constant? Answer A Slide 8-24

Checking Understanding The same spring is stretched or compressed as shown below. In which case does the force exerted by the spring have the largest magnitude? Slide 8-25

E. Not enough information to tell. The same spring is stretched or compressed as shown below. In which case does the force exerted by the spring have the largest magnitude? Answer Slide 8-26

Spring Problem 1 Slide A 20-cm long spring is attached to the wall. When pulled horizontally with a force of 100 N, the spring stretches to a length of 22 cm. What is the value of the spring constant?

Spring Problem 2 Slide The same spring is used in a tug-of-war. Two people pull on the ends, each with a force of 100 N. How long is the spring while it is being pulled?

The same spring is now suspended from a hook and a 10.2 kg block is attached to the bottom end. How long is the stretched spring? Spring Problem 3 Slide 8-29

Equilibrium and Oscillation Slide 14-12

Linear Restoring Forces and Simple Harmonic Motion Slide 14-13

Frequency and Period Period The time  t for the oscillator to make one complete cycle Frequency The number of cycles in a given amount of time. For example: the number of cycles per second (units => Hertz - Hz )

An object makes 10 revolutions going around a circle in 2 seconds. a.How long does each revolution take? b.What is the frequency of revolutions? c.If the circle has a radius r = 30 cm, what is the object's speed? Show solutions in symbols before plugging in numbers. Going in Circles Slide 8-29

Sinusoidal Relationships Slide 14-21

Frequency and Period The frequency of oscillation depends on physical properties of the oscillator; it does not depend on the amplitude of the oscillation. Slide 14-14