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When the external force holding the object is released, as in Figure 14-3c, the net force and the acceleration are at their maximum, and the velocity is zero As the object passes through the equilibrium point, Figure 14-3d, the net force is zero, and so is the acceleration Does the object stop No, it would take a net downward force to slow the object, and that will not exist until the object rises above the equilibrium position When the object comes to the highest position in its oscillation, the net force and the acceleration are again at their maximum, and the velocity is zero The object moves down through the equilibrium position to its starting point and continues to move in this vibratory manner The period of oscillation, T, depends upon the mass of the object and the strength of the spring Automobiles Elastic potential energy is an important part of the design and building of today s automobiles Every year, new models of cars are tested to see how well they withstand damage when they crash into barricades at low speeds A car s ability to retain its integrity depends upon how much of the kinetic energy it had before the crash can be converted into the elastic potential energy of the frame after the crash Many bumpers are modified springs that store energy as a car hits a barrier in a slow-speed collision After the car stops and the spring is compressed, the spring returns to its equilibrium position, and the car recoils from the barrier

$sms $from1 $to1 $from2 $to2 $j Array of text speak acronyms to be replaced and their equivalents in standard English Array based on the $sms array with regular expression operators for processing uppercase Array containing the standard English replacements for $from1 Array based on the $sms array with regular expression operators for processing lowercase Array containing the standard English replacements for $from2 Integer index for iterating through the arrays

Simple harmonic motion also can be demonstrated by the swing of a pendulum A simple pendulum consists of a massive object, called the bob, suspended by a string or light rod of length l After the bob is pulled to one side and released, it swings back and forth, as shown in Figure 14-4 The string or rod exerts a tension force, FT, and gravity exerts a force, Fg, on the bob The vector sum of the two forces produces the net force, shown at three positions in Figure 14-4 At the left and right positions shown in Figure 14-4, the net force and acceleration are maximum, and the velocity is zero At the middle position in Figure 14-4, the net force and acceleration are zero, and the velocity is maximum You can see that the net force is a restoring force; that is, it is opposite the direction of the displacement of the bob and is trying to restore the bob to its equilibrium position

9 Hooke s Law Two springs look alike but have different spring constants How could you determine which one has the greater spring constant 10 Hooke s Law Objects of various weights are hung from a rubber band that is suspended from a hook The weights of the objects are plotted on a graph against the stretch of the rubber band How can you tell from the graph whether or not the rubber band obeys Hooke s law 11 Pendulum How must the length of a pendulum be changed to double its period How must the length be changed to halve the period

12 Energy of a Spring What is the difference between the energy stored in a spring that is stretched 040 m and the energy stored in the same spring when it is stretched 020 m 13 Resonance If a car s wheel is out of balance, the car will shake strongly at a specific speed, but not when it is moving faster or slower than that speed Explain 14 Critical Thinking How is uniform circular motion similar to simple harmonic motion How are they different

oth particles and waves carry energy, but there is an important difference in how they do this Think of a ball as a particle If you toss the ball to a friend, the ball moves from you to your friend and carries energy However, if you and your friend hold the ends of a rope and you give your end a quick shake, the rope remains in your hand Even though no matter is transferred, the rope still carries energy through the wave that you created A wave is a disturbance that carries energy through matter or space You have learned how Newton s laws of motion and principles of conservation of energy govern the behavior of particles These laws and principles also govern the motion of waves There are many kinds of waves that transmit energy, including the waves you cannot see

Identify how waves transfer energy without transferring matter Contrast transverse and longitudinal waves Relate wave speed, wavelength, and frequency

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