Todays lecture will cover Textbook Sections 10.4 - 10.6
2 Review Ideal Springs
Hookes Law The force exerted by a spring is proportional to the distance the spring is stretched or compressed from its relaxed position.
FX -k x Where x is the displacement from the relaxed position and k is the constant of proportionality. (often called spring constant)
relaxed position FX - kx lt 0 x x gt 0 x0 3 Review Simple Harmonic Motion Uniform circular motion lt-gt Motion of an object attached to an ideal spring Period T (seconds per cycle) Frequency f 1/T (cycles per second) Angular frequency 2f 2/T 4 Simple Harmonic MotionQuick Review x(t) Acos(t) v(t) -Asin(t) a(t) -A2cos(t) x(t) Asin(t) v(t) Acos(t) a(t) -A2sin(t) OR Period T (seconds per cycle) Frequency f 1/T (cycles per second) Angular frequency 2f 2/T xmax A vmax A amax A2 5 Review Period of a Spring For simple harmonic oscillator 2f 2/T For mass M on spring with spring constant k Demos Amk dependence 6 Concept Question
If the amplitude of the oscillation (same block and same spring) was doubled how would the period of the oscillation change (The period is the time it takes to make one complete oscillation)
1. The period of the oscillation would double.2. The period of the oscillation would be halved3. The period of the oscillation would stay the same
x 2A t -2A 7 Potential Energy of a Spring Where x is measured fromthe equilibrium position PES x 0 8 Same thing for a vertical spring y y0 Where y is measured fromthe equilibrium position PES y 0 9 In either case... Etotal 1/2 Mv2 1/2 kx2 constant KE PE KEmax 1/2Mv2max1/2M2A2 1/2kA2 PEmax 1/2kA2 Etotal 1/2kA2 10 Concept Question
In Case 1 a mass on a spring oscillates back and forth. In Case 2 the mass is doubled but the spring and the amplitude of the oscillation is the same as in Case 1. In which case is the maximum kinetic energy of the mass the biggest
1. Case 12. Case 23. Same
11 Concept Question PE 0 KE KEMAX PE 1/2kx2 KE 0 same for both samefor both xA x0 xA x-A x0 x-A 12 Concept Question
The same would be true for vertical springs...
PE 1/2k y2 Y0 PE 1/2k y2 Y0 13 Pendulum
For small oscillation period does not depend on
Demos MAL dependence 14 Concept Question
Suppose a grandfather clock (a simple pendulum) runs slow. In order to make it run on time you should
1. Make the pendulum shorter
2. Make the pendulum longer
15 Concept Question
A pendulum is hanging vertically from the ceiling of an elevator. Initially
the elevator is at rest and the period of the pendulum is T. Now the pendulum accelerates upward. The period of the pendulum will now be
1. greater than T
2. equal to T
3. less than T
Effective g is larger when accelerating upward (you feel heavier)
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