a. Indicate with small circles the locations of maximum velocity. b. Indicate with small squares the locations of zero velocity. c. Label the period. d. Label the maximum and minimum displacements (i.e. positive and negative amplitudes). e. At which position(s) is the kinetic energy the greatest? At which position(s) is the potential energy the greatest? f. A mass of 230g stretches a hanging spring 1.35cm when at rest. When the mass is pulled an additional 3cm and released it undergoes simple harmonic motion. What is the amplitude of the oscillations? Find the period of the oscillations, and the maximum kinetic energy and maximum potential energy of the oscillator.
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Below is a plot of a system undergoing
a. Indicate with small circles the locations of maximum velocity.
b. Indicate with small squares the locations of zero velocity.
c. Label the period. d. Label the maximum and minimum displacements (i.e. positive and negative amplitudes). e. At which position(s) is the kinetic energy the greatest? At which position(s) is the potential energy the greatest?
f. A mass of 230g stretches a hanging spring 1.35cm when at rest. When the mass is pulled an additional 3cm and released it undergoes simple harmonic motion. What is the amplitude of the oscillations? Find the period of the oscillations, and the maximum kinetic energy and maximum potential energy of the oscillator.
A muscle cell (fiber) in a biceps is 20cm long and contains 1500 myofibrils arranged parallel to each other. Each myofibril is made up of many sarcomeres, organized in series, that behave as springs. A relaxed sarcomere is 2μm long. When contracted, the cell shortens to half its length and develops a force of 30mN. Each of those structures, the cell, myofibril and sarcomere, can be modeled as a spring.
a) Calculate the spring constant of a muscle cell.
b) The 1500 myofibrils in the muscle cell are arranged in parallel. Calculate the spring constant of a single myofibril.
c) The myofibrils are composed of sarcomeres that are arranged in series. Calculate the number of sarcomeres in each myofibril then calculate the spring constant of a single sarcomere.
d) When we shiver in the cold, our muscles oscillate at a frequency of 10Hz and with an amplitude of 2cm. Assume a muscle is a simple harmonic oscillator and calculate the mass of the load on that oscillator.
e) Calculate the mass of the load on a single myofiber
f) Calculate the mass of the load on a single sarcomere.
g) How would the period change if the amplitude were increased or decreased?
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