A child on a merry-go-round takes 3.9 s to go around once. What is his angular displacement during a 1.0 s time interval?
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Answer:
<em>k = 25.18 N/m</em>
Explanation:
<u>Simple Harmonic Oscillator</u>
It consists of a weight attached to one end of a spring being allowed to move forth and back.
If m is the mass of the weight and k is the constant of the spring, the period of the oscillation is given by:
If the period is known, we can find the value of the constant by solving for k:
Substituting the given values m=5 Kg and T=2.8 seconds:
k = 25.18 N/m
To solve this problem it is necessary to apply the concepts related to the conservation of energy, through the balance between the work done and its respective transformation from the gravitational potential energy.
Mathematically the conservation of these two energies can be given through
Where,
W = Work
Final gravitational Potential energy
Initial gravitational Potential energy
When the spacecraft of mass m is on the surface of the earth then the energy possessed by it
Where
M = mass of earth
m = Mass of spacecraft
R = Radius of earth
Let the spacecraft is now in an orbit whose attitude is then the energy possessed by the spacecraft is
Work needed to put it in orbit is the difference between the above two
Therefore the work required to launch a spacecraft from the surface of the Eart andplace it ina circularlow earth orbit is