Answer:
Grades ... gravity affects them and the potential energy is converted into kinetic energy. Watching a Slinky move down the stairs or vibrating while ... and kinetic energy, and finally into sound waves.
Explanation:
Answer:
acceleration due to gravity is constant anywhere on the earth .its value is 9.8m/s²
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Complete Question
A boy throws a ball on a spring scales which oscillates about the equilibrium position with a period of T = 0.5 sec. The amplitude of the vibration is A = 2 cm. Assume the ball does not bounce from the scales’s surface afterwards. Assume the vibration of the scale is expressed mathematically as x(t) = Acos(t + ). Find:
a) frequency
b) the maximum acceleration
c) the maximum velocity
Answer:
a
![f = 2 \ Hz](https://tex.z-dn.net/?f=f%20%3D%20%202%20%20%5C%20Hz)
b
![a_{max} = 3.2 \ m/s^2](https://tex.z-dn.net/?f=a_%7Bmax%7D%20%3D%20%203.2%20%5C%20m%2Fs%5E2)
c
![v_{max} = 0.25 \ m/s](https://tex.z-dn.net/?f=v_%7Bmax%7D%20%3D%20%200.25%20%5C%20%20m%2Fs)
Explanation:
From the question we are told that
The period is ![T = 0.5 \ sec](https://tex.z-dn.net/?f=T%20%20%3D%20%200.5%20%5C%20sec)
The amplitude is ![A = 2 \ cm = 0.02 \ m](https://tex.z-dn.net/?f=A%20%3D%20%202%20%5C%20cm%20%20%3D%20%200.02%20%5C%20m)
The vibration of the scale is ![Acos(wt + \phi )](https://tex.z-dn.net/?f=Acos%28wt%20%2B%20%20%5Cphi%20%29)
Generally the frequency is mathematically represented as
![f = \frac{1}{T}](https://tex.z-dn.net/?f=f%20%3D%20%20%5Cfrac%7B1%7D%7BT%7D)
=> ![f = \frac{1}{0.5}](https://tex.z-dn.net/?f=f%20%3D%20%20%5Cfrac%7B1%7D%7B0.5%7D)
=> ![f = 2 \ Hz](https://tex.z-dn.net/?f=f%20%3D%20%202%20%20%5C%20Hz)
The maximum acceleration is mathematically represented as
![a_{max} = A *(2 \pi f)^2](https://tex.z-dn.net/?f=a_%7Bmax%7D%20%3D%20%20A%20%2A%282%20%5Cpi%20f%29%5E2)
=> ![0.02 * (2 * 3.142 * 2)^2](https://tex.z-dn.net/?f=0.02%20%2A%20%20%282%20%2A%203.142%20%20%2A%20%202%29%5E2)
=> ![a_{max} = 3.2 \ m/s^2](https://tex.z-dn.net/?f=a_%7Bmax%7D%20%3D%20%203.2%20%5C%20m%2Fs%5E2)
The maximum velocity is mathematically represented as
![v_{max} = A * (2 \pi f)](https://tex.z-dn.net/?f=v_%7Bmax%7D%20%3D%20%20A%20%2A%20%20%282%20%5Cpi%20f%29)
=> ![v_{max} = 0.02 * (2 * 3.142 * 2)](https://tex.z-dn.net/?f=v_%7Bmax%7D%20%3D%20%200.02%20%2A%20%20%282%20%2A%203.142%20%2A%20%202%29)
=> ![v_{max} = 0.25 \ m/s](https://tex.z-dn.net/?f=v_%7Bmax%7D%20%3D%20%200.25%20%5C%20%20m%2Fs)