Answer: option b.
Explanation:
The kinetic energy of a spring with constant K is calculated as:
kinetic energy = (k/2)*x^2
Where x^2 is the displacement of the spring with respect to it's rest position.
This can be written as a function like:
x = A*cos(2*pi*f*t)
where:
A is the amplitude (the maximum distance that the spring can move in each direction)
f is the frequency (and 2*pi*f is the angular frequency)
and t is the variable, it represents the time.
Replacing this in the kinetic energy equation, we get:
kinetic energy = (k/2)*(A*cos(2*pi*f*t))^2
This is the same as the option b: b. 1/2kA^2cos^2(2πft)
Then the corrrect option is b.
Energy = 1/2mv^2
Mass = 130kg
Speed = 5m/s
1/2 x 130 x 25
= 1625J
Answer:
fundamental quantity can simply be defined as an independent quantity while derived quantity is dependent i.e. the derive their quantities from the fundamental
Answer:
Pluck velocity = 83.34 m/s
Explanation:
The initial angular speed of the rod before it was hit, ![w_{r} = 0](https://tex.z-dn.net/?f=w_%7Br%7D%20%3D%200)
The angular speed of the rod and pluck rotating together, ![w_{2} = \frac{2\pi }{T}](https://tex.z-dn.net/?f=w_%7B2%7D%20%3D%20%5Cfrac%7B2%5Cpi%20%7D%7BT%7D)
The period of rotation, T = 0.736 s
![w_{2} = \frac{2\pi }{0.736}\\w_{2} = 8.53 rad/s](https://tex.z-dn.net/?f=w_%7B2%7D%20%3D%20%5Cfrac%7B2%5Cpi%20%7D%7B0.736%7D%5C%5Cw_%7B2%7D%20%3D%208.53%20rad%2Fs)
Using the principle of conservation of angular momentum:
![I_{r} w_{r} + I_{p} w_{p} = (I_{r}+ I_{p}) w_{2}](https://tex.z-dn.net/?f=I_%7Br%7D%20w_%7Br%7D%20%2B%20I_%7Bp%7D%20w_%7Bp%7D%20%3D%20%28I_%7Br%7D%2B%20I_%7Bp%7D%29%20w_%7B2%7D)
![I_{p} = ml^{2}](https://tex.z-dn.net/?f=I_%7Bp%7D%20%3D%20ml%5E%7B2%7D)
![w_{p} = v_{p} /l](https://tex.z-dn.net/?f=w_%7Bp%7D%20%3D%20v_%7Bp%7D%20%2Fl)
![I_{p} w_{p} = ml^{2} * \frac{v_{p} }{l} \\I_{p} w_{p} = mlv_{p}](https://tex.z-dn.net/?f=I_%7Bp%7D%20w_%7Bp%7D%20%3D%20ml%5E%7B2%7D%20%2A%20%5Cfrac%7Bv_%7Bp%7D%20%7D%7Bl%7D%20%5C%5CI_%7Bp%7D%20w_%7Bp%7D%20%3D%20mlv_%7Bp%7D)
![I_{r} w_{r} +mlv_{p} = (I_{r}+ I_{p}) w_{2}\\mlv_{p} =( (I_{r}+ I_{p}) w_{2} ) - I_{r} w_{r}\\v_{p} = \frac{( (I_{r}+ I_{p}) w_{2} ) - I_{r} w_{r}}{ml}](https://tex.z-dn.net/?f=I_%7Br%7D%20w_%7Br%7D%20%2Bmlv_%7Bp%7D%20%20%3D%20%28I_%7Br%7D%2B%20I_%7Bp%7D%29%20w_%7B2%7D%5C%5Cmlv_%7Bp%7D%20%20%3D%28%20%28I_%7Br%7D%2B%20I_%7Bp%7D%29%20w_%7B2%7D%20%29%20-%20I_%7Br%7D%20w_%7Br%7D%5C%5Cv_%7Bp%7D%20%20%3D%20%5Cfrac%7B%28%20%28I_%7Br%7D%2B%20I_%7Bp%7D%29%20w_%7B2%7D%20%29%20-%20I_%7Br%7D%20w_%7Br%7D%7D%7Bml%7D)
![I_{r} = 1/3 ML^{2} \\I_{r} = 1/3 * 1.9 * 2^{2} \\I_{r} = 2.533 kg m^{2}](https://tex.z-dn.net/?f=I_%7Br%7D%20%3D%201%2F3%20ML%5E%7B2%7D%20%5C%5CI_%7Br%7D%20%3D%201%2F3%20%2A%201.9%20%2A%202%5E%7B2%7D%20%5C%5CI_%7Br%7D%20%3D%202.533%20kg%20m%5E%7B2%7D)
![I_{p} = ml^{2} \\I_{p} = 0.163 * 2^{2} \\I_{p} = 0.652 kgm^{2}](https://tex.z-dn.net/?f=I_%7Bp%7D%20%3D%20ml%5E%7B2%7D%20%5C%5CI_%7Bp%7D%20%3D%200.163%20%2A%202%5E%7B2%7D%20%5C%5CI_%7Bp%7D%20%3D%200.652%20kgm%5E%7B2%7D)
![v_{p} = \frac{( (2.533+0.652) 8.53 ) - (2.533* 0)}{0.163*2}\\v_{p} = 83.34 m/s](https://tex.z-dn.net/?f=v_%7Bp%7D%20%20%3D%20%5Cfrac%7B%28%20%282.533%2B0.652%29%208.53%20%29%20-%20%282.533%2A%200%29%7D%7B0.163%2A2%7D%5C%5Cv_%7Bp%7D%20%20%3D%2083.34%20m%2Fs)
True, because people should reach their full potential within themselves and human psychologist should help those that need help to reach it.