Answer:
a) x=63.0
or 6.3cm
b) x=116.0
or 11.6cm
Explanation:
a).
The elastic potential energy is modeling by equation :

b).
The work energy theorem explain which work is done in this case. the motion began from the rest so K1=K2 equal zero, Ug1 is no yet done and U2is also zero because is the potential energy

Solving for x


The negative is discard so
x=0.116m
The negatively charged rod cause charge migration within the penny. So, the protons and electrons in the penny move to seperate sides of the penny with the protons on the side closest to the iron ball. Then the penny could have been touched by a person or another object to ground the penny, removing the excess electrons in the penny. This is called charging by induction. So after grounding, the penny becomes positively charged. Opposite charges attract
Answer:
angular acceleration = 209.44 [rad/s^2]
Explanation:
First we have to convert the velocities which are in revolutions per minute to radians on second.
where:
![w_{0} = 1000 [\frac{rev}{min}]*[\frac{2\pi rad }{1rev}] * \frac{1min}{60s} = 104.7[\frac{rad}{s} ]\\w = 2000 [\frac{rev}{min}]*[\frac{2\pi rad }{1rev}] * \frac{1min}{60s} = 209.4[\frac{rad}{s} ]](https://tex.z-dn.net/?f=w_%7B0%7D%20%3D%201000%20%5B%5Cfrac%7Brev%7D%7Bmin%7D%5D%2A%5B%5Cfrac%7B2%5Cpi%20rad%20%7D%7B1rev%7D%5D%20%20%2A%20%5Cfrac%7B1min%7D%7B60s%7D%20%3D%20104.7%5B%5Cfrac%7Brad%7D%7Bs%7D%20%5D%5C%5Cw%20%3D%202000%20%5B%5Cfrac%7Brev%7D%7Bmin%7D%5D%2A%5B%5Cfrac%7B2%5Cpi%20rad%20%7D%7B1rev%7D%5D%20%20%2A%20%5Cfrac%7B1min%7D%7B60s%7D%20%3D%20209.4%5B%5Cfrac%7Brad%7D%7Bs%7D%20%5D)
Now we can find the angular acceleration:
![w=w_{0} + \alpha *t\\\alpha =\frac{w-w_{0} }{t} \\\alpha =\frac{209.43-104.71}{\0.5 } \\\alpha = 209.44[\frac{rad}{s^{2} } ]](https://tex.z-dn.net/?f=w%3Dw_%7B0%7D%20%2B%20%5Calpha%20%2At%5C%5C%5Calpha%20%3D%5Cfrac%7Bw-w_%7B0%7D%20%7D%7Bt%7D%20%5C%5C%5Calpha%20%3D%5Cfrac%7B209.43-104.71%7D%7B%5C0.5%20%7D%20%5C%5C%5Calpha%20%3D%20209.44%5B%5Cfrac%7Brad%7D%7Bs%5E%7B2%7D%20%7D%20%5D)