Answer:
a)
, b)
, c) ![k = 2930.059\,\frac{N}{m}](https://tex.z-dn.net/?f=k%20%3D%202930.059%5C%2C%5Cfrac%7BN%7D%7Bm%7D)
Explanation:
a) The change in the gravitational potential energy of the marble-Earth system is:
![\Delta U_{g} = (0.06\,kg)\cdot \left(9.807\,\frac{m}{s^{2}}\right)\cdot (22\,m)](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bg%7D%20%3D%20%280.06%5C%2Ckg%29%5Ccdot%20%5Cleft%289.807%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%5Cright%29%5Ccdot%20%2822%5C%2Cm%29)
![\Delta U_{g} = 12.945\,J](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bg%7D%20%3D%2012.945%5C%2CJ)
b) The change in the elastic potential energy of the spring is equal to the change in the gravitational potential energy, then:
![\Delta U_{k} = 12.945\,J](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bk%7D%20%3D%2012.945%5C%2CJ)
c) The spring constant of the gun is:
![\Delta U_{k} = \frac{1}{2} \cdot k \cdot x^{2}](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bk%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ccdot%20k%20%5Ccdot%20x%5E%7B2%7D)
![k = \frac{2\cdot \Delta U_{k}}{x^{2}}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B2%5Ccdot%20%5CDelta%20U_%7Bk%7D%7D%7Bx%5E%7B2%7D%7D)
![k = \frac{2\cdot (12.945\,J)}{(0.094\,m)^{2}}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B2%5Ccdot%20%2812.945%5C%2CJ%29%7D%7B%280.094%5C%2Cm%29%5E%7B2%7D%7D)
![k = 2930.059\,\frac{N}{m}](https://tex.z-dn.net/?f=k%20%3D%202930.059%5C%2C%5Cfrac%7BN%7D%7Bm%7D)
From the ohms law, the current through a conductor is directly proportional to the potential difference. Thus we get the equation I = V/R
where I is the current in Ampheres, V is the voltage in volts and R is the resistance in Ohms.
Hence; I = 3/12
= 0.25 Ampheres
Thus, the current through the flashlight is 0.25 Ampheres
In a fluid, all the forces exerted by the individual particles combine to make up the pressure exerted by the fluid
Due to fundamental nature of fluids, a fluid cannot remain at rest under the presence of shear stress. However, fluids can exert pressure normal to any contacting surface. If a point in the fluid is thought of as a small cube, then it follows from the principles of equilibrium that the pressure on every side of this unit of fluid must be equal. but if this were not a case, the fluid would move in the directions of the resulting force, So the pressure on a fluid at rest is isotropic.
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