Correct question:
Consider the motion of a 4.00-kg particle that moves with potential energy given by
![U(x) = \frac{(2.0 Jm)}{x}+ \frac{(4.0 Jm^2)}{x^2}](https://tex.z-dn.net/?f=%20U%28x%29%20%3D%20%5Cfrac%7B%282.0%20Jm%29%7D%7Bx%7D%2B%20%5Cfrac%7B%284.0%20Jm%5E2%29%7D%7Bx%5E2%7D%20)
a) Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?
b) What is the magnitude of the force on the 4.00-kg particle when it is located at x = 5.00 m?
Answer:
a) 3.33 m/s
b) 0.016 N
Explanation:
a) given:
V = 3.00 m/s
x1 = 1.00 m
x = 5.00
![u(x) = \frac{-2}{x} + \frac{4}{x^2}](https://tex.z-dn.net/?f=%20u%28x%29%20%3D%20%5Cfrac%7B-2%7D%7Bx%7D%20%2B%20%5Cfrac%7B4%7D%7Bx%5E2%7D)
At x = 1.00 m
![u(1) = \frac{-2}{1} + \frac{4}{1^2}](https://tex.z-dn.net/?f=%20u%281%29%20%3D%20%5Cfrac%7B-2%7D%7B1%7D%20%2B%20%5Cfrac%7B4%7D%7B1%5E2%7D)
= 4J
Kinetic energy = (1/2)mv²
![= \frac{1}{2} * 4(3)^2](https://tex.z-dn.net/?f=%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2A%204%283%29%5E2%20)
= 18J
Total energy will be =
4J + 18J = 22J
At x = 5
![u(5) = \frac{-2}{5} + \frac{4}{5^2}](https://tex.z-dn.net/?f=%20u%285%29%20%3D%20%5Cfrac%7B-2%7D%7B5%7D%20%2B%20%5Cfrac%7B4%7D%7B5%5E2%7D)
= -0.24J
Kinetic energy =
![\frac{1}{2} * 4Vf^2](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%2A%204Vf%5E2%20)
= 2Vf²
Total energy =
2Vf² - 0.024
Using conservation of energy,
Initial total energy = final total energy
22 = 2Vf² - 0.24
Vf² = (22+0.24) / 2
![Vf = \sqrt{frac{22.4}{2}](https://tex.z-dn.net/?f=%20Vf%20%3D%20%5Csqrt%7Bfrac%7B22.4%7D%7B2%7D)
= 3.33 m/s
b) magnitude of force when x = 5.0m
![u(x) = \frac{-2}{x} + \frac{4}{x^2}](https://tex.z-dn.net/?f=%20u%28x%29%20%3D%20%5Cfrac%7B-2%7D%7Bx%7D%20%2B%20%5Cfrac%7B4%7D%7Bx%5E2%7D)
![\frac{-du(x)}{dx} = \frac{-d}{dx} [\frac{-2}{x}+ \frac{4}{x^2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-du%28x%29%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-d%7D%7Bdx%7D%20%5B%5Cfrac%7B-2%7D%7Bx%7D%2B%20%5Cfrac%7B4%7D%7Bx%5E2%7D)
![= \frac{2}{x^2} - \frac{8}{x^3}](https://tex.z-dn.net/?f=%20%3D%20%5Cfrac%7B2%7D%7Bx%5E2%7D%20-%20%5Cfrac%7B8%7D%7Bx%5E3%7D)
At x = 5.0 m
![\frac{2}{5^2} - \frac{8}{5^3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B5%5E2%7D%20-%20%5Cfrac%7B8%7D%7B5%5E3%7D%20)
![F = \frac{2}{25} - \frac{8}{125}](https://tex.z-dn.net/?f=%20F%20%3D%20%5Cfrac%7B2%7D%7B25%7D%20-%20%5Cfrac%7B8%7D%7B125%7D)
= 0.016N
<span>Final Velocity = Vf = 0 m/s --------------> (Vf = 0 because ball's speed at its max height is 0)
Initial Velocity = Vi = ?
Total time (upward & downward) = 8.0 seconds
* Time upward = 4 seconds & ................( As time for ball upward & downward is equal )
* Time downward = 4 seconds..
Gravitational Acceleration = g = -9.8 m/s²
Use Equation;
Vf = Vi - gt
0 = Vi - 9.8 * 4
0 = Vi - 39.2
39.2 = Vi
=> Vi = Initial Velocity = 39.2 m/s</span>
I think the correct answer from the choices listed above is option D. One advantage of using electromagnets in devices would be that electromagnets can <span>easily be turned on and off. Hope this answers the question. Have a nice day.</span>
Gamma rays have the highest energies and the shortest wavelengths.
Answer:
Heat energy
Explanation:
Electrons are flowing through the circuit, they pass through a resistor, in this case a light bulb. The energy is then transformed into light and heat energy.