3 years ago

20.What factor is more important in determining electrical force

1 answer:

6 0

Answer:

20.The first factor is the amount of charge on each object. The greater the charge, the greater the electric force. The second factor is the distance between the charges. The closer together the charges are, the greater the electric force is

Explanation:

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Answer:

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Explanation:

The crane lifts the cargo twice as high so the potential energy will increase twice the amount.

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A mass with mass 4 is attached to a spring with spring constant 24 and a dashpot giving a damping 20. The mass is set in motion

aleksandrvk [35]

Answer: $x(t) = 14e^{-2t} - 10e^{-3t}$

Explanation: In a mass-spring-damper system, the differential equation that rules the motion of the mass is: mx" + cx' + kx = 0

Using m = 4, k = 24 and c = 20, we have

4x" + 20x' + 24x = 0

Simplifying, we have

x" + 5x'+ 6x = 0

The characteristic equation of this differential is

$r^{2} + 5r + 6 = 0$

The solutions for the quadratic equation are: $r_{1} = -2$ and $r_{2} = -3$

Hence:

x(t) = $C_{1}e^{-2t} + C_{2}e^{-3t}$

x'(t) = $-2C_{1}E^{-2t} - 3C_{2}e^{-3t}$

To determine the constants, we have the initial conditions x(0) = 4 and

x'(0) = 2, then:

$x(0) = C_{1} + C_{2} = 4\\ C_{1} = 4 - C_{2}$

$x'(0) = -2C_{1} -3C_{2} = 2\\-2(4-C_{2}) -3C_{2} = 2\\C_{2} = -10\\C_{1} = 4 - C_{2}\\C_{1} = 14$

Substituing the constants:

$x(t) = 14e^{-2t} - 10e^{-3t}$

The position function for this system is: $x(t) = 14e^{-2t} - 10e^{-3t}$

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3 years ago