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4 years ago

What is the metric unit for distance?

Physics

1 answer:

Gemiola [76]4 years ago

4 0

Answer:

meters

Explanation:

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A mass is attached to an ideal spring. At time t = 0 the spring is at its natural length and the mass is given an initial veloci

JulijaS [17]

Answer:

t = T/4

Explanation:

The power delivered to the mass by the spring is work done by the spring per second.

$P = \frac{dW}{dt}$

The work done by the spring is equal to the elastic potential energy stored in the spring.

$U = \frac{1}{2}kx^2$

The maximum energy stored in the spring is at the amplitude of the oscillation.

$U_{max} =\frac{1}{2}kA^2$

So the first time the mass reaches to its amplitude can be found by the following equation of motion:

$x = A\cos(\omega t + \phi)\\\phi = \pi/2 ~because ~at ~t= 0, ~ x = 0\\0 = A\cos(0 + \pi/2)\\x = A\cos(\omega t + \pi/2)$

When the mass reaches the amplitude:

$A = A\cos(\omega t + \pi/2)\\1 = \cos(\omega t + \pi/2)\\\omega t + \pi/2 = \pi$

because cos(π) = 1.

$\omega t = \pi/2$

Using ω = 2π/T,

$\omega t = \pi/2\\\frac{2\pi}{T}t = \pi/2\\t = \frac{T}{4}$

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4 years ago

According to Newton's Universal Law of Gravitation, when the distance between two interacting objects doubles, the gravitational

maksim [4K]

Answer:

<em>If the distance doubles, the gravitational force is divided by 4</em>

Explanation:

<u>Newton’s Universal Law of Gravitation </u>

Objects attract each other with a force that is proportional to their masses and inversely proportional to the square of the distance.

$\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}$

Where:

m1 = mass of object 1

m2 = mass of object 2

r = distance between the objects' center of masses

G = gravitational constant: 6.67\cdot 10^{-11}~Nw*m^2/Kg^2

If the distance between the interacting objects doubles to 2r, the new force F' is:

$\displaystyle F'=G{\frac {m_{1}m_{2}}{(2r)^{2}}}$

Operating:

$\displaystyle F'=\frac{1}{4}G{\frac {m_{1}m_{2}}{r^{2}}}$

Substituting the original value of F:

$\displaystyle F'=\frac{1}{4}F$

If the distance doubles, the gravitational force is divided by 4

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