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Tanya [424]
3 years ago
11

A spring attached to the ceiling is stretched 2.45 meters by a four kilogram mass. If the mass is set in motion in a medium that

imparts a damping force numerically equal to 16 times the velocity, the correct differential equation for the position x (t ), of the mass at a function of time, t is
Physics
1 answer:
denpristay [2]3 years ago
6 0

Answer:

d²x/dt² = - 4dx/dt - 4x is the required differential equation.

Explanation:

Since the spring force F = kx where k is the spring constant and x its extension = 2.45 equals the weight of the 4 kg mass,

F = mg

kx = mg

k = mg/x

= 4 kg × 9.8 m/s²/2.45 m

= 39.2 kgm/s²/2.45 m

= 16 N/m

Now the drag force f = 16v where v is the velocity of the mass.

We now write an equation of motion for the forces on the mass. So,

F + f = ma (since both the drag force and spring force are in the same direction)where a = the acceleration of the mass

-kx - 16v = 4a

-16x - 16v = 4a

16x + 16v = -4a

4x + 4v = -a where v = dx/dt and a = d²x/dt²

4x + 4dx/dt = -d²x/dt²

d²x/dt² = - 4dx/dt - 4x which is the required differential equation

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The fictional rocket ship Adventure is measured to be 50 m long by the ship's captain inside the rocket.When the rocket moves pa
tensa zangetsu [6.8K]

Complete question:

Part A:) The fictional rocket ship Adventure is measured to be 50 m long by the ship's captain inside the rocket.When the rocket moves past a space dock at 0.5c , space-dock personnel measure the rocket ship to be 43.3 m long. The rocket ship Adventure travels to a star many light-years away, then turns around and returns at the same speed. When it returns to the space dock, who would have aged less: the space-dock personnel or ship's captain?

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Answer

a)Who would have aged less=The Captain would have aged less

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Explanation:

From the question we are told that

Length measured by captain l_c=50m

Speed of rocket past tje space dock V=0.5c

Length measured by space-dock personnel l_c=43.3m

a)

Generally time moves slower when moving at speed of light, due to time dilation or variation.

Who would have aged less=The Captain would have aged less

b)

Generally the equation for Relativistic Momentum  is mathematically given as

p=\frac{m*v}{1 - v^2/c^2}

p=\frac{1.67*10^2-27*0.62*3.0*10^8)}{\sqrt{ 1 -0.6^2}}

p=3.96*10^{-19}kgm/s

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