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Tanya [424]
4 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]4 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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3 years ago
Article 5 of the Fundamental Orders of Connecticut is MOST LIKELY related to which idea?
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Answer:

Option A, Rule of law

Explanation:

The complete question is

Article 5 of the Fundamental Orders of Connecticut is MOST LIKELY related to which idea? A) rule of law B) personal freedom C) individual rights D) limited government

Solution

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If the temperature of water warming on a hot plate rises 10 degrees Celsius [°C], what is the change in temperature in units of
Luba_88 [7]

Answer:

Delta_temp = 18[°F]

Explanation:

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4 0
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HELP PLEASE 20 POINTS SHOW WORK, ALL EQUATIONS
nataly862011 [7]

Answer:

s = 3 m

Explanation:

Let t be the time the accelerating car starts.

Let's assume the vehicles are point masses so that "passing" takes no time.

the position of the constant velocity and accelerating vehicles are

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300 cm when rounded to the single significant digit of the question numerals.

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