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zepelin [54]
2 years ago
9

A model of a spring/mass system is 4x'' + e−0.1tx = 0. By inspection of the differential equation only, discuss the behavior of

the system over a long period of time.
Physics
1 answer:
Delicious77 [7]2 years ago
4 0

Answer:

Displacement becomes constant

Explanation:

We know that exponential raised to power infinity (when time is long) equals to zero hence the model system will be e^{-0.1t} = 0 as t tends to infinity

4x'' + e−0.1tx = 0

When t tends to infinity

4x'' = 0

Integrating the above equation we get

4x'=c

Integrating it another time we get

4x=cx+d

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The flat-bed trailer carries two 1500-kg beams with the upper beam secured by a cable. The coefficients of static friction betwe
Novosadov [1.4K]

Answer:

a) a= 8.33 m/s²,    T = 12.495 N , b)    a = 2.45 m / s²

Explanation:

a) this is an exercise of Newton's second law. As the upper load is secured by a cable, it cannot be moved, so the lower load is determined by the maximum acceleration.

We apply Newton's second law to the lower charge

            fr₁ + fr₂ = ma

The equation for the force of friction is

          fr = μ N

Y Axis

         N - W₁ –W₂ = 0

         N = W₁ + W₂

         N = (m₁ + m₂) g

Since the beams are the same, it has the same mass

        N = 2 m g

We replace

           μ₁ 2mg + μ₂ mg = m a

          a = (2μ₁ + μ₂) g

          a = (2 0.30 + 0.25) 9.8

          a= 8.33 m/s²

Let's look for cable tension with beam 2

          T = m₂ a

          T = 1500 8.33

          T = 12.495 N

b) For maximum deceleration the cable loses tension (T = 0 N), so as this beam has less friction is the one that will move first, we are assuming that the rope is horizontal

           fr = m₂ a₂

           N- w₂ = 0

          N = W₂ = mg

          μ₂ mg = m a₂

          a = μ₂ g

          a = 0.25 9.8

          a = 2.45 m / s²

4 0
2 years ago
un serbatoio d'acqua di forma cilindrica è riempito con acqua dolce fino a un livello di 6,40 m calcola la pressione dell'acqua
ohaa [14]
Per calcolare la pressione a una certa profondità, devi considerare la legge di Stevino:
<span>p = ρ · g · h

Tenendo conto che:
g = 9,81 m/s²
ρ = 1000 kg/m³

Troviamo:
p(h</span>₁) = ρ · g · h₁ = 1000 · 9,81 · 4,50 = 44145 Pa
p(h₂) = ρ · g · h₂ = 1000 · 9,81 · 5,50 = 53955 Pa


6 0
2 years ago
A wave has a frequency of 46 Hz and a wavelength of 1.7 meters. What is the wave speed wave?
arlik [135]

Answer:

Explanation:

(1.7 m/cycle)(46 cycle/s) = 78.2 m/s

4 0
2 years ago
An object falls from the Transco Tower in Houston and takes 15 seconds to reach the ground. How tall is the building:​
iVinArrow [24]

Answer: 1102.5 meters

Explanation:

7 0
2 years ago
A uniform electric field with a magnitude of 125 000 N/C passes through a rectangle with sides of 2.50 m and 5.00 m. The angle b
jeyben [28]

Answer:

6.60\cdot 10^5 Nm^2/C

Explanation:

The electric flux through the rectangle is given by

\Phi = E A cos \theta

where

E is the electric field strength

A is the area of the rectange

\theta is the angle between the direction of the electric field and of the vector normal to the plane of the rectangle

In this problem we have

E = 125 000 N/C

The area of the rectangle is

A=2.50 m \cdot 5.00 m=12.5 m^2

and the angle is

\theta=65.0^{\circ}

so, the electric flux is

\Phi = (125,000 N/C)(12.5 m^2)(cos 65^{\circ})=6.60\cdot 10^5 Nm^2/C

8 0
2 years ago
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