a pine raft (density = 373 kg/m^3) has a volume of 1.43 m^3. How much of the raft's volume is below the water line? Unit is m^3

A light platform is suspended from the ceiling by a spring. A student with a mass of 90 kg climbs onto the platform. When it sto

Ilya [14]

Refer to the diagram shown.

When the student climbs onto the platform, the spring stretches by 0.82 m to reach the equilibrium position.
The mass of the student is m = 90 kg, so his weight is
mg = (90 kg)*(9.8 m/s²) = 882 N

By definition, the spring constant is
k = (882 N)/(0.82 m) = 1075.6 N/m

When the spring is stretched by x from the equilibrium position, the restoring force is
F = - k*x.

If damping is ignored, the equation of motion is
F = m * acceleration
or
$m \frac{d^{2}x}{dt^{2}} = -kx \\ \frac{d^{2}x}{dt^{2}} + \frac{k}{m} x = 0$

Define ω² = k/m = 11.751 => ω = 3.457.
Then the solution of the ODE is
x(t) = c₁ cos(ωt) + c₂ sin(ωt)

x'(t) = -c₁ω sin(ωwt) + c₂ω cos(ωt)
When t=0, x' =0, therefore c₂ = 0

The solution is of the form
x(t) = c₁ cos(ωt)
When t = 0, x = 0.32 m. Therefore c₁ = 0.32

The motion is
x(t) = 0.32 cos(3.457t)
The single amplitude is 0.32 m, and the double amplitude is 0.64 m.

Answer:
0.32 m (single amplitude), or
0.64 m (double amplitude)

6 0

2 years ago

Imagine a particular exoplanet covered in an ocean of liquid methane. At the surface of the ocean, the acceleration of gravity i

AlladinOne [14]

Answer:

Explanation:

Atmospheric pressure = 7 x 10⁴ Pa

force on a disk-shaped region 2.00 m in radius at the surface of the ocean due to atmosphere = pressure x area

= 7 x 10⁴ x 3.14 x 2 x 2

= 87.92 x 10⁴ N

b )

weight, on this exoplanet, of a 10.0 m deep cylindrical column of methane with radius 2.00 m

Pressure x area

height x density x acceleration of gravity x π r²

= 10 x 415 x 6.2 x 3.14 x 2 x 2

=323168.8 N

c ) Pressure at a depth of 10 m

atmospheric pressure + pressure due to liquid column

= 7 x 10⁴ + 10 x 415 x 6.2 ( hρg)

= 7 x 10⁴ + 10 x 415 x 6.2

(7 + 2.57 )x 10⁴ Pa

9.57 x 10⁴ Pa

8 0

3 years ago

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−5 cos (6.20x − 3 000

nadya68 [22]

Answer:

The wavelength of this wave is 1.01 meters.

Explanation:

The variation in the pressure of helium gas, measured from its equilibrium value, is given by :

$\Delta P=2.9\times 10^{-5}\ cos(6.2x-3000t)$ ..............(1)

The general equation is given by :

$\Delat P=P_o\ cos(kx-\omega t)$ ...........(2)

On comparing equation (1) and (2) :

$k=6.2$

Since, $k=\dfrac{2\pi}{\lambda}$

$\dfrac{2\pi}{\lambda}=6.2$

$\lambda=1.01\ m$

So, the wavelength of this wave is 1.01 meters. Hence, this is the required solution.

6 0

3 years ago

a car travelling at 50m/h on a horizontal highway (a) if the coefficient of static friction between road and tyres on a rainy da

aleksandrvk [35]

Hope this helps!

-Lilly

3 0

3 years ago

What is evaporation? Condensation? Drag the terms on the left to the appropriate blanks on the right to complete the sentences.

krok68 [10]

Answer:

Evaporation is the physical change in which a substance converts from its liquid state to its gaseous state. Condensation is the physical change in which a substance converts from its gaseous state to its liquid state.

Explanation:

Evaporation and condensation are opposite processes to each other. Evaporation changes a liquid to a gas and condensation is the reverse.

7 0

3 years ago

a pine raft (density = 373 kg/m^3) has a volume of 1.43 m^3. How much of the raft's volume is below the water line? Unit is m^3​

a pine raft (density = 373 kg/m^3) has a volume of 1.43 m^3. How much of the raft's volume is below the water line? Unit is m^3