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love history [14]

2 years ago

15

3 An empty hot tub has a mass of 320 kg. When filled, the tub holds 600 gallons of water (rho = 62.4 lbm/ft3). The local acceler

ation due to gravity is 32 ft/s2. Determine the total weight of the hot tub and water in pounds-force (lbf)

1 answer:

ehidna [41]2 years ago

6 0

Answer:

Total weight of the hot tub and water is 5676.6 pounds-force

Explanation:

rho = 62.4lbm/ft^3 × 1ft^3/7.481gal = 8.34lbm/gal

Mass of water = rho × volume = 8.34lbm/gal × 600 gallons = 5004lbm = 5004×0.45359kg = 2269.8kg

Total mass of hot tub and water = 320kg + 2269.8kg = 2589.8kg

Local acceleration due to gravity = 32ft/s^2 = 32ft/s^2 × 1m/3.2808ft = 9.75m/s^2

Total weight of hot tub and water = 2589.8kg × 9.75m/s^2 = 25250.55N = 25250.55/4.4482 lbf = 5676.6 lbf

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Scientists studying an anomalous magnetic field find that it is inducing a circular electric field in a plane perpendicular to t

yarga [219]

Answer

The rate at which the magnetic field is changing is $[\frac{dB}{dt} ] = 0.000467 T/s$

Explanation

From the question we are told that

The electric field strength is $E = 3.5mV/m = 3.5 *10^{-3} \ V/m$

The radius is $r = 1.5 \ m$

The rate of change of the magnetic field is mathematically represented as

$\frac{d \phi }{dt} = \int\limits^{} {E \cdot dl}$

Where $dl$ is change of a unit length

$\frac{d \phi}{dt} = A * \frac{dB}{dt}$

Where A is the area which is mathematically represented as

$A = \pi r^2$

So

$E \int\limits^{} { dl} = ( \pi r^2) (\frac{dB}{dt} )$

$E L = ( \pi r^2) (\frac{dB}{dt} )$

where L is the circumference of the circle which is mathematically represented as

$L = 2 \pi r$

So

$E (2 \pi r ) = (\pi r^2 ) [\frac{dB}{dt} ]$

$E = \frac{r}{2} [\frac{dB}{dt} ]$

$[\frac{dB}{dt} ] = \frac{E}{ \frac{r}{2} }$

substituting values

$[\frac{dB}{dt} ] = \frac{3.5 *10^{-3}}{ \frac{15}{2} }$

$[\frac{dB}{dt} ] = 0.000467 T/s$

8 0

2 years ago

A high speed train is traveling at a speed of 44.7 m/s when the engineer sounds the 415 Hz warning horn. The speed of sound is 3

il63 [147K]

Answer:

Explanation:

Speed of the source of sound = v = 44.7 m/s

Speed of sound = V = 343 m/s

a) Apparent frequency as the train approaches = f = [V /(V -v) ] × f

= [343 / (343 - 44.7) ] × 415 = 477.18 Hz

Wave length = λ = v / f = 343 / 477.18 = 0.719 m

b) Frequency heard as the train leaves = f ' = [V / ( V + v) ] f

= [343 / { 343 + 44.7 ) ] x 415

= 367.2 Hz

Wavelength when leaving = v / f = 343 / 367.2 = 0.934 m

8 0

3 years ago

A student who weighs 500 newtons climbed the stairs from the first floor to the third floor,15 meters above, in 20 seconds. How

damaskus [11]

Work = (500N)(15m)=7500J Power= (7500J)/(20s) =375 W
Hopefully this helps

3 0

3 years ago

Discuss the phase change condition due to reflection of light from a surface. Summarize equations of interference for thin film.

Dmitrij [34]

Answer:

if this surface has a higher index than in the medium where the light travels, the reflected wave has a phase change of 180º

Explanation:

When a ray of light falls on a surface if this surface has a higher index than in the medium where the light travels, the reflected wave has a phase change of 180º this can be explained by Newton's third law, the light when arriving pushes the atoms of the medium that is more dense, and these atoms respond with a force of equal magnitude, but in the opposite direction.

When the fractional index is lower than that of the medium where the reflacted beam travels, notice a change in phase.

Also, when light penetrates the medium, it modifies its wavelength

λ = λ₀ / n

We take these two aspects into account, the condition for contributory interference is

d sin θ = (m + 1/2) λ

for destructive interference we have

d sin θ = m λ

in general this phenomenon is observed at 90º

2 d = (m +1/2) λ° / n

2nd = (m + ½) λ₀

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2 years ago

A stone is thrown vertically into the air at an initial velocity of 96 ft/s. On Mars, the height s (in feet) of the stone above

vladimir1956 [14]

Answer:

240 ft

Explanation:

t = Time taken

u = Initial velocity = 96 ft/s

v = Final velocity

s = Displacement

a = Acceleration = 12 m/s² on Mars 32 ft/s² on Earth negative due to upward direction

Mars

$s=ut+\frac{1}{2}at^2\\\Rightarrow s=96\times t+\frac{1}{2}\times -12\times t^2\\\Rightarrow s=96t-6t^2\ ft$

Earth

$s=ut+\frac{1}{2}at^2\\\Rightarrow s=96\times t+\frac{1}{2}\times -32\times t^2\\\Rightarrow s=96t-16t^2\ ft$

Differentiating the first equation with respect to time we get

$\frac{ds}{dt}=96-12t$

Equating with zero

$0=96-12t\\\Rightarrow t=\frac{96}{12}=8\ s$

Differentiating the second equation with respect to time we get

$\frac{ds}{dt}=96-32t$

Equating with zero

$0=96-32t\\\Rightarrow t=\frac{96}{32}=3\ s$

Applying the time taken to the above equations, we get

$s=96t-6t^2\ ft\\\Rightarrow s=96\times 8-6\times 8^2\\\Rightarrow s=384$

$s=96t-16t^2\\\Rightarrow s=96\times 3-16\times 3^2\\\Rightarrow s=144$

Difference in height = 384-144 = 240 ft

The stone will travel 240 ft higher on Mars

6 0

2 years ago