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2 years ago

4

S Two astronauts (Fig. P 11.55 ), each having a mass M , are connected by a rope of length d having negligible mass. They are is

olated in space, orbiting their center of mass at speeds v . Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum of the twoastronaut systems

1 answer:

vagabundo [1.1K]2 years ago

5 0

The magnitude of the angular momentum of the twoastronaut systems=mdv

How this is calculated?

Distance of each astronaut from centre of mass(m)=d/2
Moment of inertia of system,

$I=\frac{md^{2} }{2}$

Speed of astronauts=v
So, angular speed,ω = $\frac{v}{d/2}$

= $\frac{2v}{d}$

Angular momentum ,L is given by,

L=Iω

$L=\frac{md^{2} }{2}*\frac{2v}{d}=mdv$

What is angular momentum?

In physics, angular momentum is the rotational analog of linear momentum.
It is an important quantity in physics because it is a conserved quantity—the total angular momentum of a closed system remains constant.
Angular momentum has both a direction and a magnitude, and both are conserved.

To know more about angular momentum, refer:

brainly.com/question/4126751

#SPJ4

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What is the reason for converting units?

ELEN [110]

Answer:

Unit conversion is very important because the rest of the world other than three countries uses the metric system. So, converting units is important in science because it uses the metric system. The metric system is measurements like cm, m, l, mL, etc...

Explanation:

Units can: Help to show another person the exact amount you have. Assist in solving a mathematical problem, especially in chemistry, where you can follow the units to get to the answer. Show which measurement system the person is using (i.e. metric or standard)

Hope this helps :)

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3 years ago

The practical limit to an electric field in air is about 3.00 × 10^6 N/C . Above this strength, sparking takes place because air

AleksAgata [21]

Answer:

(a) x=157 m

(b) No

Explanation:

Given Data

Mass of proton m=1.67×10⁻²⁷kg

Charge of proton e=1.6×10⁻¹⁹C

Electric field E=3.00×10⁶ N/C

Speed of light c=3×10⁸ m/s

For part (a) distance would proton travel

Apply the third equation of motion

$(v_{f})^{2} =(v_{i})^{2}+2ax$

In this case vi=0 m/s and vf=c

so

$c^{2}=(0)^{2}+2ax\\ c^{2}=2ax\\x=\frac{c^{2} }{2a}$

$x=\frac{c^{2}}{2a}--------Equation (i)$

From the electric force on proton

$F=qE\\where\\ F=ma\\so\\ma=qE\\a=\frac{qE}{m}\\$

put this a(acceleration) in Equation (i)

So

$x=\frac{c^{2} }{2(qE/m)}\\ x=\frac{mc^{2}}{2qE} \\x=\frac{(1.67*10^{-27})*(3*10^{8})^{2} }{2*(1.6*10^{-19})*(3*10^{6})}\\ x=157m$

For part (b)

No the proton would collide with air molecule

7 0

3 years ago

Titania, the largest moon of the planet Uranus, has 1/8 the radius of the earth and 1/1700 the mass of the earth.What is the acc

garri49 [273]

Answer:

(a). The acceleration due to gravity at the surface of Titania is 0.37 m/s².

(b). The average density of Titania is 1656.47 kg/m³

Explanation:

Given that,

Radius of Titania $R_{t}= \dfrac{1}{8}R_{e}$

Mass of Titania $M_{t}= \dfrac{1}{1700}M_{e}$

We need to calculate the acceleration due to gravity at the surface of Titania

Using formula of the acceleration due to gravity on earth

$g_{e}=\dfrac{GM_{e}}{R_{e}^2}$

The acceleration due to gravity on Titania

$g_{t}=\dfrac{GM_{t}}{R_{t}^2}$

Put the value into the formula

$g_{t}=\dfrac{G\times\dfrac{1}{1700}M_{e}}{(\dfrac{1}{8}R_{e})^2}$

$g_{t}=\dfrac{64}{1700}\times G\dfrac{M_{e}}{R_{e}^2}$

$g_{t}=0.004705 g_{e}$

$g_{t}=0.03764\times9.8$

$g_{t}=0.37\ m/s^2$

The acceleration due to gravity at the surface of Titania is 0.37 m/s².

(b). We assume Titania is a sphere

The average density of the earth is 5500 kg/m³.

We need to calculate the average density of Titania

Using formula of density

$\rho=\dfrac{m}{V}$

$\rho_{t}=\dfrac{M_{t}}{\dfrac{4}{3}\pi\times R_{t}^2}$

$\rho_{t}=\dfrac{\dfrac{M_{e}}{1700}}{\dfrac{4}{3}\pi\times(\dfrac{R_{e}}{8})^2}$

$\rho_{t}=\dfrac{512}{1700}\times\rho_{e}$

$\rho_{t}=\dfrac{512}{1700}\times5500$

$\rho_{t}=1656.47\ kg/m^{3}$

The average density of Titania is 1656.47 kg/m³

Hence, (a). The acceleration due to gravity at the surface of Titania is 0.37 m/s².

(b). The average density of Titania is 1656.47 kg/m³

8 0

3 years ago

A makeshift swing is constructed by making a loop in one end of a rope and tying the other end to a tree limb. A child is sittin

sveticcg [70]

Answer:

a) 264.74 N

b) 91.15 N

c) 20.12°

Explanation:

Given:

Angle between the rope and the vertical, θ = 19°

Tension in the rope, T = 280 N

For the system to be in equilibrium,

The net force in vertical as well as in horizontal direction, should be zero

Therefore,

a) For Vertical direction

Weight of the child = vertical component of the tension

W = T cosθ ..............(1)

or

W = 280 cos19° = 264.74 N ............(a)

b) For horizontal

force on the child, F = T sinθ .............(2)

or

F = 280 sin19° = 91.15 N

c) Now, on dividing (1) and (2), we have

W/F = Tcosθ/Tsinθ

or

tanθ = F/W

now, for F = 97 N

tanθ = 97/264.74 = 0.3663 (W from (a))

or

θ = tan⁻¹(0.3663)

or

θ = 20.12°

3 0

3 years ago

A boat is rocking back and forth in the middle of the ocean. It takes 3 seconds for a wave to pass by before the next wave appea

Amiraneli [1.4K]

The wavelength of the water wave is 15 m.

<h3>What is wavelegth?</h3>

Wavelength is the distance of a complete cycle traveled by a wave.

To calculate the wavelength of the wave, we use the formula below.

Formula:

v = λ/T.................Equation 1

Where:

v = velocity of wave
T = period
λ = wavelength.

make λ the subject of the equation

λ = vT............... Equation 2

From the question,

Given:

v = 5 m/s
t = 3 seconds

Substitute these values into equation 2

λ = 5(3)
λ = 15 m.

Hence, The wavelength of the water wave is 15 m.
Learn more about wavelength here: brainly.com/question/10750459

8 0

3 years ago