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finlep [7]
3 years ago
10

A spherical hot air balloon of diameter 30.0 meters just floats (hovers) when the hot air inside has been heated to a density of

1.10 kg/m3 What is the weight of the balloon and cargo (not including the air inside) if the surrounding air has a density of 1.20 kg/m3? (VSphere = (4/3)nr3)
Physics
1 answer:
Rom4ik [11]3 years ago
5 0

Answer:

W = 166422.729 N

Explanation:

given,

diameter of the balloon = 30 m

density of the air = 1.10 Kg/m³

weight of the balloon and cargo = ?

density of the surrounding air = 1.20 kg/m³

we know,

Density = mass/volume

m = density x volume

m = \rho\times \dfrac{4}{3}\pi r^3

m =1.20 \times \dfrac{4}{3}\pi\times 15^3

m = 16964.6 Kg

Weight of the balloon

 W = m g

 W = 16964.6 x 9.81

W = 166422.729 N

Weight of the balloon and the cargo is equal to  W = 166422.729 N

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An electron emitted from a filament is travelling at 1.5 x 105 m/s when it enters an acceleration of an electron gun in a televi
Crank

Answer:

The acceleration of the electron is 1.457 x 10¹⁵ m/s².

Explanation:

Given;

initial velocity of the emitted electron, u = 1.5 x 10⁵ m/s

distance traveled by the electron, d = 0.01 m

final velocity of the electron, v = 5.4 x 10⁶ m/s

The acceleration of the electron is calculated as;

v² = u² + 2ad

(5.4 x 10⁶)² = (1.5 x 10⁵)² + (2 x 0.01)a

(2 x 0.01)a = (5.4 x 10⁶)² - (1.5 x 10⁵)²

(2 x 0.01)a = 2.91375 x 10¹³

a = \frac{2.91375 \ \times \ 10^{13}}{2 \ \times \ 0.01} \\\\a = 1.457 \ \times \ 10^{15} \ m/s^2

Therefore, the acceleration of the electron is 1.457 x 10¹⁵ m/s².

7 0
3 years ago
When radioactive tracers are used for medical scans, the tracers both decay in the body via radiation, as well as being excreted
irinina [24]

Answer:

Effective half-time of the tracer is 3.6 days

Explanation:

The formula for calculating the decay due to excretion for the first process is ;

\frac{dN_1}{dt } = - \lambda _e N_o

here ;

N_o = initial number of tracers

Then to the second process ; we have :

\frac{dN_2}{dt } = - \lambda _e N_o

The total decay is as a result of the overall process occurring ; we have :

\frac{dN_{total}}{dt } = \frac{dN_1}{dt} + \frac{dN_2}{dt}   ------ (1)

here ;

\frac{dN_{total}}{dt } = \lambda _{total} N_o

Putting the values in (1);we have :

- \lambda _{Total} N_o = - \lambda_e N_o + ( -\lambda r N_o})

\lambda _{Total} = \lambda_e + \lambda r

As we also know that:

\frac{1}{t_{1/2}} = \frac{[t_{1/2}]_{radiation}+[t_{1/2}]_{excretion}}{[t_{1/2}]_{radiation}*[t_{1/2}]_{excretion}}

\frac{1}{t_{1/2}}_{effective}} = \frac{[t_{1/2}]_{radiation}+[t_{1/2}]_{excretion}}{[t_{1/2}]_{radiation}*[t_{1/2}]_{excretion}}

\frac{1}{t_{1/2}}_{effective}} = \frac{9+6}{9*6}

\frac{1}{t_{1/2}_{effective}}}=\frac{15}{54}

t_{1/2}_{effective}} = \frac{54}{15}

= 3.6 days

5 0
4 years ago
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A square coil, enclosing an area with sides 2.0 cm long, is wrapped with 2 500 turns of wire. A uniform magnetic field perpendic
Delvig [45]

Answer:

The induced voltage in the coil is 0.25 V.

Explanation:

It is given that,

Area of a square coil is 2 cm or 0.02 m

Number of turns in the wire is 2500

A uniform magnetic field perpendicular to its plane is turned on and increases to 0.25 T during an interval of 1.0 s.

We need to find the induced voltage in the coil. According to Faraday's law, the induced emf in the coil is given by the rate of change on magnetic flux. So,

\epsilon=\dfrac{-d\phi}{dt}\\\\\epsilon=\dfrac{-d(NBA)}{dt}\\\\\epsilon=NA\dfrac{-dB}{dt}\\\\\epsilon=-2500\times (0.02)^2\times \dfrac{0.25}{1}\\\\\epsilon=-0.25\ V

So, the induced voltage in the coil is 0.25 V.

3 0
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Answer:

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Explanation:

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