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Gnesinka
2 months ago
10

Two astronauts on opposite ends of a spaceship are comparing lunches. One has an apple, the other has an orange. They decide to

trade. Astronaut 1 tosses the 0.130 kg apple toward astronaut 2 with a speed of vi,1 = 1.05 m/s . The 0.150 kg orange is tossed from astronaut 2 to astronaut 1 with a speed of 1.18 m/s . Unfortunately, the fruits collide, sending the orange off with a speed of 1.03 m/s in the negative y direction. What are the final speed and direction of the apple in this case?
Physics
1 answer:
Softa [3K]2 months ago
5 0

Final velocity: v= 1.23 m/s angle: θ = 75.3º

To explain:

Initially, we designate the direction in which both fruits are thrown as the x-axis, meaning all initial momenta will only have horizontal components.

In the absence of external forces influencing the collision—due to the extremely brief timeframe of the event—momentum conservation applies.

As momentum is a vector quantity, both components must be maintained, leading us to establish the following equations:

p₁ₓ = p₂ₓ ⇒ -m₁. vi₁ +m₂. vi₂ = m₁. vf₁. cos θ (1)

p₁y = p₂y ⇒ 0 =m₂. vf₂ - m₁. vf₁. sin θ (2)

Substituting in the values for m1, m₂, vi₁, vi₂, and vf₂ allows us to solve for θ, the angle between the apple and the horizontal, through the following steps:

(1) -0.13 Kg. 1.05 m/s + 0.15 Kg. 1.18 m/s = 0.13. vf. cos θ

(2) 0.15 Kg. 1.03 m/s = 0.13 vf. sin θ

Taking the ratio sin θ / cos θ = 3.82 leads to tg θ = 3.82 ⇒ θ = arc tg (3.82) = 75.3º

Substituting this θ value back into (2) gives us:

0.15 kg. 1.03 m/s = 0.13 vf. sin 75.3º = 0.13. vf. 0.967

Solving for vf yields:

vf = 0.15 kg. 1.03 m/s / (0.13. 0.967) = 1.23 m/s

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Consider an electron with charge −e and mass m orbiting in a circle around a hydrogen nucleus (a single proton) with charge +e.
kicyunya [3294]

Result:

v=\sqrt{k\frac{e^2}{m_e r}}, 2.18\cdot 10^6 m/s

Explanation:

The electromagnetic attraction between the electron and the proton in the nucleus is equivalent to the centripetal force:

k\frac{(e)(e)}{r^2}=m_e \frac{v^2}{r}

where

k represents the Coulomb constant

e denotes the charge of the electron

e denotes the charge of the proton in the nucleus

r signifies the distance from the electron to the nucleus

v indicates the velocity of the electron

is the mass of the electron

Rearranging for v, we determine

v=\sqrt{k\frac{e^2}{m_e r}}

Inside a hydrogen atom, the distance separating the electron from the nucleus is roughly

r=5.3\cdot 10^{-11}m

while the mass of the electron is

m_e = 9.11\cdot 10^{-31}kg

and the charge is

e=1.6\cdot 10^{-19} C

By plugging in the values into the formula, we achieve

v=\sqrt{(9\cdot 10^9 m/s) \frac{(1.6\cdot 10^{-19} C)^2}{(9.11\cdot 10^{-31} kg)(5.3\cdot 10^{-11} m)}}=2.18\cdot 10^6 m/s

7 0
2 months ago
If a steady-state heat transfer rate of 3 kW is conducted through a section of insulating material 1.0 m2 in cross section and 2
Maru [3345]

Answer:

\Delta T = \frac{3000 W *0.025 m}{1 m^2 (0.2 \frac{W}{mK})}= 375 K

Consequently, the temperature difference across the material will be \Delta T = 375 K

Explanation:

In this case, we apply the Fourier Law of heat conduction expressed by the following equation:

Q = -kA \frac{\Delta T}{\Delta x}   (1)

Where k = thermal conductivity = 0.2 W/ mK

A= 1m^2 denotes the cross-sectional area

Q= 3KW signifies the heat transfer rate

\Delta T is the temperature difference we need to determine

represents the thickness of the material\Delta x=2.5 cm =0.025 m

To isolate \Delta T from equation (1), we obtain:

\Delta T =\frac{Q \Delta x}{Ak}

Initially, we convert 3KW to W, resulting in:

Q= 3 KW* \frac{1000W}{1 Kw}= 3000 W

With all variables accounted for, we can substitute and calculate:

\Delta T = \frac{3000 W *0.025 m}{1 m^2 (0.2 \frac{W}{mK})}= 375 K

Thus, the temperature difference across the material will be \Delta T = 375 K

5 0
2 months ago
A coffee company wants to make sure that their coffee is being served at the right temperature. if it is too hot, the customers
Maru [3345]

Response:

The population mean is parameter = 65 c

Explanation:

In the analysis of samples and inferring population behavior, two key elements are essential.

To ascertain the population mean, we typically extract various samples and calculate their average. The average of all these means will serve as an estimate for the population mean. According to the central limit theorem, as sample sizes increase, the average of a sample tends to follow a normal distribution with an estimated mean being the sample mean.

A statistic pertains to a sample, while a parameter refers to the whole population.

In this case, 65 degrees C represents the entire population; thus, it constitutes a parameter.

4 0
2 months ago
Read 2 more answers
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