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tresset_1 [31]
3 years ago
15

The Apollo Lunar Module was used to make the transition from the spacecraft to the moon's surface and back. Consider a similar m

odule for landing on the surface of Mars. Use conservation of mechanical energy to answer these questions.
(a) As the lander is descending, if the pilot decides to shut down the engine when the lander is at a height of 1.3 m, (this may not be a safe height to shut down the engine) and the velocity of the lander (relative to the surface of the planet) is 1.3 m/s what will be velocity of the lander at impact? Note: g on the surface of mars is about 0.4 times that on the surface of the Earth.

(b) In the case of the lunar module an impact velocity of 3.0 m/s or less was essential for a safe landing. Assuming this to be the case for the Mars lander as well, at what maximum height could the pilot shut down the engines to ensure a safe landing. Assume the velocity v0 at the time the engine is shut down is 1.2 m/s.
Physics
1 answer:
lions [1.4K]3 years ago
8 0

Answer:

Explanation:

a. Landing height is

H=1.3m

Velocity of lander relative to the earth is, i.e this is the initial velocity of the spacecraft

u=1.3m/s

Velocity of lander at impact, i.e final velocity is needed

v=?

The acceleration due to gravity is 0.4 times that of the one on earth,

Then, g on earth is approximately 9.81m/s²

Then, g on Mars is

g=0.4×9.81=3.924m/s²

Then using equation of motion for a free fall body

v²=u²+2gH

v²=1.3²+2×3.924×1.3

v²=1.69+10.2024

v²=11.8924

v=√11.8924

v=3.45m/s

The impact velocity of the spacecraft is 3.45m/s

b. For a lunar module, the safe velocity landing is 3m/s

v=3m/s.

Given that the initial velocity is 1.2m/s²

We already know acceleration due to gravity on Mars is g=3.924m/s²

The we need to know the maximum height to have a safe velocity of 3m/s

Then using equation of motion

v²=u²+2gH

3²=1.2²+2×3.924H

9=1.44+7.848H

9-1.44=7.848H

7.56=7.848H

H=7.56/7.848

H=0.963m

The the maximum safe landing height to obtain a final landing velocity of 3m/s is 0.963m

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Answer:

after 6 second it will stop

he travel 36 m to stop

Explanation:

given data

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distance = 100 m

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to find out

how long does it take to stop and how far does he travel

solution

we will apply here first equation of motion that is

v = u + at   ......1

here u is speed 12 and v is 0 because we stop finally

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and

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Hydroelectric power plants can generate huge amounts of electricity. Which of these statements best describes the impact of a hy
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An automobile steering wheel is shown. What is the ideal mechanical advantage? If the AMA is 8, what is the efficiency of the st
Mars2501 [29]

1. Ideal Mechanical Advantage (IMA): 9

Explanation:

For a wheel and axle system like the steering wheel, the IMA is given by:

IMA=\frac{r_w}{r_a}

where

r_w is the radius of the wheel

r_a is the radius of the axle

For the steering wheel of the problem, we see that r_w = 18 cm and r_a=2 cm, so the IMA is

IMA=\frac{18 cm}{2 cm}=9


2. Efficiency: 88.9%

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\eta=\frac{AMA}{IMA}\cdot 100

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Two neutron stars are separated by a distance of 1.0 x 1012 m. They each have a mass of 1.0 x 1028 kg and a radius of 1.0 x 103
son4ous [18]

To develop this problem it is necessary to apply the concepts related to Gravitational Potential Energy.

Gravitational potential energy can be defined as

PE = -\frac{GMm}{R}

As M=m, then

PE = -\frac{Gm^2}{R}

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m = Mass

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U = -\frac{2Gm^2}{R}

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PART B) With a final separation distance of 2r, we have that

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v = \sqrt{Gm(\frac{1}{2r}-\frac{1}{R})}

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v = 1.83*10^7m/s

Therefore the velocity when they are about to collide is 1.83*10^7m/s

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