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yan [13]
3 years ago
5

Point masses m1 m2 are placed at opposite ends

Physics
1 answer:
tiny-mole [99]3 years ago
7 0

(a) x = \frac{m_2L}{m_1+m_2}

<u>Explanation:</u>

Given:

Moment of Inertia of m₁ about the axis, I₁ = m₁x²

Moment of Inertia of m₂ about the axis. I₂ = m₂ (L - x)²

Kinetic energy is rotational.

Total kinetic energy is E = \frac{1}{2} I_1w_0^2 + \frac{1}{2}I_2w_0^2 = \frac{1}{2} w_0^2(m_1x^2 + m_2(L-x)^2)

Work done is change in kinetic energy.

To minimize E, differentiate wrt x and equate to zero.

m_1x - m_2(L-x) = 0\\\\x = \frac{m_2L}{m_1+m_2}

Alternatively, work done is minimum when the axis passes through the center of mass.

Center of mass is at \frac{m_2L}{m_1 + m_2}

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muminat

Power P is the rate at which energy is generated or consumed and hence is measured in units that represent energy E per unit time t. This is:

P = E/t

Solving for t:

t = E/P

t = 6007 J / 500 W

t = 12.014 s

<h2>t ≅ 12 s</h2>

7 0
3 years ago
NASA is designing a mission to explore Titan, the largest moon of Saturn. Titan has numerous hydrocarbon lakes containing a mix
Vitek1552 [10]

Answer:

Total pressure in atmosphere  IS 4.36 atm

Explanation:

Given Data:

Depth of lake is 400 mtr

surface tension is 147 kilopascals

surface temperature  94 kelvin

Gravity = 1.35 m/s^2

specific gravity of methane(liquid) = 0.415

specific gravity of ethane(liquid) = 0.546

density of methane can be obtained as

\rho_{methane} = 0.415\times 1000 = 415 kg/m^3

Density of ethane can be obtained as

\rho_{ethane} = 0.546\times 1000 = 546 kg/m^3

Total pressure in atmosphere can be obtained as

P = surface\ tension + \rho_{max}gh

 = 147 +546\times 1.35\times 400\times 10^{-3}

  = 441.84 kPa

= 441.84\times 0.009869 atm\kPa

 = 4.36 atm

7 0
2 years ago
Describe each of Newton’s Laws of Motion in ice skating. What can you design/develop to improve ice skating?
denis23 [38]

Newton's three laws of motion can be used to describe the motion of the ice skating.

<h3>Newton's first law of motion</h3>

Newton's first law of motion states that an object at rest or uniform motion in a straight line will continue in that state unless it is acted upon by an external force.

  • Based on this law, once the ice skating starts, it will continue endlessly unless external force stops it.

<h3>Newton's second law of motion</h3>

Newton's second law of motion states that the force applied to an object is directly proportional to the product of mass and acceleration of an object.

  • Based on this law, the force applied to the ice skating is equal to the product of mass and acceleration of the ice skating.

<h3>Newton's third law of motion</h3>

This law states that action and reaction are equal and opposite.

  • Based on this law, the force applied to the ice skating is equal in magnitude to the reaction of ice.

Learn more about Newton's law here: brainly.com/question/3999427

3 0
2 years ago
Read 2 more answers
How do you know about Black Holes?
kondaur [170]

Answer: From space/ astronauts

Explanation:

A black hole is a place in space where gravity pulls so much that even light can not get out. The gravity is so strong because matter has been squeezed into a tiny space. This can happen when a star is dying.

Because no light can get out, people can't see black holes. They are invisible. Space telescopes with special tools can help find black holes. The special tools can see how stars that are very close to black holes act differently than other stars.

6 0
3 years ago
Read 2 more answers
022 (part 1 of 4) 10.0 points A ball is thrown vertically upward with a speed of 24.5 m/s. How high does it rise? The accelerati
svetoff [14.1K]

1)

Answer:

Part 1)

H = 30.6 m

Part 2)

t = 2.5 s

Part 3)

t = 2.5 s

Part 4)

v_f = 24.5 m/s

Explanation:

Part 1)

initial speed of the ball upwards

v_i = 24.5 m/s

so maximum height of the ball is given by

H = \frac{v_i^2}{2g}

H = \frac{24.5^2}{2(9.80)}

H = 30.6 m

Part 2)

As we know that final speed will be zero at maximum height

so we will have

v_f - v_i = at

0 - 24.5 = (-9.8)t

t = 2.5 s

Part 3)

Since the time of ascent of ball is same as time of decent of the ball

so here ball will same time to hit the ground back

so here it is given as

t = 2.5 s

Part 4)

since the acceleration due to earth will be same during its return path as well as the time of the motion is also same

so here its final speed will be same as that of initial speed

so we have

v_f = 24.5 m/s

2)

Answer:

a = 9.76 m/s/s

Explanation:

As we know that the object is released from rest

so the displacement of the object in vertical direction is given as

y = \frac{1}{2}at^2

4.88 = \frac{1}{2}a(1^2)

a = 9.76 m/s^2

3)

Answer:

v = 29.7 m/s

Explanation:

acceleration of the rocket is given as

a = 90 m/s^2

time taken by the rocket

t = 0.33 min

final speed of the rocket is given as

v_f = v_i + at

v_f = 0 + (90)(0.33)

v_f = 29.7 m/s

4)

Answer:

Part 1)

y = 25.95 m

Part 2)

d = 6.72 m

Explanation:

Part 1)

As it took t = 2.3 s to hit the water surface

so here we will have

y = \frac{1}{2}gt^2

y = \frac{1}{2}(9.81)(2.3^2)

y = 25.95 m

Part 2)

Distance traveled by it in horizontal direction is given as

d = v_x t

d = 2.92 \times 2.3

d = 6.72 m

6 0
3 years ago
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