The longer the lever, the greater the

A 1500 kg weather rocket accelerates upward at 10m/s2. It explodes 2.0 s after liftoff and breaks into two fragments, one twice

ladessa [460]

Answer:

Approximately $\rm 19.8\; m\cdot s^{-1}$ (downwards.)

Assumptions:

the rocket started from rest;
the gravitational acceleration is constantly $\rm -9.8\; m \cdot s^{-2}$ ;
there's no air resistance on the rocket and the two fragments.
Both fragments traveled without horizontal velocity.

Explanation:

The upward speed of the rocket increases by $\rm 10\; m \cdot s^{-1}$ . If the rocket started from rest, the vertical speed of the rocket should be equal to $\rm 20\; m \cdot s^{-1}$ .

The mass of the rocket (before it exploded) is 1500 kilograms. At 20 m/s, its momentum will be equal to $\rm 20 \times 1500 = 30,000\; kg \cdot m\cdot s^{-1}$ .

What's the initial upward velocity, $u$ , of the lighter fragment?

The upward velocity of the lighter fragment is equal to $v = 0$ once it reached its maximum height of $x = \rm 530\; m$ .

$v^2 - u^2 = 2g \cdot x$ .

$\begin{aligned}u &= \sqrt{v^2 - 2g\cdot x} \\ &= \sqrt{-2 (-9.8) \times 530}\\ &\approx \rm 101.922\; m \cdot s^{-1}\end{aligned}$ .

Mass of the two fragments:

Lighter fragments: $\displaystyle \frac{1}{1 + 2} \times 1500 =\rm 500\; kg$ .
Heavier fragment: $\displaystyle \frac{2}{1 + 2} \times 1500 =\rm 1000\; kg$ .

Initial momentum of the lighter fragment:

$m \cdot v = \rm 10192.2\; kg \cdot m \cdot s^{-1}$ .

If there's no air resistance, momentum shall conserve. The momentum of the lighter fragment, plus that of the heavier fragment, should be equal to that of the rocket before it exploded.

The initial momentum of the heavier fragment should thus be equal to the momentum of the two pieces, combined, minus the initial momentum of the lighter fragment.

$\rm 30000 - 10192.2 = 19807.8\;kg \cdot m \cdot s^{-1}$ .

Velocity of the heavier fragment:

$\displaystyle \rm \frac{19807.8\;kg \cdot m \cdot s^{-1}}{1000\; kg} \approx 19.8\; m \cdot s^{-1}$ .

5 0

4 years ago

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a rocket has a mass 250(10^3) slugs on earth. Specify its mass in si units and its weight in si unites. if the rocket is on the

Katena32 [7]

Answer:

$W_{earth} = 35.74 * 10^6 N$ : Rocket weight on earth

$W_{moon} = 5.91 * 10^6 N$ : Rocket weight on moon

Explanation:

Conceptual analysis

Weight is the force with which a body is attracted due to the action of gravity and is calculated using the following formula:

W = m × g Formula (1)

W: weight

m: mass

g: acceleration due to gravity

The mass of a body on the moon is equal to the mass of a body on the earth

The acceleration due to gravity on a body is different on the moon and on the earth

Equivalences

1 slug = 14.59 kg

Known data

$m_{earth} = m_{moon} = 250 * 10^3 slug = 250* 10^3slug * \frac{14.59kg}{1slug} = 3647.5* 10^3 kg$

$g_{moon}= 1.62 \frac{m}{s^2}$

$g_{earth}= 9.8 \frac{m}{s^2}$

Problem development

To calculate the weight of the rocket on the moon and on earth we replace the data in formula (1):

$W_{earth} = 3647.5* 10^3 kg * 9.8 \frac{m}{s^2} = 35.74 * 10^6 N$ : Rocket weight on earth

$W_{moon} = 3647.5* 10^3 kg * 1.62 \frac{m}{s^2} = 5.91 * 10^6 N$ : Rocket weight on moon

7 0

4 years ago

Which of the following about Dalton's theory of matter is true?

Lemur [1.5K]

D.Atoms can be divided into smaller parts.

Dalton's atomic theory was the first complete attempt to describe allmatter in terms of atoms and their properties. Dalton based his theory on the law of conservation of mass and the law of constant composition. The first part of his theory states that allmatter is made of atoms, which are indivisible.

6 0

3 years ago

Jack pushed and pushed, and finally moved the new refrigerator into the kitchen. What is the BEST explanation of what happened?

Anika [276]

Answer:

a

Explanation:

6 0

4 years ago

What do women and men prefer in partners?

hodyreva [135]

Answer:

I would say Honesty, Loyalty, and Trust

Explanation:

well, thats just in my opinion and other people have their own preferences

8 0

3 years ago

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