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marin
3 months ago
10

A rocket lifts off the pad at cape canaveral. according to newton's law of gravitation, the force of gravity on the rocket is gi

ven by f(x) = − gmm x2 where m is the mass of the earth, m is the mass of the rocket, g is a universal constant, and x is the distance (in miles) between the rocket and the center of the earth. take the radius of the earth to be 4000 miles, so that x > 4000 miles. find the work, w1, done against gravity when the rocket rises 2000 miles.
Physics
1 answer:
kicyunya [3.2K]3 months ago
8 0
The formula used is known as the Law of Universal Gravitation. The gravitational constant G is 6.67×10⁻¹¹ Nm²/kg². The Earth's mass is <span>5.972 ×10</span>²⁴ kg. The mass of the rocket is negligible in comparison to Earth’s mass, hence it is unnecessary for our calculations. Plugging in the values:

F = (6.67×10⁻¹¹ Nm²/kg²)(5.972 ×10²⁴ kg)/(4000 miles*(1.609 km/1 mile))²
F = 9616423.08 N

The work done is given by
W = Fd
W = (9616423.08 N)(2000 miles*1.609 km/mile)
W = 9.095×10¹⁰ Joules
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What is the gauge pressure of the water right at the point p, where the needle meets the wider chamber of the syringe? neglect t
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Details that are not provided: the problem figure is included.

We can address the exercise by applying Poiseuille's law. This law indicates that for a fluid flowing in a laminar manner within a confined pipe,

\Delta P = \frac{8 \mu L Q}{\pi r^4}

where:

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This law can be utilized for the needle, allowing us to compute the pressure difference between point P and the needle's end. In this scenario, we have:

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and r=1 mm=0.001 m

Substituting these values into the formula yields:

\Delta P = 3200 Pa

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