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Deffense [45]
3 years ago
12

The orbit of Halley's Comet around the Sun is a long thin ellipse. At its aphelion (point farthest from the Sun), the comet is 5

.700 × 1012 m from the Sun and moves with a speed of 10.00 km/s. What is the comet's speed at its perihelion (closest approach to the Sun) where its distance from the Sun is 8.800 × 1010 m? The mass of the Sun is 1.987 × 1030 kg.
Physics
1 answer:
Arturiano [62]3 years ago
6 0

Answer:

v_{p}=647.72\frac{km}{s}

Explanation:

According to Kepler's second law: a line segment joining an object and the Sun sweeps out equal areas during equal intervals of time. This law is equivalent to the constancy of the angular momentum, that is to say:

\Delta \vec{L}=0\\\vec{L}_{p}=\vec{L}_{a}\\m*(\vec{r}_{p}\times \vec{v}_{p})=m*(\vec{r}_{a}\times \vec{v}_{a})\\mr_{p} v_{p}sin (\theta)=mr_{a} v_{a}sin (\theta)

Here,  m is the comet's mass,  r is its distance from the Sun,  v is its speed and  \theta the angle between  \vec{r}  and  \vec{v}

The aphelion and the perihelion are the only two points in the orbit where the radius and velocity are perpendicular. Therefore, at these 2 points, the angular momentum module can be calculated as a simple product:

mr_{p} v_{p}sin (^\circ 90)=mr_{a} v_{a}sin (^\circ 90)\\mr_{p} v_{p}=mr_{a} v_{a}

Rewriting for v_{p}:

v_{p}=\frac{r_{a}v_{a}}{r_{p}}\\v_{p}=\frac{(5.7*10^{12}m)10\frac{km}{s}}{8.8*10^{10}m}\\v_{p}=647.72\frac{km}{s}

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Considering the definition of kinetic energy, the bullet has a kinetic energy of 156.25 J.

<h3>Kinetic energy</h3>

Kinetic energy is a form of energy. It is defined as the energy associated with bodies that are in motion and this energy depends on the mass and speed of the body.

Kinetic energy is defined as the amount of work necessary to accelerate a body of a given mass and in a rest position, until it reaches a given speed. Once this point is reached, the amount of accumulated kinetic energy will remain the same unless there is a change in speed or the body returns to its rest state by applying a force to it.

The kinetic energy is represented by the following expression:

Ec= ½ mv²

Where:

  • Ec is the kinetic energy, which is measured in Joules (J).
  • m is the mass measured in kilograms (kg).
  • v is the speed measured in meters over seconds (m/s).

<h3>Kinetic energy of a bullet</h3>

In this case, you know:

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Replacing in the definition of kinetic energy:

Ec= ½ ×0.500 kg× (25 m/s)²

Solving:

<u><em>Ec= 156.25 J</em></u>

Finally, the bullet has a kinetic energy of 156.25 J.

Learn more about kinetic energy:

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