1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Svetllana [295]
3 years ago
6

The maximum distance from the Earth to the Sun (at aphelion) is 1.521 1011 m, and the distance of closest approach (at perihelio

n) is 1.471 1011 m. The Earth's orbital speed at perihelion is 3.027 104 m/s. Ignore the effect of the Moon and other planets. (a) Determine the Earth's orbital speed at aphelion. m/s (b) Determine the kinetic and potential energies of the Earth–Sun system at perihelion. Kp = J Up = J (c) Determine the kinetic and potential energies at aphelion. Ka = J Ua = J (d)Is the total energy constant
Physics
1 answer:
LUCKY_DIMON [66]3 years ago
6 0

Answer:

29274.93096 m/s

2.73966\times 10^{33}\ J

-5.39323\times 10^{33}\ J

2.56249\times 10^{33}\ J

-5.21594\times 10^{33}

Explanation:

r_p = Distance at perihelion = 1.471\times 10^{11}\ m

r_a = Distance at aphelion = 1.521\times 10^{11}\ m

v_p = Velocity at perihelion = 3.027\times 10^{4}\ m/s

v_a = Velocity at aphelion

m = Mass of the Earth =  5.98 × 10²⁴ kg

M = Mass of Sun = 1.9889\times 10^{30}\ kg

Here, the angular momentum is conserved

L_p=L_a\\\Rightarrow r_pv_p=r_av_a\\\Rightarrow v_a=\frac{r_pv_p}{r_a}\\\Rightarrow v_a=\frac{1.471\times 10^{11}\times 3.027\times 10^{4}}{1.521\times 10^{11}}\\\Rightarrow v_a=29274.93096\ m/s

Earth's orbital speed at aphelion is 29274.93096 m/s

Kinetic energy is given by

K=\frac{1}{2}mv_p^2\\\Rightarrow K=\frac{1}{2}\times 5.98\times 10^{24}(3.027\times 10^{4})^2\\\Rightarrow K=2.73966\times 10^{33}\ J

Kinetic energy at perihelion is 2.73966\times 10^{33}\ J

Potential energy is given by

P=-\frac{GMm}{r_p}\\\Rightarrow P=-\frac{6.67\times 10^{-11}\times 1.989\times 10^{30}\times 5.98\times 10^{24}}{1.471\times  10^{11}}\\\Rightarrow P=-5.39323\times 10^{33}

Potential energy at perihelion is -5.39323\times 10^{33}\ J

K=\frac{1}{2}mv_a^2\\\Rightarrow K=\frac{1}{2}\times 5.98\times 10^{24}(29274.93096)^2\\\Rightarrow K=2.56249\times 10^{33}\ J

Kinetic energy at aphelion is 2.56249\times 10^{33}\ J

Potential energy is given by

P=-\frac{GMm}{r_a}\\\Rightarrow P=-\frac{6.67\times 10^{-11}\times 1.989\times 10^{30}\times 5.98\times 10^{24}}{1.521\times 10^{11}}\\\Rightarrow P=-5.21594\times 10^{33}

Potential energy at aphelion is -5.21594\times 10^{33}\ J

You might be interested in
An oscillator creates periodic waves on a stretched string.
sattari [20]

Answer:

A. The wavelength doubles but the wave speed is unchanged

Explanation:

The relationship between the period and wavelength is direct. Doubling the period of the oscillator will correspondingly double the wavelength but the wave speed is unaffected

6 0
3 years ago
An electron moves at 0.130 c as shown in the figure (Figure 1). There are points: A, B, C, and D 2.10 μm from the electron.
Olegator [25]

Hi there!

We can use Biot-Savart's Law for a moving particle:
B= \frac{\mu_0 }{4\pi}\frac{q\vec{v}\times \vec{r}}{r^2 }

B = Magnetic field strength (T)
v = velocity of electron (0.130c = 3.9 × 10⁷ m/s)

q = charge of particle (1.6 × 10⁻¹⁹ C)

μ₀ = Permeability of free space (4π × 10⁻⁷ Tm/A)

r = distance from particle (2.10 μm)

There is a cross product between the velocity vector and the radius vector (not a quantity, but specifies a direction). We can write this as:

B= \frac{\mu_0 }{4\pi}\frac{q\vec{v} \vec{r}sin\theta}{r^2 }

Where 'θ' is the angle between the velocity and radius vectors.

a)
To find the angle between the velocity and radius vector, we find the complementary angle:

θ = 90° - 60° = 30°

Plugging 'θ' into the equation along with our other values:

B= \frac{\mu_0 }{4\pi}\frac{q\vec{v} \vec{r}sin\theta}{r^2 }\\\\B= \frac{(4\pi *10^{-7})}{4\pi}\frac{(1.6*10^{-19})(3.9*10^{7}) \vec{r}sin(30)}{(2.1*10^{-5})^2 }

B = \boxed{7.07 *10^{-10} T}

b)
Repeat the same process. The angle between the velocity and radius vector is 150°, and its sine value is the same as that of sin(30°). So, the particle's produced field will be the same as that of part A.

c)

In this instance, the radius vector and the velocity vector are perpendicular so

'θ' = 90°.

B= \frac{(4\pi *10^{-7})}{4\pi}\frac{(1.6*10^{-19})(3.9*10^{7}) \vec{r}sin(90)}{(2.1*10^{-5})^2 } = \boxed{1.415 * 10^{-9}T}

d)
This point is ALONG the velocity vector, so there is no magnetic field produced at this point.

Aka, the radius and velocity vectors are parallel, and since sin(0) = 0, there is no magnetic field at this point.

\boxed{B = 0 T}

3 0
2 years ago
In an "atom smasher," two particles collide head on at relativistic speeds. If the velocity of the first particle is 0.741c to t
galina1969 [7]

Answer:

W_x = 0.9156\ c

Explanation:

given,

velocity of particle 1 = 0.741 c to left

velocity of second particle = 0.543 c to right

relative velocity between the particle = ?

for the relative velocity calculation we have formula

W_x = \dfrac{|u_x - v_x|}{1-\dfrac{u_xv_x}{c^2}}

u_x = 0.543 c

v_x = - 0.741 c

W_x = \dfrac{0.543 c - (-0.741 c)}{1-\dfrac{(0.543 c)(-0.741 c)}{c^2}}

W_x = \dfrac{0.543 c +0.741 c)}{1+\dfrac{(0.543)(0.741)c^2}{c^2}}

W_x = \dfrac{1.284c}{1+0.402363}

W_x = 0.9156\ c

Relative velocity of the particle is W_x = 0.9156\ c

5 0
2 years ago
Find the potential energy of a 2 kg ball 15 m in the air.
mart [117]

Answer:

294.3 Joules

Explanation:

2kg*9.81m/s^2*Δ15=294.3J

8 0
3 years ago
N2O is the chemical formula of a covalent compound used in the production of whipping cream. The elements that make up this comp
vlabodo [156]
 N2O is nitrous oxide becuase of the nitrogen and oxygen

7 0
3 years ago
Read 2 more answers
Other questions:
  • A car traveling with constant speed travels 150 km in 7200 s. What is the speed of the car?
    15·2 answers
  • What is the formula for calculating the efficiency of a heat engine? Answers:
    9·1 answer
  • Select all of the answers that apply. _____ is one of the primary ways that heat can be transferred. Conduction Convection Trans
    12·2 answers
  • Scientists use laser range-finding to measure the distance to the moon with great accuracy. A brief laser pulse is fired at the
    11·1 answer
  • Why cooking pans don't have have metal handles?
    10·2 answers
  • 0.30 s after seeing a puff of smoke rise from the starter pistol the sound of the firing of the pistol is heard by the track tim
    10·1 answer
  • A sparrow is flying around in a circle at a constant speed and height. there is air resistance. In what direction is the net for
    15·2 answers
  • •. What is called the error due to the procedure and used apparatuses?
    12·1 answer
  • Why do the snakes only get one unit of energy?
    13·1 answer
  • It is important to increase your flexibility. <br><br> true or false?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!