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
3241004551 [841]
3 years ago
14

(a) What is the escape speed on a spherical asteroid whose radius is 500. km and whose gravitational acceleration at the surface

is 3.00 m/s2 ? (b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 1000 km above the surface?
Physics
1 answer:
navik [9.2K]3 years ago
3 0

Answer:

a) v= 1732.05m/s

b) d=250000m

c) v= 1414.214m/s

Explanation:

Notation

M= mass of the asteroid

m= mass of the particle moving upward

R= radius

v= escape speed

G= Universal constant

h= distance above the the surface

Part a

For this part we can use the principle of conservation of energy. for the begin the initial potential energy for the asteroid would be U_i =-\frac{GMm}{R}.

The initial kinetic energy would be \frac{1}{2}mv^2. The assumption here is that the particle escapes only if is infinetely far from the asteroid. And other assumption required is that the final potential and kinetic energy are both zero. Applying these we have:

-\frac{GMm}{R}+\frac{1}{2}mv^2=0   (1)

Dividing both sides by m and replacing \frac{GM}{R} by a_g R

And the equation (1) becomes:

-a_g R+\frac{1}{2} v^2=0   (2)

If we solve for v we got this:

v=\sqrt{2 a_g R}=\sqrt{2x3\frac{m}{s^2}x500000m}=1732.05m/s

Part b

When we consider a particule at this surface at the starting point we have that:

U_i=-\frac{GMm}{R}

K_i=\frac{1}{2}mv^2

Considering that the particle is at a distance h above the surface and then stops we have that:

U_f=-\frac{GMm}{R+h}

K_f=0

And the balance of energy would be:

-\frac{GMm}{R}+\frac{1}{2}mv^2 =-\frac{GMm}{R+h}

Dividing again both sides by m and replacing \frac{GM}{R} by a_g R^2 we got:

-a_g R+\frac{1}{2}v^2 =-\frac{a_g R^2}{R+h}

If we solve for h we can follow the following steps:

R+h=-\frac{a_g R^2}{-a_g R+\frac{1}{2}v^2}

And subtracting R on both sides and multiplying by 2 in the fraction part and reordering terms:

h=\frac{2a_g R^2}{2a_g R-v^2}-R

Replacing:

h=\frac{2x3\frac{m}{s^2}(500000m)^2}{2(3\frac{m}{s^2})(500000m)-(1000m/s)^2}- 500000m=250000m

Part c

For this part we assume that the particle is a distance h above the surface at the begin and start with 0 velocity so then:

U_i=-\frac{GMm}{R+h}

K_i=0

And after the particle reach the asteroid we have this:

U_f=-\frac{GMm}{R}

K_f=\frac{1}{2}mv^2

So the balance of energy would be:

-\frac{GMm}{R+h}=-\frac{GMm}{R}+\frac{1}{2}mv^2

Replacing again a_g R^2 instead of GM and dividing both sides by m we have:

-\frac{a_g R^2}{R+h}=-a_g R+\frac{1}{2}v^2

And solving for v:

a_g R-\frac{a_g R^2}{R+h}=\frac{1}{2}v^2

Multiplying both sides by two and taking square root:

v=\sqrt{2a_g R-\frac{2a_g R^2}{R+h}}

Replacing

v=\sqrt{2(3\frac{m}{s^2})(500000m)-\frac{2(3\frac{m}{s^2}(500000m)^2}{500000+1000000m}}=1414.214m/s

You might be interested in
A small car has a head-on collision with a large truck. Which of the following statements concerning the magnitude of the averag
andrey2020 [161]

Answer:

The small car and the truck experience the same average force.

Explanation:

Here we need to remember two of Newton's laws.

The second one says that:

F = m*a

force equals mass times acceleration.

And the third one says that;

"If an object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A"

From the third law, if the car experiences a force F due to the impact with the truck, then the truck experiences the same force F due to the impact.

But this seems odd, because we would expect to see the car being more affected by the impact, right?

Well, this is explained by the second law.

Suppose that the mass of the car is m, and the mass of the truck is M.

such that M > m

Then for the small car we have:

F = m*a

And for the truck:

F = M*a'

Because the force is the same for both of them, we can write:

m*a = M*a'

a = (M/m)*a'

because M > m, then M/m > 1.

This means that the acceleration that the car experiences is larger than the acceleration for the truck, and this is why we would see that the car seems more affected by the impact, regardless of the fact that both vehicles experience the same force in the impact.

6 0
2 years ago
Is "A firecracker that has not been lit kinetic, or potential energy?
love history [14]
A firecracker before been lit has potential energy in it. It is chemical potential energy which is due to the explosives in it.When it is lit, it gets converted into heat,light and kinetic energy.
7 0
3 years ago
A 50-gram sample of water is initially at a temperature of 22 °C. The sample is heated until the temperature is 32 °C The specif
forsale [732]

Answer:

500cal

Explanation:

Given parameters:

Mass of water  = 50g

Initial temperature  = 22°C

Final temperature  = 32°C

Specific heat of water  = 1cal/g

Unknown:

Amount of heat absorbed by the water in calories  = ?

Solution:

To solve this problem, we use the expression below:

       H  = m c Ф

H is the amount of heat absorbed

m is the mass

c is the specific heat capacity

Ф is the temperature change

       H  = 50 x 1 x (32  - 22)  = 500cal

5 0
2 years ago
Calculate Speed The 2-kg metal ball moving at a speed of 3 m/s strikes a 1-kg wooden ball that is at rest. After the collision,
enot [183]

Answer:

53466kg.

Explanatiokn:

5 0
2 years ago
18. Which would be the most reliable source of information to use for a history report? (2 points)
Paladinen [302]

Answer:

encyclopedia most reliable I think

3 0
3 years ago
Read 2 more answers
Other questions:
  • Satelite communication is only possible using
    6·2 answers
  • How do I determine valence electrons from the periodic table
    15·2 answers
  • A tennis player receives a shot with the ball (0.0600 kg) traveling horizontally at 50.4 m/s and returns the shot with the ball
    14·1 answer
  • A Each time he does one pushup, Jose, who has a mass of 89kg, raises his center of mass by 25 cm. He completes an impressive set
    9·1 answer
  • The heavyweight boxing champion of the world punches a sheet of paper in midair, bringing it from rest up to a speed of 26.5 m/s
    9·1 answer
  • A motorcycle begins at rest and accelerates uniformly S7.9 we want to find a time to take the motorcycle to reach a speed of 100
    5·1 answer
  • Select the correct answer.
    11·1 answer
  • What is the speed of sound in air with temperature of 355.8 k​
    11·1 answer
  • 2
    15·2 answers
  • C) 12g/cm d) 0.2g/cm
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!