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
Masteriza [31]
3 years ago
9

In the far future, astronauts travel to the planet Saturn and land on Mimas, one of its 62 moons. Mimas is small compared with t

he Earth's moon, with mass Mm = 3.75 ✕ 1019 kg and radius Rm = 1.98 ✕ 105 m, giving it a free-fall acceleration of g = 0.0636 m/s2. One astronaut, being a baseball fan and having a strong arm, decides to see how high she can throw a ball in this reduced gravity. She throws the ball straight up from the surface of Mimas at a speed of 43 m/s (about 96 mph, the speed of a good major league fastball)."
Required:
a. Predict the maximum height of the ball assuming g is constant and using energy conservation. Mimas has no atmosphere, so there is no air resistance.
b. Now calculate the maximum height using universal gravitation.
c. How far off is your estimate of part (a)? Express your answer as a percent difference and indicate if the estimate is too high or too low.
Physics
1 answer:
Mamont248 [21]3 years ago
7 0

Answer:

a)h_{max}=14536.16 m

b)h = 15687.9 m

c)PD=7.62\% The estimate is low.

Explanation:

a) Using the energy conservation we have:

E_{initial}=E_{final}

we have kinetic energy intially and gravitational potential energy at the maximum height.

\frac{1}{2}mv^{2}=mgh_{max}

h_{max}=\frac{v^{2}}{2g}

h_{max}=\frac{43^{2}}{2*0.0636}

h_{max}=14536.16 m  

b)  We can use the equation of the gravitational force

F=G\frac{mM}{R^{2}}   (1)

We have that:

F = ma    (2)

at the surface G will be:

G=\frac{gR^{2}}{M}

Now the equation of an object at a distance x from the surface.

is:

F=\frac{mgR^{2}}{(R+x)^{2}}

m\frac{dv}{dt}=\frac{mgR^{2}}{(R+x)^{2}}

Using that dv/dt is vdx/dt and integrating in both sides we have:

v_{0}=\sqrt{\frac{2gRh}{R+h}}

h=\frac{v_{0}^{2}R}{2gR-v_{0}^{2}}

h=15687.9

c) The difference is:

So the percent difference will be:

PD=|\frac{14536.16-15687.9}{(14536.16+15687.9)/2}*100%

PD=7.62\%

The estimate is low.

I hope it helps you!

You might be interested in
A 0.20 kg mass attached to the end of a spring causes it to stretch 3.0 cm. What is the spring constant? What is the potential e
SVEN [57.7K]

Given that the mass is m = 0.2 kg and the displacement is x = 3 cm = 0.03 m

We have to find the spring constant and potential energy.

The spring constant can be calculated by the formula

\begin{gathered} F=\text{ kx} \\ mg\text{ = kx} \\ k\text{ = }\frac{mg}{x} \end{gathered}

Here, k is the spring constant.

g = 9.8 m/s^2 is the acceleration due to gravity.

Substituting the values, the spring constant will be

\begin{gathered} k=\frac{0.2\times9.8}{0.03} \\ =\text{ 65.33 N/m } \end{gathered}

The potential energy can be calculated as

\begin{gathered} U=\frac{1}{2}kx^2 \\ =\frac{1}{2}\times65.33\text{ }\times(0.03)^2 \\ =\text{ 0.0293 J} \end{gathered}

8 0
1 year ago
What involves the movement of electrons in neutral objects due to the electric field produced by a charged object?
ELEN [110]

Answer: Polarization

Explanation: Polarization is the movement of electrons within a neutral object because of the electric field of a nearby charged object. It occurs without direct contact between the two objects.

For example, electrons in a metal plate can repelled by the negative charges in a plastic rod if the plastic rod is placed near the metal plate. The electrons move away from the plastic rod, thereby causing one side of the metal plate to be positively charged and the other side to become negatively charged.

4 0
4 years ago
A tablecloth can be pulled out from underneath a fully set table without breaking plates or glassware. The reason is that the ob
bekas [8.4K]

Answer:

newtons law of force

newtons law of force explains that something may or can or canot move depending on the objexts mass.

6 0
3 years ago
What is the upper temperature range for stars?
padilas [110]
The upper temperature range for stars is : c. 40,000 K

Every object has their own upper and lower temperature
This indicate the maximum possible energy that a star could release to its surrounding if its somehow exploded.
6 0
3 years ago
Read 2 more answers
Which of the following is evidence of Earth's age provided by fossils?
Paladinen [302]
I think the answer is Fossils formed gradually over time.
7 0
3 years ago
Read 2 more answers
Other questions:
  • A measurement standard is defined as ____.
    10·2 answers
  • HELLLLLLLLLLLLLLLLP QUICKKKKKKKK PLZZZZZ
    5·2 answers
  • A changing magnetic field can produce an electric current. True or False?
    15·1 answer
  • Can the sum of the magnitudes of two vectors ever be equal to the magnitude of the sum of the same two vectors? If no, why not?
    5·1 answer
  • The African and South American continents are separating at a rate of about 3 cm per year, according to the ideas of plate tecto
    10·1 answer
  • A cement truck of mass 14,000 kg moving 10m/s slams into a wall and comes to a halt in .2s. What is the force of impact on the t
    9·1 answer
  • HELPPP I NEED HELP ASAP NOW
    8·1 answer
  • To measure the wavelength of any longitudnal wave, one should measure distance
    12·1 answer
  • Modern rechargeable batteries require rare earth elements to build. Why are modern rechargeable batteries expensive and a concer
    6·1 answer
  • Can someone please answer this, ill give you brainliest and your getting 100 points.
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!