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
Varvara68 [4.7K]
3 years ago
12

(a) Calculate the magnitude of the gravitational force exerted by Mars on a 80 kg human standing on the surface of Mars. (The ma

ss of Mars is 6.4multiply1023 kg and its radius is 3.4multiply106 m.)
(b) Calculate the magnitude of the gravitational force exerted by the human on Mars.

(c) For comparison, calculate the approximate magnitude of the gravitational force of this human on a similar human who is standing 4 meters away.

(d) What approximations or simplifying assumptions must you make in these calculations? (Note: Some of these choices are false because they are wrong physics!)

-Use the same gravitational constant in (a) and (b) despite its dependence on the size of the masses.

-Treat Mars as though it were spherically symmetric.

-Treat the humans as though they were points or uniform-density spheres.

-Ignore the effects of the Sun, which alters the gravitational force that one object exerts on another.
Physics
1 answer:
andrew11 [14]3 years ago
4 0

Answer:

a) F=1.044\times 10^9\ N

b)F'=1.044\times 10^9\ N

c) F_p=1.0672\times10^{-7}\ N

d) Treat the humans as though they were points or uniform-density spheres.

Explanation:

Given:

  • mass of Mars, M=6.4\times 10^{23}\ kg
  • radius of the Mars, r=3.4\times 10^{6}\ m
  • mass of human, m=80\ kg

a)

Gravitation force exerted by the Mars on the human body:

F=G.\frac{M.m}{r^2}

where:

G=6.67 \times 10^{-11}\ m^3.kg^{-1}.s^{-2} = gravitational constant

F=6.67\times10^{-11}\times \frac{6.4\times 10^{23}\times 80}{(3.4\times 10^{6})^2}

F=1.044\times 10^9\ N

b)

The magnitude of the gravitational force exerted by the human on Mars is equal to the force by the Mars on human.

F'=F

F'=1.044\times 10^9\ N

c)

When a similar person of the same mass is standing at a distance of 4 meters:

F_p=6.67\times10^{-11}\times \frac{80\times 80}{4}

F_p=1.0672\times10^{-7}\ N

d)

The gravitational constant is a universal value and it remains constant in the Universe and does not depends on the size of the mass.

  • Yes, we have to treat Mars as spherically symmetric so that its center of mass is at its geometric center.
  • Yes, we also have to ignore the effect of sun, but as asked in the question we have to calculate the gravitational force only due to one body on another specific body which does not brings sun into picture of the consideration.
You might be interested in
E14. A ball rolls off a table with a horizontal velocity of 5 m/s. If
Shkiper50 [21]

a) Vertical velocity: 5.9 m/s

b) Horizontal velocity: 5 m/s

Explanation:

a)

The motion of the ball is the motion of a projectile, which consists of two independent motions:

- A uniform motion (constant velocity) along the horizontal direction)

- A uniformly accelerated motion (constant acceleration) along the vertical direction

Here we want to find the vertical component of the ball's velocity. This can be done by using the suvat equation for the vertical motion:

v_y = u_y +gt

where:

v_y is the vertical velocity at time t

u_y=0 is the initial vertical velocity (zero because the ball has been thrown horizontally)

g=10 m/s^2 is the acceleration of gravity (here we take downward as positive direction)

Substituting t = 0.6 s, which is the total time of flight, we find the vertical velocity of the ball just before it hits the ground:

v_y=0+(9.8)(0.6)=5.9 m/s

b)

The motion along the vertical direction is an accelerated motion, because there is a force (the force of gravity) acting on the ball and that it causes an acceleration in the ball.

However, there are no forces acting in the horizontal direction on the ball (if we neglect the air resistance): this means that the acceleration of the ball in the horizontal direction is zero.

As a consequence, this also means that the horizontal component of the ball's velocity is constant during the motion.

Since the ball was thrown from the table with an initial horizontal velocity of 5 m/s, this means that the horizontal velocity of the ball just before it hits the floor is still

v_x =  5 m/s

8 0
3 years ago
Manipulate the equation "v=d/t" to find the answers to these problems using
OLEGan [10]
Yo no me voy a ir a la cama a
4 0
3 years ago
Suppose a firm is producing 2,475 units of output by hiring 50 workers (W = $20 per hour) and 25 units of capital (R = $10 per h
Neko [114]

Answer

given,

firm is producing  = 2,475 units

output by hiring 50 workers W = $20 per hour

25 units of capital R = $10 per hour

marginal product of labor = 40

marginal product of capital = 25

\dfrac{MP_l}{MP_c}=\dfrac{40}{25}

\dfrac{MP_l}{MP_c}=\dfrac{8}{5}

\dfrac{W}{R}=\dfrac{20}{10}

\dfrac{W}{R}=2

\dfrac{MP_l}{MP_c} < \dfrac{W}{R}

Firm is not minimizing the cost because the firm use more capital and less labor.

3 0
3 years ago
4 properties of light
Neko [114]
-reflection and refraction of light
-dispersion of light
-absorption of light
-polarization of light
3 0
2 years ago
A small branch is wedged under a 200 kg rock and rests on a smaller object. The smaller object is 2.0 m from the large rock and
Alexxandr [17]

Answer:

a

  F  =326.7 \ N

b

  M  = 6

Explanation:

From the question we are told that

          The mass of the rock is  m_r  =  200 \ kg

          The  length of the small object from the rock is  d  =  2 \ m

          The  length of the small object from the branch l  =  12 \ m

An image representing this lever set-up is shown on the first uploaded image

Here the small object acts as a fulcrum

The  force exerted by the weight of the rock is mathematically evaluated as

      W =  m_r *  g

substituting values

     W =   200 *  9.8

     W =   1960 \ N

 So  at  equilibrium the sum  of the moment about the fulcrum is mathematically represented as

         \sum  M_f  =  F * cos \theta *  l  -  W cos\theta  *  d =  0

Here  \theta is very small so  cos\theta  *  l  =  l

                               and  cos\theta  *  d  =  d

Hence

       F *   l  -  W  * d =  0

=>    F  = \frac{W * d}{l}

substituting values

        F  = \frac{1960 *  2}{12}

       F  =326.7 \ N

The  mechanical advantage is mathematically evaluated as

          M  = \frac{W}{F}

substituting values

        M  = \frac{1960}{326.7}

       M  = 6

6 0
3 years ago
Other questions:
  • You skip north for 12 minutes to your best friend's house that is 1.5 kilometers away. What is your average velocity?
    7·1 answer
  • Determine for which class of lever the output force is always greater than the input force. for which class is the output force
    14·2 answers
  • In tin at room temperature, the mobility of mobile electrons is about 1.5 ✕ 10⁻³ (m/s)/(V/m), and there are about 3.7 ✕ 10²⁸ mob
    12·1 answer
  • Define 1 kilowatthour​
    10·2 answers
  • Find the acceleration of a car with the mass of 1,200 kg and a force of
    10·1 answer
  • Any clue on this one I know it’s not D
    14·2 answers
  • An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. It consists of a solenoid (
    6·2 answers
  • Two speakers in a stereo emit identical pure tones. As you move around in front of the speakers, you hear the sound alternating
    11·1 answer
  • If the ratio between the frequency of a man's voice and that of a girl's voice is 3/4, what
    15·1 answer
  • A 65 kg woman is horizontal in a push-up position. What are the vertical forces acting on her hands?​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!