The maximum speed you can walk on the Mars

[lengleng]

Homework Statement

You are an astronaut-in-training for the first mission to Mars by humans. You are about to go into a Mars simulator and need to know the answers to the following questions to complete the simulation correctly. You already have memorized basic information about Mars such as its mass (6.42x1023 kg), its radius (3.37x10^6 m) and its rotation period (its “day”) which is 24.8 hours. You also know that Newton’s universal gravitational constant (“big G”) is 6.67x10^-11 Nm2/kg2.

What is the speed at which you will be able to walk on the surface of Mars?

Homework Equations

F_net=N-mg_M=mv²/r
v_M=(g_M r)^(1/2)

F=GM_Mm/r_M^(1/2)=mg_M
g_M=GM_M/r_M^1/2

The Attempt at a Solution

use r= radius of the Mars, I got v_M=3.56 km /s
use r= radius of my leg=0.7 m, I got v_M=1.6 m/s.

Which one is right?

 

[Andrew Mason]

Your problem refers to "the following questions" but there are none. What are questions?

AM

 

[JHamm]

r is for the radius of Mars, your first equation uses it as the radius of the arc of the circle you move over.

 

[Andrew Mason]

What limits the speed that you can walk on the surface?

Also the denominator is r^2 not r^1/2 in:

F=GM_Mm/r_M²=mg_M
g_M=GM_M/r_M²

AM

 

[asteriatic]

The correct answer is 1.6 m/s. The equation vM=(gM r)(1/2) is used to calculate the escape velocity of an object from the surface of a planet, not the walking speed. The walking speed on Mars would be determined by the force of gravity and the strength of the person's leg muscles, not the escape velocity. Therefore, using the equation vM=1.6 m/s is the correct approach for calculating the maximum walking speed on Mars.