Question

Your spaceship lands on an unknown planet. to determine the characteristics of this planet, you drop a 1.50 kg wrench from 5.50 m above the ground and measure that it hits the ground 0.811 s later. you also do enough surveying to determine that the circumference of the planet is 6.28×104 km . part a what is the mass of the planet, in kilograms?

Answer 1

1. calculate the value of acceleration that objects gains in that period of time
•calculating acceleration
5.50 = 1/2at^2
5.50*2/t^2 = a
11.00/0.657 = a
16.74=a
now you got the acceleration
2. you have laws of gravitation for that

g = Gm/r^2
where g is the acceleration value
16.74 = 6.754*10^-11 × m/ 6.28*10^4
105.14*10^4 /6.754*10-11 = m
15.567*10^15 = m
that would be the mass of the planet ...

Answer 2

The mass of the planet is
`M=2.5*10^(25)kg`

Step-by-step explanation:

We have a first part of the problem, which we resolve with kinematics, knowing that

`d=d_(0)+v_(0)t+(1)/(2)at^2`

where d is given (5.50m), d₀ is zero, v₀ is zero too (as the wrench starts falling from static position), t is given (0.811s), and a is what we want to know for the second part of the problem. We clear a

`a=(2*5.5m)/((0.811s)^2)=16.72(m)/(s^2)`

Then for the second part, we use Newton's gravitational Law, where

`F_(g)=G(mM)/(r^2)`

m is the wrench mass, M is the planet mass, G is the gravity universal constant, and r is calculated from the given circumference (with the correct units) as

`2\pi r=6.28*10^7m\Leftrightarrow r=(6.28*10^7m)/(2\pi)=9994930.4m`

Finally, we have that

`F_(g)=G(mM)/(r^2)\Leftrightarrow ma=G(mM)/(r^2)\Leftrightarrow a=G(M)/(r^2)\Leftrightarrow M=(ar^2)/(G)`

Therefore, replacing with the data calculated, and the known value of G, we can calculate M of the planet

`M=(16.72*9994930.4^2)/(6.67428*10^(-11))=2.5*10^(25)kg`