Acceleration due to gravity problem.Help

In summary: Thanks for looking!In summary, Homework Equations state that G=6.67*10^-11 and Mp=3.30*10^23 kg on Mercury. The Attempt at a Solution finds that G=3.70 and Mp=2.439 kg on Mercury.
  • #1
NewtonJR.215
10
0

Homework Statement


"Determine the acceleration due to gravity on the planet Mercury which has a mass of 3.30*10^23kg and a diameter of 4878 km.



Homework Equations


Gmp/rp2
Mp is mass of planet
Rp is radius of planet



The Attempt at a Solution


First off I needed to change the diameter into the radius. In my class I have to convert km to m.

4878 km*1000= 4,878,000 m

4,878,000/2= 2,439,000

2,439,000 is the radius

Next, plugged in.

G=6.67*10^-11

Gmp/rp2
(6.67*10^-11)(3.30*10^23)/2,439,000^2 = 3.70 g on Mercury.


I'm pretty sure this is correct just want to make sure. Thanks for looking it over!
 
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  • #2
Welcome to PF!

NewtonJR.215 said:
Gmp/rp2
(6.67*10^-11)(3.30*10^23)/2,439,000^2 = 3.70 g on Mercury.


I'm pretty sure this is correct just want to make sure. Thanks for looking it over!

Hi NewtonJR! Welcome to PF! :smile:

That's a very well-laid out solution … I can see exactly what you're doing!

Yes, that's fine … except I think you don't mean that "g" at the end, do you? :smile:

btw, as a check (which is often useful to make sure we're not 1000 out!), if we assume that Mercury's density is roughly the same as the Earth's, then mass is proportional to r³, so surface gravity is proportional to r, so should be about 40% of g, = about 4. Yippee! :biggrin:
 
  • #3
tiny-tim said:
Hi NewtonJR! Welcome to PF! :smile:

That's a very well-laid out solution … I can see exactly what you're doing!

Yes, that's fine … except I think you don't mean that "g" at the end, do you? :smile:

btw, as a check (which is often useful to make sure we're not 1000 out!), if we assume that Mercury's density is roughly the same as the Earth's, then mass is proportional to r³, so surface gravity is proportional to r, so should be about 40% of g, = about 4. Yippee! :biggrin:

Thanks for the welcome! Thanks for the feedback also. No, I didn't mean to put that "g" at the end.:cool:
 
  • #4
This problem is SOLVED.
 

1. What is acceleration due to gravity?

Acceleration due to gravity is the acceleration that an object experiences when falling towards the ground due to the force of gravity. On Earth, the average acceleration due to gravity is 9.8 meters per second squared (m/s^2).

2. How is acceleration due to gravity calculated?

To calculate acceleration due to gravity, you can use the formula a = g, where "a" represents acceleration and "g" represents the acceleration due to gravity. Alternatively, you can use the formula a = F/m, where "F" represents the force of gravity and "m" represents the mass of the object.

3. Does acceleration due to gravity vary on different planets?

Yes, acceleration due to gravity can vary on different planets depending on their mass and radius. For example, on Mars, the acceleration due to gravity is approximately 3.7 m/s^2, while on Jupiter, it is approximately 24.8 m/s^2.

4. How does air resistance affect acceleration due to gravity?

Air resistance can affect acceleration due to gravity by slowing down the rate at which an object falls. This is because air resistance creates an opposing force on the object, reducing its acceleration.

5. What are some real-life examples of acceleration due to gravity?

Some real-life examples of acceleration due to gravity include objects falling to the ground, a pendulum swinging, and a roller coaster going down a steep hill. These all demonstrate how gravity affects the acceleration of objects on Earth.

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