Calculating acceleration due to gravity on a planet

In summary, calculating the acceleration due to gravity on a planet involves using the planet's mass and radius to determine its gravitational force and then dividing that force by the mass of an object to find its acceleration. This value can vary depending on the planet's size and composition, but it is typically around 9.8 meters per second squared on Earth. Other factors, such as altitude and rotation, can also affect the acceleration due to gravity on a planet. This calculation is important in understanding the behavior of objects in the planet's gravitational field and is a key concept in physics.
  • #1
Bryon
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Homework Statement



The data is taken from a graph. The initial velocity is 31m/s. I found the horizontal velocity to be 21m/s. The time the ball travels is 5 seconds. The total distance the ball traveled is 105m. The ball lands at the same vertical level at which it starts. Air resistance can be neglected.


Homework Equations



Im pretty sure I have to use this equation, where t= 2.5.

v = v(initial) + at

I used the pythagoreum theorem to find the initial vertical velocity to be 22.8m/s. Then divided it by 2.5. What I came up with, -9.12, which is wrong.

I just can't find the acceleration due to gravity. It looks straight forward but I am missing a step. Any ideas?

Thanks!
 
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  • #2
Your method appears to be correct and the answer follows from the numbers that you gave. If the answer is incorrect, then you need to make sure that you read the graph correctly. When you say "the initial velocity is 31 m/s", you mean the initial speed is 31 m/s, right?
 
  • #3
Here is a link to the graph, which plots the velocity over time (sorry i didnt think to add it)

https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/fall/homework/Ch-03-04/golfball_plot/golfball_plot-1.jpg

Thanks for the help!
 
Last edited by a moderator:
  • #4
Ahh, it was +9.12. However, I am not sure as to why it is positive.
 

1. How is the acceleration due to gravity calculated on a planet?

The acceleration due to gravity on a planet can be calculated using the formula g = Gm/r^2, where g is the acceleration due to gravity, G is the universal gravitational constant, m is the mass of the planet, and r is the distance from the planet's center.

2. What is the universal gravitational constant?

The universal gravitational constant, denoted by G, is a fundamental physical constant that relates the strength of the gravitational force between two objects based on their masses and distance. Its value is approximately 6.67 x 10^-11 N*m^2/kg^2.

3. How does the mass of a planet affect its acceleration due to gravity?

The acceleration due to gravity is directly proportional to the mass of the planet. This means that the larger the mass of the planet, the stronger its gravitational pull and therefore, the higher the acceleration due to gravity.

4. Why does the acceleration due to gravity vary on different planets?

The acceleration due to gravity varies on different planets because it is dependent on both the mass and the radius of the planet. Each planet has a different mass and radius, resulting in a different gravitational pull and therefore, a different acceleration due to gravity.

5. Can the acceleration due to gravity change on a planet?

Yes, the acceleration due to gravity on a planet can change if there are changes to either the mass or the radius of the planet. For example, if a planet's mass increases, its gravitational pull will also increase, resulting in a higher acceleration due to gravity. Similarly, if a planet's radius decreases, its gravitational pull will also decrease, resulting in a lower acceleration due to gravity.

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