Acceleration due to gravity help

In summary, the mass of 1kg would take about 2.2 minutes to fall 1 meter to the surface of the moon due to the gravitational force.
  • #1
sheevz
7
0
acceleration due to gravity help!

Homework Statement



PROB: How long would it take for a mass of 1kg to fall a distance of 2m to the surface of the moon?

Homework Equations



G=6.673*10^-11 Nm^2/kg^2
R of moon = 1.76*10^6m
m of moon = 7.35*10^22kg

The Attempt at a Solution


i started by finding the acceleration due to gravity by using g= (m)(G)/r^2
(m=mass of moon, G as the gravitational constant, r= radius of moon)
finding that g is 1.58m/s^2
now i am lost in what formula to use to get the displacement of this object?
 
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  • #2
Check your acceleration due to gravity for the moon, it should be ~1.62m/s^2

To solve for time t, use the formula [tex]x=v_{0}t+\frac{1}{2}at^2[/tex]
 
  • #3
ok i don't know if this is a type o or not but yes the acceleration due to gravity for the moon is ~1.62m/s^2 but in this prob, the radius is given @ 1.76*10^6 thus giving an acceleration due to gravity @ ~1.58m/s^2
and in using the above formula you gave me, X=Vot+.5at^2
is Vo my accel due to gravity on the moon and a my G constant? why in the original problem was G given to me, is it necessary in this? (probably a stupid question)
 
  • #4
Those pieces of data were given to you so you could work out the acceleration due to gravity, to sub into the formula konthelion gave to you. Obviously you did this through Newtons Universal Law of Gravitation. After we have the force, Using Newtons Second Law we can have the acceleration. We can take the Force and acceleration to be practically constant, because the change in the value of r in the Universal Gravitation Law changes by one 1m, very small in comparison to the radius of the moon. Although yes, it is true it is not exactly constant.
 

1. What is acceleration due to gravity?

Acceleration due to gravity is the rate at which an object falls towards the Earth due to the force of gravity. It is commonly denoted as "g" and has a constant value of 9.8 meters per second squared near the Earth's surface.

2. How is acceleration due to gravity calculated?

Acceleration due to gravity can be calculated using the equation g = G * M / R^2, where G is the gravitational constant, M is the mass of the larger object (such as the Earth), and R is the distance between the two objects.

3. Does acceleration due to gravity change with the mass of an object?

No, acceleration due to gravity does not change with the mass of an object. It is a constant value near the Earth's surface and is only affected by the mass of the larger object (such as the Earth).

4. How does altitude affect acceleration due to gravity?

As altitude increases, the distance between an object and the Earth's center increases. This results in a decrease in the acceleration due to gravity, since it is inversely proportional to the square of the distance between two objects.

5. How does acceleration due to gravity vary on different planets?

The value of acceleration due to gravity varies on different planets depending on their mass and radius. For example, it is lower on Mars due to its smaller mass and size, while it is higher on Jupiter due to its larger mass and size.

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