A at disk of material has the same mass as the Earth, 5.98E+24 kg, and has a radius of 6.25 E+07 m. Point A is
located a distance of 5.8E+06 m above the center of the disk. Point B is located right at the center of the disk. Treat all of the mass as if it were located in the x-y plane.
An object of mass 250 kg is located near the disk.
a. Find the gravitational potential energy (J) when the object is at point A.
b. Find the gravitational potential energy (J) when the object is at point B.
Answers:
a)-2.88E+09 (I keep getting 1.59 E+09)
b)-3.19E+09 (I can kinda get this)
I used the Following
a) (-GMm)/x, where I used pythagorean and them to get x based on radius and height
b) (-Gmm)/r and I used (the r given/2)
that seems to work
I am really confused on what I am doing wrong on part A and if any suggetions on how to correct part B so i don't have to fudge it would be wonderful
The formula you are using for potential energy applies to a spherical object, not a disc.
See http://www.physicsforums.com/showthread.php?t=449947
for the appropriate formula
So I get most of what the website is saying however, it says M squared, but I have two masses
and only one radius, so I am still a little confused. Please help
As I recall from that link, the gravitational PE for a point above a disc involves both the distance to the center of the disc and the distance to the edge of the disc.
In both cases, the point must be at or above the center of the disc. That is true in your case.
Right and I have two different masses that need to be multiplied. The my r0 is 6.25 E 7, and R is 5.8 E 6, but using these number i am still getting 1.48 E 9 and not 2.88 E 9, so I am not sure, I have tried it different ways, am I missing something obvious here?
To find the gravitational potential energy at a certain point, we need to use the formula:
PE = -GMm / r
Where:
PE is the gravitational potential energy,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),
M is the mass of the large object (in this case, the disk),
m is the mass of the small object (in this case, 250 kg), and
r is the distance between the centers of mass of the two objects.
Let's work through the calculations step by step for both part a and part b.
a. Gravitational potential energy when the object is at point A:
To find the distance (r) between the disk and the object at point A, we need to use the Pythagorean theorem. The distance between the center of the disk and point A is given as 5.8E+06 m, and the radius of the disk is 6.25E+07 m.
Using the Pythagorean theorem, we get:
r = √(radius^2 + distance^2)
r = √((6.25E+07)^2 + (5.8E+06)^2)
r ≈ 6.378E+07 m
Now we can substitute the values into the formula to calculate the gravitational potential energy:
PE = -GMm / r
PE = -((6.67430 × 10^-11) * (5.98E+24) * (250)) / (6.378E+07)
PE ≈ -2.88E+09 J
So the correct answer for part a is -2.88E+09 J.
b. Gravitational potential energy when the object is at point B:
In this case, the object is located right at the center of the disk, so the distance between the centers of mass is equal to the radius of the disk.
Substituting the values into the formula:
PE = -GMm / r
PE = -((6.67430 × 10^-11) * (5.98E+24) * (250)) / (6.25E+07)
PE ≈ -3.19E+09 J
So the correct answer for part b is -3.19E+09 J.
If you're getting slightly different answers, it could be due to rounding errors or using slightly different values for G and the mass of the Earth. Make sure to use the correct values and perform accurate calculations.