How Long Does It Take a Package to Travel Through a Planet in a Gravity Tunnel?

[chaotixmonjuish]

A tunnel is bored through the center of a planet, as shown in the Figure (this drawing is NOT to scale and the size of the tunnel is extremely exaggerated). Assume that the planet is a homogenous sphere with a total mass M = 3.6 × 1024 kg and a radius R = 7300 km. A package of mass m = 7.8 kg is dropped into the tunnel. If the tunnel is used to deliver mail from one side of the planet to the other, how long would it take for a letter to travel through the planet?

I got the magnitude of gravitation as 23.1 Newtons, but I'm not sure what to do with it and how to use it to figured out how long it would take to travel through the planet.

My next question:
Four spheres form the corners of a square whose sides are 10 cm long. The masses of the spheres are m1 = 950 kg, m2 = 200 kg, m3 = 600 kg, and m4 = 950 kg. What is the magnitude of the net gravitational force from them on a central sphere with mass m5 = 950 kg?

img:http://i242.photobucket.com/albums/ff106/jtdla/prob10.gif

I tried using the pytagorean theorem to get a hypotenouse (5^2+5^2=radical(50)) and putting that in the denomentator of the various masses times 950. After summing them up I still didn't get the answer. Any ideas?

 

[Shooting Star]

Q1.

Find the grav force at a dist r from the centre of the earth, where r<R of earth. It's not a constant force, as you have written. But you'll be surprised to see that it's another kind of force very common in Physics.

 

[matthew1991]

Q2: Start by turning the square into a diamond by rotating it so that the middle ball lies at the origin and te others lay on axis in an xy plane. Separate the forces into components and allow them to cancel where able. Then subtract the forces from each other until you are left with net gravitation.

 

[zorro]

Q1.
I think the mail will never reach the other side of the planet.
It executes SHM

 

[matthew1991]

the object moves with SHM, but energy is conserved. The object will reach the other side of the planet at the heigt it was dropped from at the exact moment its speed reaches zero. for more information look up Hooke's theory of gravity trains.