Calculation of Speed for Message Packet on Small Planet

In summary, residents of a small planet have created a communication system by drilling a hole through its center and using a tube to pass messages. By removing air and reducing friction, messages can be sent by dropping packets through the tube. The planet's density is 3790kg/m3 and its radius is 5.25×106m. The speed of a message packet passing a point at a distance of 0.380R from the center of the planet can be calculated using the equation v = -R sin(2pit/T) * 2pi/T, where t = 1147.695s and the final answer is -1.08x10^5m/s.
  • #1
dantechiesa

Homework Statement


The residents of a small planet have bored a hole straight through its center as part of a communications system. The hole has been filled with a tube and the air has been pumped out of the tube to virtually eliminate friction. Messages are passed back and forth by dropping packets through the tube. The planet has a density of 3790kg/m3, and it has a radius of R=5.25×106m. Remember, as we saw in class, this 'oscillator' will have a period equal to the period of a satellite in orbit at the surface of the planet

a) What is the speed of the message packet as it passes a point a distance of 0.380R from the center of the planet?

Homework Equations


x = A cos wt
v = -A sin wt * 2pi/t

The Attempt at a Solution


I have T = 6106 s

Utilizing x = A cos wt to find t at .380R (A = R)

.380R = R Cos(2pi*t/T)
R's cancel

Cos-1(.380) = 1.181
1.818 * 6106 / 2pi

t = 1147.695 (can someone confirm this, I've done it a few time and get the same answer

Then I plug t in the derived velocity equation

v = -R sin(2pit/T) * 2pi/T

and the answer I get is -1.08x10^5m/s

Any thoughts?, Thanks
 
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  • #2
Redo your calculation of v. I get a different value using your numbers. Everything else looks fine. Also, make sure you give your final answer as the speed.
 
  • #3
dantechiesa said:
1.818 * 6106 / 2pi
Typo. It was 1.181.
dantechiesa said:
v = -R sin(2pit/T) * 2pi/T
That looks ok, but I calculate from that something of the order of 1000 to 10000.
 
  • #4
haruspex said:
Typo. It was 1.181.

That looks ok, but I calculate from that something of the order of 1000 to 10000.
Thank you!
 
  • #5
RedDelicious said:
Redo your calculation of v. I get a different value using your numbers. Everything else looks fine. Also, make sure you give your final answer as the speed.
Thats what it was, Thanks!
 

1. How is the speed of a message packet calculated on a small planet?

The speed of a message packet on a small planet is calculated using the formula: speed = distance/time. The distance is the length of the path the packet will travel, and the time is the duration of the journey. This calculation takes into account the size and shape of the planet, as well as any obstacles or terrain features that may affect the speed.

2. What units are used to measure the speed of a message packet on a small planet?

The speed of a message packet on a small planet is typically measured in meters per second (m/s) or kilometers per hour (km/h). These units are commonly used in scientific calculations and are easily converted to other units if needed.

3. How does the speed of a message packet on a small planet compare to that on a larger planet?

The speed of a message packet on a small planet will generally be slower than that on a larger planet, assuming all other factors are the same. This is because the smaller planet has less surface area and therefore a shorter distance for the packet to travel. However, other factors such as terrain and atmosphere can also affect the speed.

4. Are there any factors that can affect the speed of a message packet on a small planet?

Yes, there are several factors that can affect the speed of a message packet on a small planet. These include the size and shape of the planet, the terrain and any obstacles on the path, the atmosphere and air resistance, and the technology used to send and receive the message.

5. Can the speed of a message packet on a small planet be increased?

Yes, the speed of a message packet on a small planet can be increased by reducing the distance it needs to travel, optimizing the path to avoid obstacles, and using advanced technology for transmission and reception. However, there may be limitations based on the size and conditions of the planet.

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