Centripetal Acceleration Space Shuttle Problem

In summary, to find the centripetal acceleration of a space shuttle orbiting 400 km from Earth's surface, we can use the equation a = v^2/r. With the given time of 90 minutes or 5400 seconds, we can calculate the velocity using the equation v = 2πr/t. Plugging in the values, we get a velocity of 465.2 m/s. Then, using the equation a = v^2/r, we get an acceleration of 0.084 m/s^2. To express this in terms of g, we multiply by the gravitational acceleration at Earth's surface, 9.8 m/s^2, and get an answer of 0.824 m
  • #1
C^2
1
0

Homework Statement


Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g, the gravitational accleration at the Earth's surface.

Known Variables:

time(t)= 5400seconds
centripetal acceleration(a)= ?
radius(r)=400,000 meters


Homework Equations


v=2pir/t
a=v^2/t
g=9.8 m/s^2

The Attempt at a Solution



So, what I thought I was supposed to do was use the first equation and plug in the numbers:

v= 2(3.14)(400,000)/5400s

=465.2 m/s

then I plugged the result into the second equation:

a= (465.2)^2/5400

=.084 m/s^2

and since they ask to express the answer in terms of g,

.084 m/s^2 * 9.8 m/s^2

=.844 m/s^2

but the book says the answer should be .9g's. I don't know if I'm just splitting hairs here, but .844 does not round up to .9.
Can someone point out where I went wrong?
Thanks in advance
 
Physics news on Phys.org
  • #2
Hi,

where did you get a = v^2 / t ?

v is a velocity in metres per second
t is a time in seconds
a is an acceleration in metres per second squared

the dimensions (units) do not add up!

Hope that helps cheers
 
  • #3


Your calculations are correct. The book may have rounded up to .9 for simplicity, but your answer of .844 m/s^2 is more accurate. Sometimes in scientific calculations, we have to round off the numbers for simplicity, but it is important to keep track of the significant figures. In this case, your answer has three significant figures, while .9 only has one. So, your answer of .844 m/s^2 is more precise. Keep up the good work in your calculations!
 

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration of an object moving in a circular path. It is always directed towards the center of the circle and is necessary to keep the object moving in a circular motion.

2. How is centripetal acceleration calculated?

The formula for centripetal acceleration is v^2/r, where v is the velocity of the object and r is the radius of the circular path. This means that as the speed of the object increases or the radius of the circle decreases, the centripetal acceleration will also increase.

3. How does centripetal acceleration affect the space shuttle?

The space shuttle experiences centripetal acceleration as it orbits around the Earth. This acceleration is necessary to keep the shuttle in orbit and prevents it from flying off into space.

4. How does the space shuttle's speed affect centripetal acceleration?

The faster the space shuttle travels, the greater the centripetal acceleration it experiences. This is because the velocity of the shuttle is directly related to the centripetal acceleration, as shown in the formula v^2/r.

5. How is centripetal acceleration important for the safety of the space shuttle?

Centripetal acceleration is crucial for the safety of the space shuttle as it keeps the shuttle in orbit and prevents it from crashing into the Earth. If the centripetal acceleration were to decrease or disappear, the shuttle would no longer be able to maintain its orbit and could potentially crash.

Similar threads

Replies
12
Views
583
  • Introductory Physics Homework Help
Replies
28
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
974
  • Introductory Physics Homework Help
Replies
11
Views
3K
  • Introductory Physics Homework Help
Replies
8
Views
810
  • Introductory Physics Homework Help
Replies
13
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
2K
Back
Top