Measuring g in the Indian Ocean with a Submarine Pendulum

In summary, a scientist is conducting precise measurements of g at a certain point in the Indian Ocean using a pendulum in a submerged submarine. When the submarine is in motion, a slightly different value for g is obtained due to the centripetal acceleration. The change in g, (g'-g) in mm/s2, when the submarine is moving east at 11.3 kph is calculated using the equation a=v^2/r, where v is the speed of the submarine and r is the radius of the earth. The final value obtained is compared to the standard value of 9.81 mm/s2.
  • #1
bebop721
10
0
A scientist is making a precise measurement of g at a certain point in the Indian Ocean (on the equator) by timing the swing of a pendulum of accurately known construction. To provide a stable base, the measurements are conducted in a submerged submarine. It is observed that a slightly different value for g is obtained when the submarine is in motion. What is the change in g, (g'-g) in mm/s2, if the submarine is moving east at 11.3 kph? (Include the sign of the change in your answer.) Use as the equatorial radius of the Earth 6378.2 km

i have no clue how to do this any help would be appreciated
 
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  • #2
Hint: What kind of motion does the submarine (and pendulum) undergo?
 
  • #3
it undergoes centripcal acceleration but the equation for that is v^2/r
 
  • #4
or do you mean constant motion I am so lost for this question
 
  • #5
it's centripedal ACCELERATION. Constant velocity will have no effect on the pendulum nor on g.
 
  • #6
bebop721 said:
it undergoes centripcal acceleration but the equation for that is v^2/r
Yes, the submarine is centripetally accelerated. Now use that fact to figure out the change in the measured value of g.
 
  • #7
so take the speed we right now are going because of the Earth's rotation and divide it by the radius then add the speed of the submarine to the speed were going right now and find the difference between them
 
  • #8
no that won't work, i still don't know how to use the fact that it is centripedal acceleration to my advantage (a=v^2/r) using that doesn't give me a value close to g
or anything close to 9.81 to compare the subs accerations to
 
  • #9
Note that the problem says: "It is observed that a slightly different value for g is obtained when the submarine is in motion."

How does the centripetal acceleration change when the submarine moves?
 
  • #10
it changes slightly but how do you calculate that
 
  • #11
Hint: When the submarine is "at rest" in the water it is moving at the same rate as the rotating earth.
 
  • #12
thanks for the help i got the answer last night, thank-you
 

What is a submarine pendulum?

A submarine pendulum is a device used to measure the depth of the ocean. It consists of a weight attached to a rope or chain that is dropped from a ship or submarine to the ocean floor. The time it takes for the weight to reach the bottom and return to the surface is used to calculate the depth of the water.

How does a submarine pendulum work?

A submarine pendulum works by utilizing the principles of gravity and motion. The weight at the end of the rope or chain is pulled downward by gravity, and as it falls, it creates a swinging motion. This motion is affected by the resistance of the water, which allows for accurate depth measurements.

What are the advantages of using a submarine pendulum?

One of the main advantages of using a submarine pendulum is that it does not require any external power source, making it a reliable and cost-effective method for measuring depth. It is also a relatively simple and easy-to-use device, making it ideal for use in remote or challenging ocean environments.

How accurate is a submarine pendulum?

The accuracy of a submarine pendulum depends on several factors, including the length of the rope or chain, the weight of the weight, and the resistance of the water. However, with proper calibration and use, a submarine pendulum can provide depth measurements with an accuracy of within a few meters.

What are the limitations of a submarine pendulum?

One of the main limitations of a submarine pendulum is that it can only measure the depth directly underneath the location of the ship or submarine. It also requires calm seas and a relatively flat ocean floor to provide accurate measurements. Additionally, the weight may get caught on underwater obstacles, making it difficult to retrieve and potentially causing damage to the device.

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