Mechanics - Gravity at 55 Degrees North

In summary, when a pendulum bob is suspended from a long pole at a latitude of 55 degrees north on Earth, the combined action of gravity and Earth's rotation causes the bob to deviate towards the south. The angle of deflection can be found by using the equation for centrifugal force, which takes into account the mass of the bob, the angular velocity of the Earth's rotation, and the radius at 55 degrees north.
  • #1
ronny45
21
0
[SOLVED] Mechanics - gravity

Homework Statement



A pendulum bob is suspended from a long pole at a latititude of 55 degrees north on the Earth. When the pendulum is at rest, the combined action of gravitation and Earth's rotation makes the bob deviate towards the south. By how much does the bob deviate?
(Radius of Earth = 6378km)

The Attempt at a Solution



Okay... firstly, I'm assuming that the tension is divided into components so that the vertical component equals the weight of the bob. Therefore, the horizontal force is indeed acting towards the south. Now, the rotational speed of the Earth is obviously 1 day = 86400s. The angle of deflection (theta) is what I'm looking for. Any ideas?
 
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  • #2
What will be the centrifugal force acting on the pendulum?

P.S. The rotational speed of the Earth is not one day.
 
  • #3
Centrifugal force = m (Omega)^2 r

Sorry, the time it takes the Earth to rotate is one day... how would I get the rotational speed then? Is it the angular velocity?
 
  • #4
Omega is just the angular velocity and is given by [itex]\omega = \frac{2\pi}{T} [/itex]. Be careful with r.
 
  • #5
2pi/86400 = 7.27*10^-5m/s
(7.27*10^-5)^2 *6378000*5.9742 × 10^24 kilograms (mass of earth)
=2.01388*10^23 N (not sure if Newtons are the correct unit of centrifugal force)
Does this seem a reasonable figure?
 
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  • #6
I said to be careful with r. The radius will not be that of the Earth. There is no need to work out the speed anyway since you have an equation for force with angular velocity and r in anyway.

Drawing a diagram may help you visualise this.
 
  • #7
Of course... it's the radius at 55 degrees north, which is 962,461m.
Centrifugal force = m (Omega)^2 r = 5.9742 × 10^24(7.27*10^-5)^2(962461)
= 3.04*10^22
 
  • #8
The mass will be that of the pendulum bob and I don't know how you've calculated the radius at 55 degrees north but that's not correct.
 

FAQ: Mechanics - Gravity at 55 Degrees North

What is gravity at 55 degrees north?

Gravity at 55 degrees north refers to the gravitational force experienced at a location on Earth that is 55 degrees north of the equator. This force is due to the mass of the Earth and is responsible for the downward pull we feel on our bodies.

How does gravity at 55 degrees north differ from other locations?

The strength of gravity at any location on Earth is directly affected by the distance from the center of the Earth. Since the Earth is not a perfect sphere, the gravitational force can vary slightly at different latitudes. At 55 degrees north, the force of gravity is slightly weaker compared to the equator.

Why is gravity at 55 degrees north important to study?

Understanding the variations in gravity at different locations on Earth can provide valuable information about the structure and composition of our planet. It also plays a crucial role in many scientific fields, such as geology, oceanography, and space exploration.

Can gravity at 55 degrees north be measured?

Yes, gravity can be measured using specialized instruments called gravimeters. These instruments measure the minute changes in gravity and can provide accurate readings for different locations, including 55 degrees north.

How does gravity at 55 degrees north affect daily life?

The effects of gravity at 55 degrees north may not be noticeable in our daily lives. However, it does play a significant role in determining the tides, ocean currents, and the Earth's rotation. It also affects the weight of objects, making them slightly lighter than at the equator due to the weaker gravitational force.

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