How much will it weigh at the equator?

[huybinhs]

Homework Statement

Take the Earth to be a perfect sphere of 1.274×107 m. If an object has a weight of 96.9 N while on a scale at the south pole, how much will it weigh at the equator? take the equatorial spin speed to be 465 m/s.

Homework Equations

No ideas.

The Attempt at a Solution

I have no ideas where to start. Please help! Thanks!

 

[ideasrule]

Start by drawing a free-body diagram of a person standing at the equator. Remember that part of gravity goes into providing the centripetal force.

 

[huybinhs]

Start by drawing a free-body diagram of a person standing at the equator. Remember that part of gravity goes into providing the centripetal force.

Ok. I got:

a = v^2 / r = 465^2 / (6378100) = 0.0321 m/s^2 (I took 6378.1 km as radious. Is this still correct?)

If yes, then:

m = F / a = 96.9 / 0.0321 = 3020 kg. Correct?

 

[huybinhs]

Just submited 3020 kg, and the system stating "INCORRECT". Please help!

 

[ideasrule]

Ok. I got:

a = v^2 / r = 465^2 / (6378100) = 0.0321 m/s^2 (I took 6378.1 km as radious. Is this still correct?)

If yes, then:

m = F / a = 96.9 / 0.0321 = 3020 kg. Correct?

No. You haven't drawn a free-body diagram. Do that, label all forces, and write out Newton's second law before doing anything else.

 

[huybinhs]

If the person is standing at the equator, then force of gravity will be equal 0. Is this correct?

 

[huybinhs]

any one?

 

[ideasrule]

If the person is standing at the equator, then force of gravity will be equal 0. Is this correct?

Do you really think there's no gravity for people at the equator? The people there don't just float around.

 

[huybinhs]

Do you really think there's no gravity for people at the equator? The people there don't just float around.

You r right. It still has gravity even at the equator. What should I do next please?

 

[ideasrule]

Again, draw a free-body diagram, label all the forces, and write down Newton's second law. If you've done any of these steps, you haven't shown them here.

 

[huybinhs]

Again, draw a free-body diagram, label all the forces, and write down Newton's second law. If you've done any of these steps, you haven't shown them here.

There will be 2 forces in the diagram: gravity and the normal force. The normal force represents the apparent weight of the of the object = 96.9 N.

the acceleration of the object = v² / r = 465² / (1.274×10^7 /2) = 0.03394 m/s^2.

Then I got equation forces:

96.9 - m (0.03394) => m = 2855 kg. Then my normal force = 2855 * 9.780 = 27922 N = final answer. (Note that 9.780 is gravity at equator). Is this correct?

 

[ideasrule]

There will be 2 forces in the diagram: gravity and the normal force. The normal force represents the apparent weight of the of the object = 96.9 N.

The normal force is the apparent weight of the object, but it isn't 96.9N. That's the normal force at the pole, which is just equal to mg since Earth's rotation has no effect there. From this you can find m, and from there the normal force at the equator (which is what the question asks for).

the acceleration of the object = v² / r = 465² / (1.274×10^7 /2) = 0.03394 m/s^2.

Seems right.

Then I got equation forces:

96.9 - m (0.03394) => m = 2855 kg. Then my normal force = 2855 * 9.780 = 27922 N = final answer. (Note that 9.780 is gravity at equator). Is this correct?

Where's your Newton's second law? Newton's second law says Fnet=ma. Fnet is composed of two forces: the normal force and gravity. a is just the acceleration that you calculated earlier.

 

[huybinhs]

The normal force is the apparent weight of the object, but it isn't 96.9N. That's the normal force at the pole, which is just equal to mg since Earth's rotation has no effect there. From this you can find m, and from there the normal force at the equator (which is what the question asks for).



Seems right.



Where's your Newton's second law? Newton's second law says Fnet=ma. Fnet is composed of two forces: the normal force and gravity. a is just the acceleration that you calculated earlier.

Ok. So, 96.9 = mg => m = 96.9 / 9.81 = 9.88 kg.

Fnet = ma <=> 96.9 - mg = ma <=> 96.9 -(9.88) * g = 9.88 * 0.03394

=> g = 9.77 m/s^2 => F at equator = 96.5 N which less than F at the south poles. Is this correct?

 

[huybinhs]

Yep. I got it right. Thanks so much ideasrule ;)

BTW, could u help me with this:

https://www.physicsforums.com/showthread.php?t=381935

 

[mparsons06]

How would the equation be set up to get g = 9.77 m/s^2?

I have different numbers, but I was just curious how the equation would look on the other side of g.

Then where did you plug g back into?

 

[huybinhs]

How would the equation be set up to get g = 9.77 m/s^2?

I have different numbers, but I was just curious how the equation would look on the other side of g.

Then where did you plug g back into?

After I found out my g is 9.77 m/s^2. I use the equation F at equator = m*a = 9.77 * 9.88 = 96.5 N . Hope this helps!

 

[mparsons06]

After I found out my g is 9.77 m/s^2. I use the equation F at equator = m*a = 9.77 * 9.88 = 96.5 N . Hope this helps!

How did you get the 9.77?

Is it like:

96.9 - (9.88) * g = (9.88)(0.03394)
g = (9.88)(0.03394)/96.9 - 9.88

I'm so confused??

 

[huybinhs]

How did you get the 9.77?

Is it like:

96.9 - (9.88) * g = (9.88)(0.03394)
g = (9.88)(0.03394)/96.9 - 9.88

I'm so confused??

96.9 -(9.88)g = 9.88 * 0.03394 => -9.88g = 0.33353 - 96.9 => g = 96.56 / 9.88 = 9.77 m/s^2. Hope this helps! ;)

 

[mparsons06]

I get it now. Thank you.

Do you know how to start out problem #2?

 

[huybinhs]

I get it now. Thank you.

Do you know how to start out problem #2?

Please check your inbox ;)