Circular motion and Newton's law question

In summary, at the equator, the scale reading will be higher by 0.5 N due to the difference in centripetal force caused by the Earth's rotation. This is because the man's weight is measured by a spring scale which measures the sum of all forces acting on him except for gravity. The forces acting on the man are the centripetal force and the normal force, which is equal to -mg. At the equator, the normal force will be smaller due to the centripetal force pulling the man away from the surface of the Earth. The difference in the normal force results in a higher scale reading at the equator compared to the north pole. To calculate this difference, one would need to know the
  • #1
bokonon
20
0
1. A 78.0 kg man weighs himself at the north pole and at the equator. Which scale reading is higher? By how much?



2. I think that this has to do with with the radius being different at the north pole and equator, which would cause different centripetal accelerations. So I assume I'm supposed to find the net force on the man in both places.


3. I'm lost on how to visualize this. A man on the north pole, on the very top of the axis, isn't in circular motion at all, except around the sun, ,right?

Any help, much appreciated.
 
Physics news on Phys.org
  • #2
Forget about the Sun. It is irrelevant to this problem.

I'm assuming you are talking about a spring scale here, which measures force, as opposed to a fancy doctor's scale, which measures mass.

Most introductory physics texts define weight as mass times acceleration due to gravity. Others define it as what a spring scale weighs. These are two different things. A spring scale measures the sum of all forces acting on a body except for gravity. What you have to do then is find all of the forces except for gravity that act on the person, sum them up, and voila! you have the scale measurement.

So, what forces act on the person? Are they the same everywhere on the surface of the Earth, or different?
 
  • #3
Thanks. So the forces acting on the man other than gravity are the centripetal force and the normal force. The normal force would be -mg, and the centripetal force would be mass*omega^2*radius?
 
  • #4
bokonon said:
So the forces acting on the man other than gravity are the centripetal force and the normal force.
Correct.
The normal force would be -mg
Correct, but the way you wrote that suggests you think g is the same everywhere. What makes you think that?
and the centripetal force would be mass*omega^2*radius?
Correct, but what is the radius?
 
  • #5
Is gravity different based on how far from the center of the Earth one is? Am I supposed to look up the radius at the Earth vs. the equator? How do I calculate different g's? I'm conceptually lost on this one . . .
 
  • #6
bokonon said:
Is gravity different based on how far from the center of the Earth one is?
What is Newton's law of gravitation?
Am I supposed to look up the radius at the Earth vs. the equator?
That is a very good idea.
 

What is circular motion?

Circular motion is the movement of an object along a circular path. This means that the object is constantly changing direction, but its distance from the center remains constant.

What is Newton's first law of motion?

Newton's first law of motion, also known as the law of inertia, states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity, unless acted upon by an external force.

What is the relationship between circular motion and Newton's first law?

In circular motion, an object is constantly changing direction, which means there is a continuous change in its velocity. However, according to Newton's first law, an object in motion will remain in motion at a constant velocity. Therefore, in order for an object to continue moving in a circular path, there must be a continuous application of an external force, such as centripetal force.

What is centripetal force?

Centripetal force is the force that acts towards the center of a circular path, keeping an object in circular motion. It is necessary for an object to continue moving in a circular path, as according to Newton's first law, an object in motion will continue moving in a straight line unless acted upon by a force.

How is centripetal force related to Newton's second law of motion?

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting upon it, and inversely proportional to its mass. In circular motion, the centripetal force acts as the net force, causing the object to accelerate towards the center of the circle. The mass of the object also plays a role, as a larger mass will require a larger centripetal force to maintain the same circular motion.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
602
  • Introductory Physics Homework Help
Replies
5
Views
297
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
2
Replies
42
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
3K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
974
Back
Top