Calculus 1 Help: Solving Weight Formula for Distance

In summary, the conversation is about a calculus test question involving the weight of an object being inversely proportional to the square of the distance from the center of the earth. The correct formula for calculating weight in terms of distance is w=(25*12756^2)/r^2, not w=k/r^2 as initially suggested. The question also raises confusion about the use of the diameter of the Earth (12,756 km) and its relation to the center of the Earth. It is suggested to consider the distance from the surface of the Earth to the center when using the diameter in the equation.
  • #1
sharingan80
2
0
Okay I had a calculus test and we got it back and I got this question wrong. I tried it again but I can't figure it out.

The weight, w, in kg of an object is inversely proportional to the square of the distance, r, in km, from the center of the earth. Assume a stone of the ground has weight 100 kg and that the diameter of the Earth is approximately 12,756 km. What is the formula of w in terms of r?

I said w=k/r^2 but the question was multiple choice and I wasn't entirely sure so i chose the answer:
w=(100*12756^2)/r^2
but the right answer was
w= (25*12756^2)/r^2
 
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  • #2
Why did you use the diameter for r? Where is the center of the Earth in relation to its diameter?
 
  • #3
That's what I'm confused about. I don't know what 12,756 stands for in the equation.
 
  • #4
You don't think it's coincidental that 12756 is also the value given for the diameter of the Earth in kilometers?

Ask yourself, if the diameter of the Earth is 12756 km, how far is the surface of the Earth from the center of the earth?
 

1. What is Calculus 1?

Calculus 1 is the introductory course in calculus, a branch of mathematics that deals with the study of change and motion.

2. Why is it important to solve weight formula for distance?

Solving weight formula for distance is important because it allows us to calculate the distance an object will travel based on its weight and the force acting upon it.

3. How do I solve weight formula for distance?

To solve weight formula for distance, you will need to use the equation d = F/W, where d is the distance, F is the force, and W is the weight of the object. Simply plug in the values for F and W and solve for d.

4. What are the units for weight formula for distance?

The units for weight formula for distance will depend on the units used for the force and weight. Common units for force include newtons (N) and pounds (lbs), while common units for weight include kilograms (kg) and pounds (lbs).

5. Can weight formula for distance be used for all objects?

Yes, weight formula for distance can be used for all objects as long as the force acting upon the object is known and the weight of the object is constant. However, for objects with varying weights, a more advanced formula such as the impulse-momentum equation may be needed.

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