Calculating Force of Gravity at Different Elevations with a Robot

[Zerd_2011]

I am working on a formula to help me calculate the force of gravity at different elevations on a robot as it climbs up a skyscraper. The robot is attached to four magnetic wheels (each with a pull force of 4 lbs) which attaches to the steel framer.

In order to find the g's on the robot, i have used three different formulas:
(g+r)/g
(torque)=Fr
F=ma

and i have come with this equation to find the number of g's on the robot:

g's= ((torque) + gmr)/(gmr) using those three formulas

Now that i have figured out the value of g, how do i find the force at different elevations?
How do i use the gravitational law with the formula i already have?

Am i going about this all wrong? Any input would be appreciated.

 

[mathman]

Gravity at the Earth's surface is 9.8 meters/sec². In general, it is proportional to r², where r is the distance to the center of the earth. If you want to be VERY precise, you need to multiply by (R/(R+h))², where R is the radius of the Earth and h is the height of the elevator. Unless h gets very big, the adjustment is probably unnecessary.

 

[spancho]

Im going to assume that you know how tiny the difference in weight is going to be from the top of the building to the bottom. The best way to calculate the force of gravity is to use Newtons approximation G*(g1*g2)/r^2.

It looks like your also calculating the centrifugal force due to the object rotating around the Earths axis. Although this will effect the net force on the object it has no bearing on the force of gravity.

 

[tatiana]

For torque you also need to consider once you draw out a picture, teh equationg T=mgx x being teh centrial mass and mg ofcouurse mass times gravity or even T=r(Fsin theta)

 

[pmacias]

Your approach to calculating the force of gravity at different elevations is a good start. However, there are a few things to consider in order to accurately calculate this force.

Firstly, the formula you have come up with only takes into account the gravitational force and the force applied by the magnetic wheels. It does not consider other factors such as air resistance, friction, or the weight of the robot itself. These factors could significantly affect the force of gravity at different elevations.

Secondly, the formula you have used is based on the assumption that the robot is moving at a constant speed and is not accelerating or decelerating. In reality, as the robot climbs up the skyscraper, it will experience changes in acceleration due to the varying slope of the building. This will also affect the force of gravity.

To accurately calculate the force of gravity at different elevations, you will need to take into account all of these factors. One way to do this is to use the laws of motion, specifically Newton's second law, which states that force is equal to mass multiplied by acceleration (F=ma). By accurately measuring the mass of the robot and the acceleration it experiences at different elevations, you can calculate the force of gravity using this formula.

Additionally, you can also use the gravitational law, which states that the force of gravity is proportional to the mass of the objects and inversely proportional to the square of the distance between them (F=G(m1m2)/r^2). By using this law, you can calculate the force of gravity at different elevations by determining the distance between the robot and the center of the Earth.

In conclusion, your approach is a good start, but to accurately calculate the force of gravity at different elevations, you will need to consider all the relevant factors and use appropriate formulas, such as Newton's second law and the gravitational law. I would also recommend conducting experiments to gather data and validate your calculations.