I need help in calculating work.
following quantites are given.
* G: 6.67E-11
*Mass of earth:5.98E24
*mass of satelightt:80kg
*x(initial) center of the earth-7E6 m
*x(final) center of the earth 12E6 m
How do I make integral equation I need use 20 interval.
To calculate the work for this problem, you need to use integration. Work is given by the equation:
Work = ∫F dx
where F is the force and dx is the displacement.
In this case, the force can be calculated using Newton's law of universal gravitation:
F = (G * mass1 * mass2) / r^2
where G is the universal gravitational constant (6.67E-11 N m^2/kg^2), mass1 is the mass of the Earth (5.98E24 kg), mass2 is the mass of the satellite (80 kg), and r is the distance between the Earth's center and the satellite.
Given that x(initial) is -7E6 m and x(final) is 12E6 m, you need to divide this interval into 20 equal parts to use in the integral. This will give you 21 points, including the initial and final points.
To calculate the displacement for each interval, you can use the formula:
Δx = (x(final) - x(initial)) / 20
Next, you need to calculate the force at each interval. Plug in the given values into the gravitational force equation to find the force at each interval, using the respective distances for each interval.
Once you have the force values for each interval, you can integrate using the following formula:
Work ≈ ∑(F * Δx)
where ∑ denotes summation. Calculate the product of force and displacement for each interval, and then sum them up to get the approximate value of work.