Example: Curvilinear integral of a vector field
Example: work to lift a body up to a certain height
There is a certain work W = m·g·h (g accelleration of gravity, g = 9,81 m/s²) necessary to lift a body with mass m in the gravity field of earth along a certain curve up to a height h.
This work W is not dependent on the specific form of the curve.
Hint:
Lifting a body gives a negative work. If the body is falling down the sign of the work is positive.
Task
Change the height h and the shape of the curve by moving point A, B, C and D.
Check if there is always the same work necessary to lift a body up to the height h.
How does th work change if point D is on the x-axis or below?