To calculate the work done when we lift a weight or mass vertically some distance, we’ll use the integration formula for work, where W is the work done, F(x) is the force equation, and [a,b] is the starting and ending height of the weight or mass. Oftentimes problems like these will have us use a rope or cable to lift an object up some vertical height. In a problem like this, we’ll need to determine the combined force required to lift the rope and the object.

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