Question

When building the pyramids in Egypt, skilled workers (not slaves ... your history teacher lied) had to lift large stone blocks. Suppose a 22 ton stone needs to moved upward 9 feet. b 41 9 40 (a) One way would be to lift the stone vertically. This requires the workers to exert a constant force of 2.5 tons vertically (to overcome the weight of the stone). Set up and evaluate the integral to determine how much work is done to lift the 2.5 ton stone 9 feet. (b) Another method is to slide the stone up a ramp that rises 9 feet over a 41 foot ramp (with horizontal distance 40 feet). What is the displacement vector to move the stone along the ramp? đ=( (c) Find the unit vector ū pointing in the same direction as d. ū ~ 2 Parts (b) & (c) are very straightforward. Don't overthink it. (d) If a constant force F is exerted parallel to the incline of the ramp, it must also be a scalar multiple of ū and can be written as F = ||F ||ū (where ||F || is to be determined). Ignoring friction, the work done lifting the stone via the ramp must be the same as the work done to lift it directly as we did in part (a) since the stone is ultimately lifted 9 feet against the force of gravity. By moving the stone a greater distance (along the length of the ramp versus vertically), we can reduce the force required. Use this equivalence of work done to find the magnitude of the force (1 Fil) required to move the stone along the ramp. Approximate the percent of the force needed to lift the stone vertically that is required to push the stone up the ramp. (sF(x) dx = F. d)

Answer 1