On this path the box exerts an equal and opposite force on \"Whenever we want to move some weight, if we tie a rope to you but there is no work done by that force on you. If you this weight we pull with as much force as is equal to the bur- walked 3 km rather than 3 m you would probably notice den. But if we untie the rope from the weight, and tie one of its that you had used a lot more of your internal energy. Many ends to a stationary point and pass its other end over a pulley students claim that the extra energy you used is transferred fastened to the burdSn and draw on the rope, we will more eas to the box. Evaluate this claim and justify your answer. 11y move the weight. e. How would your answer to part (c) change if you did not In Hero's machine a rope runs over a pulley connected to a neglect when you were changing the velocity of the box? stationary beam (A), then 1'111'15 through a second PUHCY (B) that is attached to the \"burden,\" then [m runs back to the beam where it is tied as A - shown in the diagram. :i 'r E 8. Some technologies are ancient. One example b- This machine is used 170 lift the bur i E is the pulley. To lift a burden above the floor i a pulley is attached to the ceiling and a rope den to the same height, Ax. Predict . : . the work done on the burden, the = runs over the pulley and is attached to the burden (as shown in the figure). A force F is external force that must be exerted _. : exerted on the rope and the burden is then to do this work, and the displace- displaced upward by Ax at a constant speed. Skills in Action ment of the free end of the rope as the burden is raised. Assume that pulley B has a negligi- a. Express the work done on the burden by the external ble H1353- force in terms of F and Ax. c. Justify the claim that this technology reduces the effort Hero of Alexandria wrote about what we now call required to achieve the same outcome required to lift the simple machines in the first century C.E. burden to the same height