A 102-N sack of grain is hoisted to a storage room 55 m above the ground of a grain elevator(a) How much work was required?1 J(b) What is the potential energy of the sack of grain at this height?2 J(c) The rope being used to lift the sack of grain breaks just as the sack reaches the storage room. What kinetic energy does the sack have just before it strikes the ground floor?3 J
a. The trick for the first one is remembering that mg = weight in newtons Also, work and energy have the same units, Joules. finally, N m = J (Newtons multiplied by meters is Joules) E = mgh = (102 N)(55 m) = 5610 J b. 5610 J c. At the moment the sack hits the ground all potential energy has been converted to kinetic energy and so the kinetic energy is 5610 J.
Energy = Work Energy is conserved Potential Energy @ storage room = Kinetic Energy of falling sack at bottom PE = MGH KE = 0.5 MV^2 Work = Force * distance 1) 102 N * 55 m = 5,610 J or Weight = 102 N = MG = 10.41 kg PE = MGH = 10,41 * 9.8 m/s^2 * 55 m = 5610 J 2) 5610 J 3) 5610 J
Work changes the total mechanical energy of a system. We can assume the initial energy of the sack was zero (0 kinetic and 0 potential) since it is not moving and we can set the height at the ground level for determining potential energy. Once the bag has been hoisted up 55m, the potential energy has changed to mgh, where mg is the weight of the sack of grain, and h is the height. Therefore the work done on the sack of grain is 55*102 = 5610 J Note that we've also solved part b. The potential energy of the sack of grain at this height is also 5610 J. Amusingly enough, we've also solved part c (assuming there is no air resistance or other things to interfere with our perfect physics model :P). The law of conservation of energy says that energy is neither created nor destroyed, though it can change forms. Initial Kinetic + Potential Energy = Final Kinetic + Potential Energy. Since our Initial kinetic energy is zero and our final potential energy is also zero (since they ask for the kinetic energy when it hits the floor), we can simplify the problem to Initial Potential Energy = Final Kinetic Energy. Plugging in the numbers tells us that 5610 J = Final Kinetic Energy. So your answer for a, b, AND c are all the same. 5610 J. Pretty tricky.
