Question
Consider atwood's machine (consists of a pulley and two blocks with different masses attached to both ends of the rope) height between the two blocks is 1.2 m, m1= 3.7 kg and m2=4.1 kg. a) is the change in mechanical energy for block 2 as it drops through the height h positive, neg, or zero? b) use energy conservation applied to the entire system to calculate the change in mechanical energy for block 2 as it drops through height "h". c) using part B find the magnitude of the tension in the rope.
Explanation / Answer
(a) change in mech energy for block 2 is negative. This meansthat block 2 loses energy. How do we know? Block 1 gains kineticenergy AND potential energy (as it rises), and the total energy forboth blocks combined remains the same. Since block 1 gainsmechanical energy, block 2 loses mechanical energy. . (b) block 2 loses potential energy of mgh = 4.1*9.8*h = 40.18 h . block 1 gains PE of m1gh = 3.7 *9.8 * h = 36.26 h . the gain in KE for both blockstogether is the difference in PE: 40.18 h - 36.26h = 3.92 h . block 1 gets its proportional shareof this KE: 3.92 h * 3.7 / (3.7 + 4.1) = 1.86 h . Since block 1 gains 1.86 + 36.26 = 38.12 h in energy, change in mech energy forblock 2 is - 38.12 h . (c) tension in rope can be found using the work energytheorem: . change in KE for block 2 + change inPE for block 2 = work done by tension . -38.12 h = force of tension * distance . -38.12 h = tension * h . tension = 38.12Newtons (the minus signjust means tension pulls up while the block moves down)