Assignment:
Problems:
1) Jack and Jill are assigned the task of mowing Joe's yard. To add to their woes, the mowers given to them are identical, heavy, unmotorized and old-fashioned. Both are lazy and want to do minimum work (i.e. mechanical work) while mowing. Jack pushes the mower with minimum force P1 (as shown) while Jill pulls her mower with miniumum force P2. Both mowers are initially at rest. The ground obviously is rough (µs, µk).
Both mow till distance ‘d'.
a. Who did more (mechanical) work: Jack or Jill? Why? Justify by finding the expressions for work done by both Jack and Jill.
b. Having covered a distance ‘d', whose mower is moving faster: Jack's or Jill's? Justify by finding the expressions for final speeds of Jack and Jill's mowers.
2) The two masses shown in figure have round frictionless massless pulleys. The inextensible cord connecting them is always taut. Given that F = 130 N; mA = mB = 30 kg, find the acceleration of the two blocks and tension in the cable when the system is released/pulled from rest. The floor is rough with µs = 0.2 and µk = 0.1. [You must show that motion exists]. g = 10 m/s2
3) What initial deformation (compression), δ, in the spring will make the mass leave the circular ramp at 40° (as shown)? The path is entirely frictionless. The mass initially starts off from rest. Note the mass and the spring are not rigidly attached to each other. (m = 1 kg, k = 200 N/m, R = 25 cm, d = 1 m, g = 10 m/s2)
