(a) A mass of 2-Kg box hangs by an inextensible and massless string from a support. A horizontal force of 10 N acts on the box until it is in equilibrium as shown in the figure. Find the angle that the rope makes with the vertical. F= 10 N 2 kg

(2) A force with magnitude 8.86 N pushes three boxes with masses m₁ = 1.30 kg, m2 = 3.20 kg, and m3 = 4.90 kg, as shown in the figure below. The surface the boxes are sliding on is so slippery that the surface can be considered to be frictionless. (a) Calculate the force that boxes 1 and 2 exert on each other and the force that boxes 2 and 3 exert on each other. [answer: F2-on-1 = F1-on-2 = 7.63 N; F3-on-2 = F2-on-3 = 4.62 N]. (b) To obtain the values of F1-on-2 and F3-on-2 in (a), you needed to assume that Newton's 3rd Law is valid. If you examine the FBD for m2, you should see that F1-on-2-F3-on-2= m2a. Verify the validity of Newton's 3rd Law by showing that the values of F1-on-2 - F3-on-2 and m2a are indeed equal. [answer: They are both equal to 3.0 N.] Fnet = ma F = 8.86 N 1.30 kg 3.20 kg t 4.90 kg

Fig. 1 422 N 185 N 1. In Fig. 1, the weight of the block on the table is 422 N and that of the hanging block is 185 N. Ignoring all frictional effects and assuming the pulley to be massless, find: (a) the magnitude of the acceleration of the two blocks and (b) the magnitude of the tension in the cord.