Question

QUESTIONS A block of mass m, resting on a horizontal frictionless surface, is attached to one end of a spring; the other end is fixed to a wall. It takes 3.6J of work to compress the spring by 13 cm; then it is released from rest. It experiences a maximum acceleration of 15 m/s2. Find the value of (a) the mass of the block. As the block passes through its equilibrium position, a lump of putty of mass mi - 1.2 kg is dropped from a small height and sticks to it. (b) Find the new amplitude and the new period of motion. (e) Write the equation of motion of the block (with the putty), x = f(t), starting from the initial conditions of the equilibrium position. (15 points)

Answer 1

Mean position belegbeeseen 13 cm. x=0 tal Maxm Accelaration A w2 A. K 15 1.1344) 47-A = 0.13 m) Given رنا Alse P.E stored 1/2 Kg2 At corner, PE I KAZ 2 3.6 I K_(0.13) 2 K - 3.6 X 2 = 426.036 ارور ها زنا - From (2) & (نا m, 0.13 X n26.036 = 3.69 kg 15 CS Scanned with CamScanner

(b) Since there is force in in Horizontal direction Momentum rem ain con ser red. Mence m, v - = (m, + m2) v V 3.694 vi 13.69 +1.1) ti) Calcu latim for vi 1. E at Mean position 3.6 I ie 1 / ✓ m, 1,2 = 3.6 V 2 X 3.6 3.69 1.396 mis ܝ 3.69 X 1.396 (3.69 +1.2 = 1.054 mis CS Scanned with CamScanner

New K.EE 1 x losa (1.05472 2.7 16 J. Also P-E at Corner New K..E . 2 ž K A2 2.716 2 A = 2x 2.716 426.036 O. || 3 ma T = 21 1 m, tmy k 3.69!:2 426.036 2T 0.673 sec أعلم Initial condition xo) 0.13 m. v (0) = omis We know, xlt) A ces (ot) 2 TT 271 0.673 9.34 rad see T 2,13 m. X(L) = 0.13. Cos 19.34 ) cs Scanned with CamScanner