Question

7) 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 3.6 J of work to compress the spring by 0.13 m. If the spring is compressed, and the mass 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 m1 = 1.2 kg is dropped from a small height and sticks to it. (b) Find the new amplitude and the new period of motion. (c) Write the equation of motion of the block (with the putty), x = f(t), starting from the equilibrium position.

Answer 1

0132 amax = 62A wa - 15 mis? kxoo13 15 426X0.13 15 b) i5 Xon3 = 1.39m 0.2 ti We have w=3.63 for x=0-1600 Yk22=W yk = 2X3. 6 = 426 N/m [A = 0-13 m) Joma Jo va Sharma a) Im - - 13.7kg! At equilibrium velocity of im' v= WA= Now for collision let's use conservation of momentum » mv=(m+m, DV » v' = mxv 3.7X1-39 = 1.05mis After Collision of new amplitude is A » Y₂kAl2 = 2 mitmjvie w'=lk A'T 4.9 x 1.05=10.1lm 426 - 9.32 radis v' = velocity mtmi 3.7+ 1.2 mom. mitm voz wa 426 c) XLERA' sin wit To 11 sin 9.32t)