Question

mass (kg) stretch (mm) stretch (mm) 0 0 100 0.1 80 1.63 60 0.2 Stretch (mm) 3.27 40 20 0.3 4.9 0 0.5 8.17 0 1 2 3 4 5 6 Mass (kg) 1 16.3 5 81.7 You want to find the spring constant of a certain spring. You hang a series of masses on the spring, one at a time, allowing the spring to stretch slowly so that it comes to rest in equilibrium. For each mass you measure the amount the spring stretched from its original length. The data table shows the amount of stretch for each mass, and the graph shows stretch as a function of mass. From these data, and what you know about forces in equilibrium, find the k for this spring. (Hint: It will help to remember Newton #2 and to graph the data, and mind the units.) Select one: a. 16.3 x 10 N/m O b. 600 N/m O c. 5000 N/m O d. 16 N/m e. 61 N/m

Answer 1

to Fonce acting on mass due (my gravity mg m-mass, g acceleration due to gravity) acting -kx (Kaspring constant, 27 strech) For equilibrium netfronce should be equal to zero Force due to spring ↑ KX ting m Hence, ke=0 mg mg ka = or k = mg g 2 we know that, (acceleration due to gravity = 9.8ms2 K = 9.8m x for, m=0.1 kg x=1.63mm = 1:63x10 m K = 9.8 (0.1) 6.018/0² 1.63x10 K = 601 N/m 3 for, m= = 0.2 kg, 4 = 3.27mm = 3.27x10° K = 9.8) (2.10.2) 603 N/m 3:27X 1073

For m = 0.3 kg x=4.9 mm = 4.9x10²m K - 918)0:3) 600 N/m (4.9 x103) 2 Hence, the value of k is approx. 600N/m from value of m and x every Therefore, spring constant k = 600 Non (Answer Option (b) is correct