Hello, Here is the question
****An elastic cord is 80. cm long when it is supporting a mass of 10. kg hanging from it at rest at rest. When an additional 4.0 kg is added, the cord is 82.5 cm long. HINT: 4 kg stretches the cord 2.5 cm!!
(a) What is the spring constant of the cord? (1600 N/m)
(b) What is the length of cord when no mass is hanging from it? (74 cm) HINT once you have the k value, work the equation for spring force backwards!! THINK: How much does 10.kg STRETCH the cord??
I dont understand how to do part b. How do I find how much a spring is stretched with no mass. What steps do I follow?
+33661 Let L0 be unstretched length::
Using Hookes law and gravity:
a) 10*9.8 = k*deltaL1 ...(1) using g = 9.8 m/s^2
14*9.8 = k*(delta1+0.025) ...(2) 2.5cm is 0.025m to keep units consistent
Subtract (1) from 2) to get 4*9.8 = 0.025k so k = 4*9.8/0.025 kg/s^2 or k = 1568 N/m
b) Using k in (1) we have 10*9.8 =1568*delta1 so delta1 = 10*9.8/1568 m or delta1 = 0.063m = 6.3cm
Since L0 + delta1 = 80cm we must have L0 = 80 - 6.3 = 73.7 cm
