What is the unstretched length of the spring? An apple weighs 1.09 N . When you

Question

What is the unstretched length of the spring? An apple weighs 1.09 N . When you hang it from the end of a long spring of force constant 1.45 N/m and negligible mass, it bounces up and down in SHM. If you stop the bouncing and let the apple swing from side to side through a small angle, the frequency of this simple pendulum is half the bounce frequency. (Because the angle is small, the back and forth swings do not cause any appreciable change in the length of the spring.) What is the unstretched length of the spring?

Explanation / Answer

weight of the apple w = mg = 1.09N , spring constant k = 1.45 N/m

the bounce frequency    fb = 1/2 *(k/m)0.5

frequency of this simple pendulum fs = 1/2*(g/l)0.5 ( l = lenght of the streched spring )

given frequency of this simple pendulum is half the bounce frequency.

fs = 1/2 *fb

1/2*(g/l)0.5 = 1/2*[1/2 *(k/m)0.5 ]

solving we get

lenght of the streched spring   l = 4 mg / k = 4*1.09/1.45 = 3.006 m

from hookes law   F = kx , mg = kx , strech x = mg/k = 0.7517 m

lenght of the unstreched spring = l - x = 3.006 -0.7517 = 2.2542 m

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.