Question

A mass 25kg is attached to a spring which is held stretched a distance 120 cm by a force F=300N (Fig. 7-28), and then released. The spring compresses, pulling the mass. Assuming there is no friction, determine the speed of the mass m when the spring returns: (a) to its normal length (x = 0). (b)find the spring constant k?

Answer 1

Explanation:

Spring is stretched by force f to distance

"X"

now here by force balance we can say

f = kx

k = !

now here we will we say that energy stored in the spring will convert into kinetic energy

kx² = mv²

(x² = mv²

now solving above equation we will have

PART 2)

now for half of the extension again we can use energy conservation

ka²-k(x/2)² = 1 {mv²

¾fx=mv²

now the speed is given as

3 fr 4m V=