Two blocks, each with a mass = 0.168 kg, can slide without friction on a horizontal surface. Initially, block 1 is in motion with a speed = 1.28 m/s; block 2 is at rest. When block 1 collides with block 2, a spring bumper on block 1 is compressed. Maximum compression of the spring occurs when the two blocks move with the same speed, /2 = 0.640 m/s. If the maximum compression of the spring is 1.55 cm, what is its force constant?

Question

Two blocks, each with a mass  = 0.168 kg, can slide without friction on a horizontal surface. Initially, block 1 is in motion with a speed  = 1.28 m/s; block 2 is at rest. When block 1 collides with block 2, a spring bumper on block 1 is compressed. Maximum compression of the spring occurs when the two blocks move with the same speed, /2 = 0.640 m/s. If the maximum compression of the spring is 1.55 cm, what is its force constant?

drwls · Answer

At maximum compression, the spring potential energy will equal the drop in Total kinetic energy. Total KE goes from (M/2)Vo^2 to 2*(M/2)*(Vo/2)^2
= (M/4)Vo^2/4

M is the mass of one block; Vo is its initial speed of block 1

(M/2)Vo^2/4 = (k/2)X^2

Solve for k

Lilly · Answer

Im still confused. Ive tried solving for k a couple of different ways and the website tells me that I am wrong. My answers have ranged from .0286 to 791.1 N/m. Ive tried converting 1.55 cm to m, and it still says that I am wrong.

drwls · Answer

X = 1.55*10^-2 m M = 0.168 kg Vo = 1.28 m/s k = (Vo/X)^2*M = 1146 N/m You apparently did not use the formula I provided.