Physics spring compression problem?

  • Thread starter Thread starter dovii
  • Start date Start date
D

dovii

Guest
Two air blocks with masses 144g and 144g are equipped with identical springs(k = 4550 N/m). The blocks move toward each other with identical speeds of 2m/s on a horizontal air track and collide, compressing the springs. Find the maximum compression of the spring attached to the 144g mass. Answer in units of cm.

I know that F= (1/2)kx^2 but i can't figure out a way to make this work and keep getting wrong answers. Any help would be appreciated.
 
Firstly, F does not = 1/2kx^2 for a spring, it is = kx

Anyhow,
Do this as an energy balance. From the info, you know that the kinetic energy in each block is 0.5mv^2 = 0.5(0.144)(2)^2=0.288 J

We know that at the maximum compression, the blocks velocity will be 0, that is, all of the kinetic energy will then be potential energy.

For a spring - mass system, PE = 0.5kx^2

so .288 = 0.5(4550)x^2

x^2 = 0.288*2/4550 = 0.000126593407

x = sqrt (0.000126593407) = 0.0112513736 = 11.25mm

Astrobuf
 
Back
Top