Question

A 0.294 kg mass slides on a frictionless floor with a speed of 1.25 m/s. The mass strikes and compresses a spring with a force constant of 42.2 N/m. How far does the mass travel after contacting the spring before it comes to rest? How long does it take for the spring to stop the mass?

Answer 1

x will be a max (maximum compression when sin((k/m)^0.5*t) = 1, or

(k/m)^0.5*t = pi/2

k is the spring constant
x is the amount of compression.


so t = (pi/2)/(k/m)^0.5

= (3.14/2)/((42.2N/m)/(0.294kg))^0.5

= 0.131 seconds.

Kinetic energy before it hits the spring equals the potential energy after it hits the spring.
Potential energy= 1/2 k x^2

KE=1/2 mass*velocity^2

KE= 1/2 (0.294)(1.25)^2= 0.229 J

0.229= 1/2 (42.2) x^2

solve for x and you get x= 0.104 meters