A 20.5kg ball moving at 38.5m/s on a horizontal frictionless surface runs into a light spring of force constant 5.15N/cm. Use the work-energy theorem to find the maximum compression in M of the spring

Answer 1

Maximum compression occurs when all the kinetic energy of the ball is converted to elastic potential energy of the spring.

mv²/2 = kx²/2

x = √(mv²/k) = v √(m/k)

You were given m in kg, v in m/s, and k in N/cm. Convert k to N/m.

k = 5.15 N / (0.01 m) = 515 N/m

Now plug in m, v, and k (in N/m) into the equation above for x, and you are done.