Answer to Question #150544 in Mechanics | Relativity for Uday sharma

Question

A cumin canister of mass m=0.4kg slides across a horizontal frictionless counter with
speed v=0.5m/s. It then runs into and compresses a spring of spring constant k=
750N/m. When the canister is momentarily stopped by the spring, by what distance d
is the spring compressed

Answer 1

m = 0.4 kg

speed v = 0.5 m/s

spring constant k = 750 N/m

kinetic energy just before it hits the spring = potential energy at maximum compression

Using the conservation of energy we can write:

$\frac{1}{2}mv^2 = \frac{1}{2}kd^2 \\ d=v\sqrt{\frac{m}{k}} \\ d = 0.5\sqrt{\frac{0.4}{750}} = 0.0115 \;m$

Answer: 1.15 cm