Question

A 0.400-kg block is attached to a horizontal spring that is at its equilibrium length, and whose force constant is 24.0 N/m . The block rests on a frictionless surface. A 6.00×10⁻²-kg wad of putty is thrown horizontally at the block, hitting it with a speed of 2.20 m/s and sticking.

Part A

How far does the putty-block system compress the spring? in cm

Answer 1

here,

mass of block, mb = 0.4 kg

spring constant, k = 24 N/m

mass of putty, mp = 0.06 kg

velocity of putty, vp = 2.2 m/s

From conservation of momentum,
before collision = after collision
mp*vp = (mp + mb)*V

combined velocity, V = mp*vp/(mp+mb)
combined velocity, V = (0.06*2.20)/(0.06 + 0.06)
combined velocity, V = 1.1 m/s

From conservation of energy:
loss in kinetic energy = gain in potential energy
0.5*(mb + mp)*V^2 = 0.5 * k * x^2

compression in spring, x = sqrt( ((mb + mp)*V^2)/k )
compression in spring, x = sqrt( ((0.4 + 0.06)*1.1^2)/24 )
compression in spring, x = 0.152 m or 15.2 cm