Question

A 12.0-g piece of clay is launched horizontally at a 105-g wooden block that is initially at rest on a frictionless horizontal surface and connected to a spring having spring constant 45 N/m. The piece of clay sticks to the side of the block. If the clay-block system compresses the spring by a maximum of 16.0 cm, what was the speed of the piece of clay at impact with the block?

Answer 1

here,

mass of clay, m = 0.012 kg

mass of woooden block , mw = 0.105 kg

spring constant , k = 45 N/m

compression in the spring , x = 0.16m

let the initial velocity of the bullet be u

using conservation of momentum for block and bullet

m * u = ( M + m ) * v

v = u *m / ( M + m)

and for the spring

0.5 * k * x^2 = 0.5 * (M + m) * v^2

0.5 * k * x^2 = 0.5 * (M + m) * (u *m / ( M + m))^2

k * x^2 = ((u *m )^2/ ( M + m))

45 * 0.16^2 = ((u *0.012 )^2/ ( 0.105 + 0.012))

u = 30.6 m/s

the initial speed of the clay before impact is 30.6 m/s