A 10.0-g bullet is fired into, and embeds itself in, a 2.30-kq block attached to

Question

A 10.0-g bullet is fired into, and embeds itself in, a 2.30-kq block attached to a spring with a force constant of 19.7 N/m and whose mass is negligible. How far is the spring compressed if the bullet has a speed of 300 m/s just before it strikes the block and the block sides on a frictionless surface? Note. You must use conservation of momentum in this problem because of the inelastic collision between the bullet and block. _______ m A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 40.0 J and a maximum displacement from equilibrium of 0.239 m. What is the spring constant?

Explanation / Answer

Let, mass of bullet = m

mass of block = M

Let, speed of the block immediately after being hit = v

From conservation of momentum,

m*v1 + M*v2 = (m +M) * v

0.01*300 + 0 = (2.3 + 0.01) * v

v = 1.298 m/s

From energy conservation,

KE1 + PE1 = KE2 + PE2

(1/2)Mv^2 + 0 = 0 + (1/2)kx^2

0.5*2.3*(1.298)^2 = 0.5*19.7*x^2

x = 0.44 m

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