A 8.6 bullet is fired horizontally at 500m/s into a 1.0kg wooden block that is i

Question

A 8.6 bullet is fired horizontally at 500m/s into a 1.0kg wooden block that is initially at rest on a frictionless horizontal surface and connected to a massless spring of constant 160 n/m. The bullet becomes embedded in the block A) Velocity of the block bullet composite immediately after impact? B) Change of the system's kinetic energy upon impact? C) what is the maximum compression of the spring? D) what is the speed of the block bullet composite when the spring is compressed by half of the maximum compression?

Explanation / Answer

(a)

0.0086 x 500 = 1.0086 x v

v = 4.263 m/sec

(b)

1/2 x 0.0086 x 5002 - 1/2 x (1.0086)(4.2632)

= 1068.83 J

(c)

1/2 (1.0086)(4.2632) = 1/2 160 x2

so, x = 0.34 m

(d)

1/2 (1.0086)(4.2632) = 1/2(1.0086)v2 + 1/2(160)(0.172)

s0, v= 3.69 m/sec

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