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Class 14 Examples(work, work-energy theorem- spring): adapted from &.79) A rifle

ID: 1472770 • Letter: C

Question

Class 14 Examples(work, work-energy theorem- spring): adapted from &.79) A rifle ballet with mass 8.00 g strikes and embeds itself in a block with mass 0.992 kg that rests on a frictionless, horizontal surface and is attached to a coil spring. The impact compresses the spring 15.0 cm Calibration of the spring shows that a force of 0.750 N is required to compress the spring 0.250 cm I. (adapted from 8.79) A rifle a. Find the spring constant b. Find the speed of the block (with the embedded bullet) right after the bullet strikes the block. Hint: after this event the mechanical energy is conserved, so apply this principle. d Now find the initial speed of the bullet using the conservation of momentum principle for colli- sions Interesting. There is a simple way to measure the speed of a fast moving bullet

Explanation / Answer

a) Spring constant

F = kx

k = F/x

= 0.750 / 0.250 * 10^-2
= 300 N/m

b)
Speed of block right after impact

Through conservation of energy, (right after collision --> max compression)

Ei = Ef

1/2 (Mb + MB)*v^2 = 1/2 *k*x^2

v = sqrt (kx^2 / Mb+MB)

= sqrt((300)(15.0*10^-2) / (8.00 *10^-3 + 0.992))

= 2.6 m/s

c) Not provided

d) Initial speed of bullet

By conservation of momentum,

MbVbi = (Mb + MB)v

Vbi = (Mb + MB)v / Mb

= ( 1 kg * 2.6 m/s ) / (8.00 * 10^-3 kg)

= 325 m/s