A spring requires a force of 0.750 N to compress it 0.250 cm. Now, a rifle bulle

Question

A spring requires a force of 0.750 N to compress it 0.250 cm. Now, a rifle bullet with mass 8.00 g is fired horizontally at a 0.992 kg block, resting on a frictionless, horizontal surface, and attached to the spring (see figure). The bullet strikes and embeds itself in the block, causing the spring to compress 15.0 cm before the block comes to rest. Find the spring constant of the spring. Find the kinetic energy of the bullet-block combination immediately after impact? Find the magnitude of the velocity of the bullet-block combination just after impact. What was the speed of the bullet immediately prior to impact?

Explanation / Answer

a) Using

F = -kx

Where F is the force

k is spring's constant

x is compression

Substituting values

0.75 = -k*-0.0025

k = 300N/m

b) This force is applied bycombination of block and bullet of mass = 0.992+0.008 = 1kg

Potential energy stored in spring = 0.5kx2 = 0.5*300*0.152 = 3.375J

Which will be KE of block bullet combination after impact

c) Magnitude of velocity can be calculated from the formula of KE = 0.5mv2

0.5*1*v2 = 3.375

v = 2.6 m/s

d) Using conservation of momentum

Before collision = After collsion

0.008*v + 0 = 1*2.6

v = 325m/s

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