and connected to a spring having spring constant 152 N/m. The other end of the h

Question

and connected to a spring having spring constant 152 N/m. The other end of the horizontal spring is attached to an immovable wall. The bullet becomes embedded in the block. If the bullet-block system compresses the spring by a maximum of 86.0 cm, what was the speed of the bullet at impact with the block? 2. A 10.0 g bullet is fired horizontally into a 108 g wooden block that is initially at rest on a frictionless horizontal surface (1) 808 m/s (2) 303 m/s (3) 404 m/s (4) 364 m/s (5) 266 m/s 3. An ultracentrifuge slows from an initial angular velocity of 57.3 rad/s at a rate of 0.706 rad/s?. How many revolutions does it make before stopping? (1) 156 rev (2) 678 rev (3) 370 rev (4) 266 rev (5) 490 rev

Explanation / Answer

First Problem:

(2) Solve this problem using conservation of energy.

k = 152 N/m

x = 86 cm = 0.86 m

Initial kinetic energy of the bullet + block = energy stored in the spring system

=> (1/2)*k*x^2 = (1/2)*(m+M)*v^2

=> 152*0.86^2 = 118*10^-3*v^2

=> v^2 = 952.7

=> v = 30.9 m/s.

Now apply conservation of momentum to know the velocity of the bullet.

m*v1 = (m+M)*v

=> v1 = (m+M)*v / m = 118*30.9/10 = 364 m/s.

Hence option (4) is the correct answer.

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