A 24-g bullet moving at 1,200 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s. What is the kinetic energy of the block that results from the collision if the block had not been moving prior to the collision and was free to move?Select one:a.0.01 kJb.0.35 kJc.0.49 kJd.1.05 kJe.0.41 kJ
Question
A 24-g bullet moving at 1,200 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s. What is the kinetic energy of the block that results from the collision if the block had not been moving prior to the collision and was free to move?Select one:a.0.01 kJb.0.35 kJc.0.49 kJd.1.05 kJe.0.41 kJ
Solution
To solve this problem, we need to use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.
Step 1: Calculate the initial momentum of the bullet. The initial momentum (P_initial) of the bullet is its mass times its velocity. P_initial = mass_bullet * velocity_bullet P_initial = 0.024 kg * 1200 m/s = 28.8 kg*m/s
Step 2: Calculate the final momentum of the bullet. The final momentum (P_final_bullet) of the bullet is its mass times its final velocity. P_final_bullet = mass_bullet * velocity_final_bullet P_final_bullet = 0.024 kg * 100 m/s = 2.4 kg*m/s
Step 3: Calculate the final momentum of the block. The final momentum of the block (P_final_block) is the initial momentum minus the final momentum of the bullet (because momentum is conserved). P_final_block = P_initial - P_final_bullet P_final_block = 28.8 kgm/s - 2.4 kgm/s = 26.4 kg*m/s
Step 4: Calculate the velocity of the block. The velocity of the block (v_block) is its final momentum divided by its mass. v_block = P_final_block / mass_block v_block = 26.4 kg*m/s / 1 kg = 26.4 m/s
Step 5: Calculate the kinetic energy of the block. The kinetic energy (KE) is 0.5 times the mass of the block times the square of its velocity. KE = 0.5 * mass_block * (v_block)^2 KE = 0.5 * 1 kg * (26.4 m/s)^2 = 348.16 J = 0.34816 kJ
So, the closest answer is b. 0.35 kJ.
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