As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed (0.506)v after passing through the target. The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction [(0.443)KEb BC] of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.)
As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed (0.506)v after passing through the target. The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction [(0.443)KEb BC] of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.)
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As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed
(0.506)v
after passing through the target.The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction
[(0.443)KEb BC]
of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.)V = vM = m
Transcribed Image Text:**Diagram Description:**
Two scenarios displayed as illustrations:
**(a) Before Collision:**
- A mass \( m \) (represented by a small block) is moving horizontally with velocity \( v \).
- The block is approaching a larger mass \( M \) (represented by a bigger block) that is hanging from a string attached to the ceiling.
- The diagram visually suggests that the smaller mass is about to collide with the larger mass.
**(b) After Collision:**
- After the collision, the larger mass \( M \) is shown moving with velocity \( V \) at an angle, indicating that it has been set in motion.
- The smaller mass \( m \) is deflected, moving in the opposite direction with velocity \( v_{\text{bAC}} \).
- The path of \( m \) after the collision is depicted with a dashed arrow, illustrating its new trajectory.
This diagram is commonly used to illustrate concepts such as conservation of momentum and energy in inelastic collisions involving pendulum-like setups.
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